In a random walk where trials are independent, variance scales linearly with time. Since standard deviation is the square root of variance, volatility scales with sqrt(T).

This sublinear power law scaling gets smuggled into option math that answers practical questions. For example, assuming implied vol is constant, a 12-month ATF straddle is twice the price of a 3-month ATF straddle because sqrt (12/3) = 2.

This scaling is commonly used to convert raw vega into weighted vega. Raw vega is an extremely low-resolution number. If you own 50k 12-month vega vs being short 40k 3-month vega then it appears like you are long vol. But 12-month IV doesn’t whip around as much as 3-month IV, so this position will not act like it’s long vol on a large move higher in vol as the term structure will not “parallel shift” higher. The 3-month will increase faster as the term structure steepens into a downward sloping shape. A shape referred to as “inverted” or “backwardated”.

A simple way to modify raw vega is to scale all your monthly vegas by 1/sqrt(T) by normalizing them to a fixed DTE, for example 3 months. In that case, using the same math we did above, a 12-month vega is cut in half relative to the 3-month.

So your re-weighted vega is now short 15k vega instead of being long 10k vega!

12-month vega x scaling factor relative to 3m vega = +50k * 1/sqrt(12/3) = +25k

3-month vega x scaling factor relative to 3m vega = -40k * 1/sqrt(3/3) = -40k

Net: -15k

That volatility changes should move in proportion to 1/sqrt(T) is not a commandment brought down from Moses. It’s a convenient scaling factor that corresponds better, even if imperfectly, to empirical vol surface behavior. It also has a handy interpretation. If IV’s change in proportion to 1/sqrt(T) then ATM time spreads are unchanged (net of theta). In other words, the 3m/12month straddle spread is unchanged in such a regime.

Again, this scaling doesn’t need to hold. Sometimes we have parallel shifts in term structure and sometimes term structures steepen faster or slower than sqrt(T) scaling would predict. But the scaling is still a better prediction than the raw vega measure, which would have you believe IVs from all months are directly comparable without adjusting for how slow long-dated IVs change or how fast a weekly IV can move.

Random walks and the derivative pricing theory built upon them assume returns are independent. In hindsight, random walks still exhibit stretches that can be labeled “trend” (like a run of heads) or “mean reversion” (period of frequent alternating). But it’s one thing to label these stretches and hindsight vs predict them.

It should be self-evident that being able to predict trends or reversion would be marvelously profitable for a directional trader. But, direction aside, it would be a gift to volatility traders as well. It would influence not only how they priced vertical spreads and time spreads but the deltas in their models and their delta-hedging strategies. In other words, it would change everything if you had an edge on the probability of the next move being up or down, even if you did not have an edge on the fair value of the stock (this would occur if you had an edge on probability but not on the magnitude of up move vs down move). Option structures allow fine-grained bets that can isolate probability from magnitude.

If an asset trends over weeks or months, you will underestimate its volatility by scaling its daily volatility by sqrt(T). That makes sense. If it trended, that’s similar to saying the moves were auto-correlated and therefore dependent. Again, this is descriptive, not predictive, but relating measures of volatility to this interdependence lets us see how sensitive option pricing is to the random walk assumption. A few articles I’ve written in this vein:

• how a high implied vol can be cheap | 9 min read

• The Option Market’s Point Spread (Part 2) | 11 min read

• Thinking In N not T | 6 min read

These articles have a unifying concern. If prices are random, then sure, the power function that specifies how volatility scales is the familiar:

But if prices trend or mean-revert, the exponent is no longer 1/2.

Over any historical sample, H can be observed to be something other than 1/2. For it to be 1/2 would mean that annualized volatility over 2 different sampling windows was identical. In hindsight, that will rarely occur. But it’s also true for any exponent you pick. It’s hard to make the persistent case for a value other than 1/2, especially when it carries the financial totem of randomness.

In Retail Options Trading, Euan Sinclair says markets aren’t random, but they’re close to random. The question of whether there’s enough life growing in the gap between “random” and “almost random” for a skilled hunter to eat is existential professional investors’ careers.

We need to examine randomness.

Read more

I’m taking a break to have some fun family time for the next couple weeks. Paid posts will still go out.

Friends,

I know today’s email is off-cycle. It’s a message to hopefully spark inspiration.

The 10-year-old is into art. Ahead of our Rome trip, he’s telling me all about Da Vinci. He’s also taking an art class from our long-time friend, the amazing surrealist artist Juan Pablo (whose art is all over our house).

This was taken years ago:

Juan Pablo is surprised at how mature the kid’s questions and knowledge are. We already went through that suprise. The reward he chooses for fulfilling his monthly Math Academy quotas is going to the Blick Art store in Oakland for supplies. When he talks to the clerks in the store they are stunned about how specific he is about what he’s looking for and they just look at us like “who is this guy?”

We shrug. We don’t know anything about this stuff. He taught himself using the Shrimpy YT channel. Just the channel, we’ve never enrolled him in the courses even.

With summer upon us it’s a great time for projects. (Our older kid turns 13 soon and his project is to convert a portion of the garage into home gym). The little guy and I are building a simple gallery website where he can start displaying his efforts. Of course, we’re overthinking what domain name to buy.

Anyway, if you have a burgeoning artist in your life, below are the links to Shrimpy and the app Max uses for digital art and animation (he’s taken to animation as well due to the app, but it’s still early on that. Other than making flip books in class while bored growing up, I wasn’t into animation, but I can appreciate the soothing bliss of frame-by-frame incremental progress).

📺Shrimpy Art Channel

📲Procreate app

This has been the first time Juan Pablo has taught children (he does teach adults) and knowing him for a long time, I totally expected him to crush this. He’s patient and carries the wonder and inquisitiveness we associate with children throughout his life. He also treats everyone with such respect, and I hear him level with Max as he would an adult, giving him credit in a way that builds a sense of quality, care and standards in Max's attempts. I’ve never seen Max so alive on a project, as Juan Pablo's approach is boosting the kid’s light (and that’s quite a statement since he’s generally dialed up in the passion department vs say his brother who’s more “chill”. If you’re a parent, you know what I mean and everyone else can probably relate from thinking about when they were young regarding differences like this).

JP is frustratingly modest, so I feel a duty to encourage him to teach more because we are so thankful for Max’s experience. I’ll keep nudging him because nothing would make me happier than promoting his art lessons. I’ll let you know if I make progress on that front. I think I will.

You’re learning how to see. You’re not assuming. You’re not making up what’s there. You are now seeing what’s in front of you.

-Words of encouragement I overheard after Max’s revisions after accepting feedback.

As I eavesdrop from the neighboring room, the detail of the conversation is awesome. So many little things that live at the level of craft. I have no idea what role art will play in Max’s life, but my hope is the broader appreciation of what craft and honesty look like and what it requires will apply to anything he pursues.

A few pics from the week, including in-class and homework:

A few older works from the spring…

Stay groovy

☮️

,

I’ll be taking some summer family time for the next 2 weeks. The paid posts will still be sent out, but no Wednesdays or Sundays.

Friends,

If you’re local or follow me on X, you might know that Tuesday afternoon went from routine to a shot of adrenaline very quickly. I was picking my eldest son up when I get a phone call from my 14-year-old nephew who was at home with my 10-year-old, his 2 friends, and their grandma:

“There’s a man who jumped the fence in the yard. We are upstairs hiding in the closet. We locked the doors.”

I was sitting in bumper-to-bumper traffic about 4 miles from home.

I tell the whole story here but that evening between cameras and phone logs we put the timeline together.

I left the house at 2:17pm

The kids were playing in the backyard when the man came over the fence at 2:28pm

My nephew called me at 2:29pm.

Once the traffic cleared, I was weaving down the main drag very likely close to 100. Ironically, right past the police station. By the time I was halfway there, the sirens were flying right past me as I just drafted right behind them. We’re going to the same place bruh.

I was running into the house by 2:36 pm. 7 impossibly long minutes.

There were uniformed and plainclothes cops from 3 towns and the county sheriff’s vehicles already on the block, guns drawn.

Makes sense. It was a chase.

Full story:

One wrinkle I didn’t dwell on was how the first group of officers thought the suspect left the area and were just patrolling around the house (with 3 choppers overhead taking a larger radius) in case he returned.

I was being a lookey-loo and examining a bunch of surrounding area around my property. The K9 officer came and spoke to me and it was clear he wasn’t briefed by the other officers. I didn’t want to bias him so I just abstained from telling him the other cops’ theory that the man escaped through a creek area. The K9 officer, operating without any strong prior asked to see the camera footage himself. When I showed it to him he immediately concluded that the man was not fit enough to have gone too far (I shared the footage online briefly, you can hear him panting way too much as he passes the camera).

So this officer decided to start the K9’s trail right next to the house. That dog took an aberrant path but it was clearly being jerked by the pull of the scent and it did not take long to hear it start barking. The megaphone was suddenly blaring right outside our living room window: “You are under arrest. If you turn yourself in, the dog will not bite you”.

The dude did not escape by the creek. He had been hiding right under everyone’s nose about 50 feet from my sideyard for over an hour. The majestic dog took less than 5 minutes to track him down.

I don’t think I consciously thought “guardrail against groupthink” but we felt uneasy about the suggestion that the suspect was already gone (actually it was Yinh who questioned that theory most and expressed that to me before I went snooping around) so when this officer was piecing together the events, it felt natural to just stay quiet to see where this goes.

Been a lot of recent chatter about volatility funds as a strategy and as a business. I’ll host a live webinar today for paid subs to chat vol funds, do some AMA, and chat markets today at 4pm ET. It’ll be recorded as well.

Zoom invitation:

Read more

Guitar and commencement speech. Yes, please. This was great:

📺How the World’s Largest Oil Derivatives Trading Firm Is Navigating the Iran War | Odds on Open

I’m biased considering I traded oil options for nearly 20 years but this interview is pure heat. Ethan Kho’s sat for a lengthy interview with Greg Newman, co-founder of Onyx, the world’s largest liquidity provider in oil.

Let’s go right to the excerpts (emphasis mine).

Interviewer: The oil markets have been crazy recently. How do I make sense of it all?

Greg: Honestly, I’d argue to begin with that it’s not like you should know something. There have been many crises, but this is unprecedented, and as a trader in particular it’s been very, very difficult.

There are so many oil contracts and so many liquidity pools out there. Brent and WTI are the key contracts that most traders and finance people know — that’s really the pool people dip into to hedge. But even that market, which is normally super liquid, has had its basis completely break down for a lot of these hedges. We’re used to at least one, two, three cents bid/offer, deep liquidity, lots of high-frequency traders, all that. We’re now talking 50 cents per barrel bid/offer minimum. And as you’re hedging, the price swings dollars per barrel at a time. It just breaks the whole system, because so many things in the oil world — all the contracts for every different product around the world, every region — ultimately link back to those core liquidity pools. When everything is broken from that sense, it’s incredibly hard to get a handle on it. So speculation has, to some extent, been out of the water. It’s been very difficult to do… What’s actually going on in the physical market gets reflected in these more niche contracts, of which there are many, many more, but they’re less liquid. That’s our specialty. Unless you’ve had exposure to those, it’s probably been very difficult to get an accurate reflection of what you should really be trading to profit from this.

How Onyx manages process when liquidity breaks down

Greg: We are market makers. There’s obviously a proprietary element to that, as you and your audience know very well. The temptation always is to combine your market making, look for some arbitrage-type opportunities, and then layer a discretionary element on top of that — ride momentum, things like that. But to begin with, it was really about getting to grips with the fact that you’ve got to take that discretionary overlay off the table. It just doesn’t serve you, because you’ve got people defaulting, people who can’t finance their positions. There are people whose only job is to take risk off the table because they’ve either blown up or they need to hedge, and it’s just not an orderly move. So you go back to your core business model — and you have to ask whether your core model is even suitable for that regime. The discretionary, hedge-fund-style approach is just not going to fare well in this scenario, certainly not at the beginning.

All the high-frequency traders looked like they were out of the game, to some extent. Maybe in the last couple of days they’ve been back in, bits and pieces, but certainly nowhere near the kind of medium-frequency trading they usually do. That’s been blown out of the water, and you can see it in the volatility. So you go back to your core model. Any model you had, any automation you had — it just doesn’t mean anything in this market. You go back to manual. You’ve got to be fully on top of it. It’s kind of basic in its process: you have a month-one price, you add your time spread, you infer the rest of the curve, then you keep adding differentials. That’s not too hard to see how to do. But they’re all moving so aggressively that just keeping everything in line is 90% of what we focused on. Because then what you’re able to do is spot the things that are so far offside that you can take them on — not to hold a proprietary view, but to back out of the liquidity with a correlated contract, something traded a bit further down the forward curve. Just going back to basics — fair value, trading what’s in front of you.

[Kris: This is exactly what I meant in Timing the Market when I describe taking off the discretionary trader pipe and glasses and putting on the market-maker boots and scrubs:

Trading is compensation for a service. In other words, a role. Don’t lose sight of the role. The easiest way to remember that is to ask yourself, “If I’m buying X at this price, what is it cheap against?”

The mantra stops you from drawing lines in the sand. From turning a relative value game into a…timing game. That’s what an outsize position relative to your business is — a timing bet.]

As you build infrastructure and a brand for liquidity and people come to you because you’re reliable, that’s when it pays off, because they’re not really looking for a good economical price — they’re looking for liquidity, and that’s what we do. So it was a good test of our business model. If you didn’t have that, honestly, the only move was to stay out of it until you could spot something not obvious but where you felt relatively safe — and that was just very, very dangerous to do.

Pricing fair value on Sunday night with no precedent

[Kris: I love this. Mock traders only need apply. Back to basics in a fast market. Snap judgements born from reps.]

Greg: Breaking it down — you have the Friday-night indications, and it’s our job to be completely 100% in the know. It cannot be partially in the know. So the moat we’ve got is our relationship with the brokerage firms around the world and the dark pool of liquidity we’ve got great visibility over. It’s not like other markets where it’s all electronic. It’s barely electronic, and in a time like now, electronic trading basically goes out the window, apart from the core one or two contracts. So this is where the niche expertise comes in.

Number one: you did know where it was Friday night. That’s not going to be completely irrelevant — you’ve at least got your starting point. We’ve also got traders who’ve been doing this long enough that they have a general sense of the relationship between big moves in the outright contracts — WTI and Brent — and Middle East wars, and generally what should happen to the refined products, how the curve should behave, how the time structure should behave, how clients tend to behave. And if you’re in our game with the kind of market share we have — 20–30%, sometimes 50% of some of these contracts — you’ve got a very good sense of how people are positioned. You know the weak spots in the curve, the strong parts in the curve. That’s not going to change, because at the very least people are going to sell what they own and buy what they don’t own. So you at least know where those things are going to come in.

So it becomes about having a very good feel for how the curvature started and how the relationships were working before, overlaid with analysis. You’ve got a weekend in oil, thankfully, where nothing trades, and you can use that time to look at previous times — what’s happened before. For example — it’s getting a little niche — naphtha, which we use for cracking to make petrochemicals, is a really key contract with Iran. They produce so much of it and send a lot of it to China, and China makes a lot of petrochemicals. So that’s a real sweet spot for Iran when an Iran situation kicks off. You’re expecting a reaction there.

Physical market participants and the reflexivity of hedging behavior

Greg: And then you’re expecting — okay, if all these things were to get higher, we know the behavior of, say, refiners is going to change. That’s the other thing about this market that’s different to maybe every other asset class. In a way it’s relatively illiquid, but so sophisticated. What that means is, for most contracts around the world, when there’s a big price move of any differential or time spread — let alone the outright price — it can reveal or destroy someone’s economics very quickly.

For example, a refiner says, “okay, I’ve got to hedge what I produce versus what I buy” — what we call the margin. They’re selling this kind of diff. And if it suddenly goes up $5, some of these bigger refiners have made an extra $5 billion on paper for the rest of the year. So they want to lock that in. Their behavior changes at certain price levels. The producers change their activity. And again, going from $80 to $120 oil, you’ve gone from maybe pretty good economics for a producing country to suddenly the best budget they’ve had in five years. So if they can lock that in, that’s what they’re going to do.

Another thing that’s unprecedented: how involved governments and producing countries have been in the futures market. Usually they’ve said, “look, we’re too big, we don’t want to hedge everything, it’ll just mess things up.” But we saw the US Treasury sell WTI — or at least it was reported that way — selling WTI swaps throughout the year, 11 million barrels, which isn’t a huge amount, but in a market like this it’s huge. You’ve got Saudi Aramco, BP, Shell — these guys who own a lot of the oil infrastructure in the world — they’re hedging. In real time you’re seeing their economics change, them trying to lock it in on paper, then suddenly those economics flipping on their head and deteriorating, and then the reverse.

Shipping companies are like, “look, this is great for my economics.” Airlines have done incredibly well from their hedges because they’re long, and they’re very active hedgers, and suddenly the hedge is way in the money. They’re going to want to lock it in. The airlines are a good example, because they hedge based on predetermined travel and fuel usage — that’s what determines the size of their hedge. So suddenly the price skyrockets as much as it does, and then you have disruption for airlines — there have been reports of something like a thousand flights a day cancelled around the Middle East. Suddenly they don’t have that physical consumption anymore. So they’re like, “well, we’ve just got a long position then, we’re just speculators now.” So they rush to take profit.

The jet fuel market in particular got most of the talk in our game, and there was some serious blood in the streets. It found its way onto X if you want to check it out, because it went in a straight line from probably about $90 a barrel — it carries a premium to Brent, so let’s say $10–15 above Brent — and it just went bang. And when I say bang, I mean no trades, all the way up to $200, and messing around since. How can that happen? It’s an example of the market being unbelievably short that trade — taking on airline trades, thinking the market’s not too volatile, “I’ll just wear this as a carry trade” — then bang. Some of the biggest oil traders in the world have the biggest position on. They can’t just go and buy it back; if they buy it back, it’s probably going to move another $100 a barrel, maybe more. So they just have to wear it. And so you’re hearing about oil traders in the market having huge margin calls — but these businesses are $10–15 billion-a-year businesses, and they’re getting margin called. This is the kind of craziness I’m talking about.

Voice brokers, people talking their book, and where the information actually lives

Greg: Why is it so incredibly difficult to replicate and do yourself? Because oil still has some very interesting dynamics — inter-dealer brokers and voice brokers. People hear that and say, “what, voice brokers?” Yeah — 80% of the volume is through voice brokers. If they don’t know you, if they don’t like you, if they don’t give you information about who — or not even who, just what — is buying and selling, you’re just in the dark. Literally a dark pool. The exchanges hate it, but it’s a very well-protected industry, because it’s a community, and these guys get paid a ton of money. There are huge companies that see the edge in having relationships with these brokers and probably keeping it that way. So unless you’re plugged into that game, it’s going to be very, very difficult to have the kind of visibility I’m talking about — who’s positioned where.

And then you could say, “well, look, I’ve got some friends, I’ve got some good information.” But that’s classic — we laugh about it all the time. That used to be a thing: go to a Mayfair pub and talk about who’s doing what. But the whole time, they’re talking their book. And unbelievably, people still fall for it. They go, “oh, I know this guy at this company, he said everyone’s buying, it’s going to be bullish.” He’s probably on the offer. You cannot rely on that information whatsoever. People talk their book. We’ve gone from traders talking their book to OPEC talking their book — they’re always out in the market feeding information, they know the headline sensitivity. Now you’ve got Trump talking the US book. It’s actually crazy.

Prediction markets as an information signal — and why Onyx stopped using them

Greg: It’s like the financial market — it’s so financialized, and the world’s governments know that and are more familiar with that than ever before, so they use it. They spoof the market, feed information, see how it reacts. That adds another layer. In that sense, there have been scenarios where huge option trades go through the night before Iran kicks off — huge, huge — someone clearly knows something. And even Polymarket being pretty useful. Something’s kicking off in Polymarket, an event that would clearly have a big impact on oil, and there’s now a dark area of oil where you’re saying, “someone might come in and do something pretty serious now.” And it’s not the oil traders, not people with physical information — it’s people with government information. So the dynamics are getting super interesting, but like any other financial asset class, I guess.

Interviewer: You brought up Polymarket, and this was something I was curious about before our conversation. I haven’t looked too closely into the types of contracts on these prediction markets related to the conflict in Iran, but I’m sure you have because of its implications in your industry. In general, how accurate a forecast do these prediction markets tend to bring? Is there enough volume on them? And more importantly, how do you think about them as a source of information?

Greg: To begin with, it was great. There really was nothing like it. Funnily enough, it was the Iranian situation last year — I forget exactly which month — but it was very useful then, because it was a new concept. A lot of people were betting on whether the Strait of Hormuz would be closed. People have talked about the Strait being closed as a hypothetical — you put it in your scenario analysis, you talk about it as a hypothetical — but no one ever believed, one, that it was even possible, and two, that it would happen. We even had a research guy, adamant, been in the game for 50 years, saying, “you cannot close the Strait.” So it was really interesting to see people actually believing it would. For a time in Polymarket, we were watching it live, going up to 80% yes, and we’re like, “come on, someone knows something.” And then you get all these messages of people saying, “I’m literally on a ship in the Strait, it’s fine.” That kind of transparent information, in real time, you can’t beat it. This is the good part of capitalism — using people’s greed for transparency, for the better functioning of markets and day-to-day life. No one in any other way would be incentivized to tell you what’s really going on. So suddenly you have something like Polymarket, and someone has information and wants to trade it, and that finds its way into the ecosystem of information.

So I thought it was a really good thing to begin with. Then what started happening, unfortunately, is it got more and more popular, and we started to realize the way it settles is just not ideal. Even with that Strait example, some people felt it had technically closed — ships slowed down for a time. How do you define “closed”? The settlement matters. It’s funny, because in our market in particular, with so many of these contracts, the big thing is to let contracts expire — which is actually quite unusual. A lot of us take these contracts to expiry. You might hold things against it, but expiry is incredibly important — how the contract expires and to what methodology. So we’re very used to studying these underlying methodologies, and that’s where relative-value opportunities — maybe not arbitrage, but relative value — can become very important.

So when we studied that from a Polymarket perspective, we lost confidence very quickly in what the game was all about. You have to own the tokens — you have to own a big portion of it — to be able to decide. So who decides is as important as anything else. And then — I’m not even saying it’s rigged — it’s just inefficient. So to use it as a reliable source of information, it kind of lost its gravitas quite quickly. So then we stopped looking at it.

Options flow as the real tell

Greg: …when someone has good information — and you can empathize — if you have good information, you don’t know when it’s going to kick off. So you just want the straddle, you want some good convexity. An option is a great thing to use. The interest in options became so overwhelming that it’s been a better indication of information being out there than anything else. So we kind of moved from Polymarket to options open interest and options activity at key times, right around the moment.

[Kris: Umm yea. The oil options market has been smart af for a long time]

And just to finish on that: the oil market historically has been quite orderly around its market hours. But after 7:30pm our time — which is the US close, up to maybe 6pm their time — that window is meant to be dead. It’s meant to not really trade, and it’s been very, very active around these times. So now we’re doing the hours later on, to see what’s going on, because the order book will reveal things. If you’ve got the visibility of all the contracts, that’s where you’re in the best position to know: has someone selected something in particular, and what could that mean? Because there’s no other reason why you would trade at that time. If you want to hedge, you go for the peak times. If you want to speculate, you want liquidity, so again you go for peak times. So why are you trading in these evening-to-nighttime trades? It makes no sense, other than maybe you’ve just got the information. And I think Trump knows that as well, because he makes a lot of his announcements either on the weekend — when the market will gap up or down — or at night. And we’re forced to be very ready up until the actual close of the exchange now, rather than the close of the market day.

That’s my favorite stuff because it’s about the nitty-gritty of trading but the rest is full of good business talk and a bit more on trading:

• Regime-break risk: when the exchanges themselves are the risk. Greg’s worst moment last week wasn’t market risk but a flashback to 2022 TTF, when the EU floated capping the European gas futures price. A delta-flat book against expiry administrative volume becomes a billion-dollar naked short the instant nobody can sell you the futures to close on. He puts it in the same family as the Treasury basis trade.

• What it’s like running the book through it. Sleeping bags in the office, WhatsApp blaring, the fighter-pilot bit.

• The 26-hour evacuation. 55 people and 9 dogs chartered out of Dubai because the office was being bombed. Flight paths changed five times. They traded the next morning.

• Countercyclical hiring during the lull. 2024 and 2025 were horrendous; that’s when they bought a team from a competitor, set up Dubai, and did the cultural reformation.

• Why Onyx hasn’t taken outside capital, despite being asked repeatedly. Energy at the hedge funds has seriously underperformed outside of, say, Citadel. Capital isn’t the constraint; deployment and conviction are.

• From prop shop to liquidity infrastructure. The flywheel: data, training, single-dealer platform, retail brokerage, credit/mini-bank. All of it leveraged off the core engine of being the most-liquid price.

• The Glassdoor review that turned Greg into a LinkedIn presence. And the Hamilton line about who tells your story.

• What’s surprised him most after 14 years. Spoiler: it’s not technical.

Finally, I was chatting with an oil trader about this interview and he recommended a book I immediately lifted:

Stay groovy

☮️

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In this issue:

• streetlight effects

• Investment Beginnings Class 5 was a delight

• thoughts on the current market cycle and options

I’ll be short up here with one rec since the investing sections are a little longer. Just have extra exhaust since last week’s graduation issue skipped finance stuff.

everything is a nail, or at least it ought to be | 5 min read

This is a short book review by Dan Davies of The Irrational Decision by statistician Ben Recht.

Recht argues that if a hammer is genuinely your best tool, it’s actually smart to look for nail-shaped problems or reshape problems them so they’re more hammer-friendly.

In Recht’s case, the hammer is mathematical optimization (especially linear optimization). The book traces how, over the past century, people haven’t just used optimization to solve problems, they’ve restructured problems to fit optimization’s strengths. He gives the example of the feedback loop between chip design and optimization algorithms where better chips enable better optimization, which enables better chip design, repeat.

If you recall, in my post slashing away parts of their humanity, Davies plugs C.Thi Nguyen's book The Score (which I bought as I enjoyed Nguyen’s first book about games). Davies’ latches on to the manner in which metrics ultimately create “streetlight” effects by optimizing not necessarily for what really matters but for what’s easy to measure.

Well, as you might expect from any self-respecting James C. Scott fan, Davies praises Recht for resisting the profitable route of hyping this trajectory into AI singularity cheerleading. Instead, Recht asks: what do we lose when we reshape problems to make them algorithmically manageable? Once you’ve defined what to measure and set a success metric, an optimizer will always confess an answer. But all the real judgment happens upstream, in choosing what counts as success in the first place. That same process that advances chips is a convenient way to persuade overly left-brain, ahem, “data-driven” decision-makers.

Recht’s book ends with a thoughtful chapter on how we should make decisions, but Davies also flags an argument that knocks you a bit off balance. He makes the case that randomized controlled trials are better understood as a regulatory tool than a scientific one. I found that a bit haunting. It’s a dark thought that also casts a shadow on our accepted standards of rigorous epistemology.

Recht, Nguyen, and Davies are all quantitatively minded scholars converging on nuanced skepticism of data in what I’d describe as a next-gen version of How To Lie With Statistics. In the first gen, inferences were distortions of what the data told us (i.e. sleights of hand like substituting causation for correlation), but is the new deception to do inference honestly but use proxy measures that, to use a trading term, have a lot of basis risk to the thing we actually care about. And then the bigger question is how much of that is laziness vs trying to manipulate the terms of discourse.

Money Angle

This week I taught Class 5 of the Investment Beginnings series I’ve been doing with the 12+ year olds.

It’s the last class in the series before we do “labs” in July. During lab, we’ll convene when the market’s open and I will give each kid individual attention as they execute an investment. I want to make sure they know how to read the screen, navigate their broker site, see the confirmation of the execution etc.

This last class was special. I’ve been posting all the materials online and there are families following along remotely. One dad sent me an app that consolidated and vibecoded the slides and games. He and his son worked on the project together:

https://investment-class.vercel.app/

And this next part blew people’s minds in the class, not to mention my own. A mom brought her son from Miami because he’s been obsessed with the class and wanted to be here in person with the other kids. I’m speechless. Supermom and superkid.

We took them to dinner with my family and brought along my son’s good buddy so our visiting friend would know a few people before stepping into the class. I can’t gush enough about how nice this all was.

When Class 5 ended, a lot of parents came to talk to me and said all this kind stuff and gave me totally unnecessary, generous gifts (I would have done the same so I get it but also just feels like too much). The most important thing is how all these kids’ gears are turning. It feels like a no-brainer to really clean this up (I learned a lot from doing it and know how I’d mod it in the future) and turn it into something. Maybe a well-produced YT thing, but I’m stretched pretty thin. We’ll see, I guess. Famous last words.

Anyway, here’s the outline of class 5 and link to all the materials from the classes.

Class 5 — Making Trades & Reading Markets

• Different kinds of auctions and how markets are continuous auctions

• The order book: bids, asks, spread, and what “depth” actually looks like

• Price discovery as consensus — the price aggregates what everyone knows

• Market hours, plus what pre-market and after-hours really are (and why beginners should avoid them)

• Public vs. private markets, with real estate as the bridge example

• How an IPO turns a private company into a publicly traded one

• Why baskets exist: the easy button for diversification (callback to Class 4)

• Three kinds of baskets — index, themed/sector, manager-picked

• ETF vs. mutual fund: same idea, different checkout (auction all day vs. one daily NAV)

• Index construction math: cap-weighted vs. equal-weighted, with four real stocks

• Why SPY and RSP — the same 500 names — can produce materially different returns

• 🔨 Homework: talk to parents about a brokerage account, ahead of the July lab where students place their first real trades

We spent much of the class doing a mock trading game:

How the game worked

There are 16 kids.

• Each gets 2 cards — that’s private info

• There are 3 “stocks”: Hearts, Spades, and Red

• At the end of the game, each stock settles to the sum of the cards held collectively in that category across all 32 dealt cards

• Card values run 1 to 13 (ace to king)

Kids bid, offer, and trade with each other based on what they think final settlement will be. They log transactions on index cards they carry.

Every few minutes, news hits — I reveal some of the remaining 20 cards. These are cards that will NOT contribute to the value of the 3 stocks.

The Teaching Moments

Basic valuation

1. What’s the maximum value of each of the 3 stocks? (Also a fun way to teach someone to quickly compute the sum 1 to N.)

2. What is the fair value of the stocks at the start of the game, when no common information has been revealed?

Information and private signals

1. What is the fair value of Hearts if you’re holding the 9 of Hearts?

2. Ask the kids: what’s a good hand to be dealt, and why? (A very simple exploration of what “information” actually is.)

3. After news is revealed, how do you update fair value? Walk through the exact math.

Reading flow

1. Your fair value is always subject to adjustment based on flow. What is Alice’s bid generally saying about Spades? What is Mike’s offer suggest about Red?

2. At the end, computing P/L is a big exercise — marking trades to settlement.

We didn’t go into crazy depth on any of these. Just getting a basic understanding easily takes a group of 16 kids an hour, and even then some are lost. Totally expected. Honestly, many adults are too.

It’s super interesting to see who gets it very quickly though.

The origin of the game

This was the first trading game I remember doing as a trainee at SIG. All the new hires in NYC played while the trainees who had been around for 3-9 months traded options on these “stocks.” Their hedge orders would get sent into our trainee market!

Money Angle for Masochists

Not to deter any stubborn bears, but just understand your history. In 1999, the Nasdaq returned 86%.

If we ignore the small 3.2% down year in 1994, that run looks even crazier and capped with an insane blow-off top.

The 1999 blow-off top is pretty interesting from a how-do-I-reconcile-option-pricing-with-real-world lens.

I’ve written a bunch on how volatility measures are sensitive to sampling periods.

See:

• Volatility Depends On The Resolution

• The Coastline Paradox in Financial Markets

Volatility scaling can feel unintuitive.

If an asset’s annual standard deviation (ie volatility) is 16%, then its daily standard dev is ~1%

Well, from that, it’s clear that you can have say a 10 sigma move in a day, but not in a year. That alone seems to point to a weakness in how we scale volatility through time.

But this is mostly resolved by measuring distances in lognormal space correctly. When you do that, you find that +86% is MUCH closer than -86%.

Just screenshot the formula in the post and treat Gemini like a calculator:

This explains why calls that are 50% OTM calls are worth more than puts that are 50% OTM (even if the spot and forward were the same).

To consolidate knowledge, it’s why collars can look so attractive in high vol stocks:

“Stock pickers market”

I’m old enough to remember when investment managers complained that the Fed drove the market, everything was correlated, and there was little reward for discerning between companies.

Well, we’re in the opposite world.

This is showing put skew falling and call skew rising in QQQ:

This is front-and-center to the options market:

There’s a record disconnect unfolding in the trading pits right now

A chart from the article shows the spread between the weighted avg stock vol in the SPX vs the index vol. It’s another proxy for cross-correlation as the index vol is dampened relative to the stock vols because the stocks are doing a great job diversifying each other.

A stretched relationship can get more stretched. But as it stretches, there is a mathematical reason why the spread would revert. Think of the limit. If 1 company achieved singularity and ate all the other companies, its weight would increase relatively as each dollar it made was a dollar less for the others until it was the index. This is NOT a tradable idea. That is a make-believe world. I’m only being pedantic to help you move the pieces around in your brain to help you see how they fit together.

But the price action of anything related to AI ripping vs everything else is a giant singularity trade, and from that context, the low correlation makes superficial narrative sense for now…a handful of companies are expected to eat the rest.

But I’ll pose this one…if instead this handful of companies are becoming the COGS of all other companies, wouldn’t that look more like the stories we’ve heard that I had Claude reconstruct by asking it to describe the circular revenue phenomena in bubbles:

Company A buys ads on Company B’s site. Company B uses that revenue to buy servers/software from Company C. Company C buys ads on Company A’s site. Everyone books revenue, everyone’s growth numbers look great, valuations rip higher — but no net new money is entering the system from outside customers. It’s just the same dollars chasing themselves around a closed loop, with each pass inflating reported revenue.

The poster children were the late-90s telecom and dot-com names. Global Crossing and Qwest got nailed for swapping fiber capacity with each other and booking both sides as revenue (”capacity swaps”). AOL was accused of round-tripping ad deals. A lot of dot-coms were essentially selling ads to each other, with VC money funding the ad budgets — so the “revenue” was really just recycled venture capital.

The concern isn’t fake deals today, but the circularity possibility means index vol will have its revenge. Good luck with timing though.

SpaceX

It’s interesting to hear Mitchell step through the numbers of how much day 1 shares need to be absorbed and how unprecedented this is. Recall in PTJ’s interview on Invest Like The Best:

2000 was the easiest bear market I’ve ever seen in my whole life. It’s got so many similarities to right now, in the sense that the bear market of 2001 and 2002 were a consequence of all the IPOs in ’99 and 2000. And then as they unlocked, you just had this never-ending cascade of selling, that’s a great way of putting it. And we’re getting ready – I want to say that the contemplated IPOs for next year are going to be five or six percent of market cap. So why are we where we are right now? Because we’ve been retiring two or three percent of market cap, probably a little less than 2% of market cap, every year without fail for the past 10 years [through buybacks.]

And so now all of a sudden, you’re gonna completely reverse that math. And so, I don’t think it necessarily happens instantaneously with the IPOs, but then there’ll be the unlocks. So you can see a situation where, okay, maybe we go through some kind of rolling top. And then 18 months from now – six months, we’ll have to look at the unlock schedule. But you’re going to want to watch those because that’ll just be adding equity supply. And you’ve already gonna be diminishing the buybacks because of all the commitment to capex from the hyper-scalers. They’re already gonna be eating into their cash flow.

The current set-up feels very strange. It seems too easy to think it’s going to be a local top right? But it’s a hard idea to resist. It feels like it’s a negative for gross returns and then under the hood, possibly chaotic for sector flows (like to absorb the IPO do people rebalance out of what went up the most recently? That feels like a pretty natural idea).

You have pockets of extreme bullishness manifesting in options with cheap put skew and risk reversals and left-for-dead implied correlations but the bearish factors are also common knowledge:

• IPO issuance

• Midterms (assuming Dems are the bear choice)

  

• elevated bond yields

In other words, current prices are NET of everyone knowing about these factors. By the way, this is always the problem with markets. If you see something on the horizon and think it’s bearish, whose to say the current market wouldn’t just be higher if that thing you’re latching on to is observable by others.

What’s the more contrarian position right now, to be bullish or bearish?

The option point spreads have shifted in a way that suggest bullishness is consensus.

Moontower agent

The moontower agent has been in the wild for a month now, and it’s been an awesome companion to help you reason through trading questions. It’s connected to the data we buy and process, and it’s tuned and under ongoing reinforcement learning for trading contexts.

=> 🤖Ask the agent a question

It’s powered by AI harnesses, of course, so the output is non-deterministic, so it’s helpful to report back on what it does well and poorly so we can keep course-correcting.

Thursday webinar

Been a lot of recent chatter about volatility funds as a strategy and as a business. There’s a lot of misconceptions about them. Which makes sense, it’s an opaque world.

I’ll host a live webinar on Thursday for paid subs to share some thoughts on the topic.

Details to follow this week.

This Week In The Options Trench

Everyone’s favorite option topic

Stay groovy

☮️

Moontower Weekly Recap

• nunchuck

• what new grads should focus on

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In light of graduation season, this week’s material has been focused on a mix of inspiration and general course of action to what I would characterize as an overarching sense of thriving.

When I’m not yapping about trading or options, much of my writing or curation revolves around learning, motivation, and creativity. These 3 factors are in a continuous conversation with each other. That internal conversation has far-reaching effects because it guides our actions which in turn feed back to this internal conversation. We’re these complicated black boxes hosting billions of hormonal and electrical collisions that mean on some level we’re all the same in that we can be described generally as such a machine, but profoundly different since the infinite combinations of those reactions make us unique as, well, precious snowflakes.

Any perspective that fails to appreciate both how general and specific we are is an incomplete description of our condition. Which brings us to the fundamental tension of advice. It’s tempting to give it because on one level we’re not that different, but on another level it’s impossible for any general advice to be right-sized for any individual.

It is with this uneasy marriage of humility and hubris that I dare to offer a few thoughts for those pulling up to the staging areas of their careers. It is the same answer I give to those insistent enough to figuratively sign a waiver acknowledging all the disclaimers that an honest person would give before proffering advice.

The magical words that indicate such an insistence, an insistence which places earnestness above omniscience, which may be the best we can do in wicked domains, are “what would you tell your kids to do?”

In the face of such an approach, I’m cornered. But since I know that you know my kids are not your kids, I can trust you will be able to adapt the advice to your own or your loved ones’ situation.

What should a new grad pursue?

Read more

This Rob Henderson tweet caught my eye because while it rings true, it feels incomplete in an interesting way.

First, here’s the tweet in its entirety.

Adam Carolla was on Joe Rogan’s podcast. Here I’ll paraphrase one of Carolla’s most important points from this discussion:

“I realized that you have a skill set. Like martial arts. You know it, you’re comfortable with it, you’re secure in it. You know your abilities there, just like you know your abilities as a comedian or as an archer.

For me, I’m a carpenter. I have a skill, a trade. There are things I know well, so I don’t feel insecure. I know what I’m good at, and I’m grounded in that.

But a lot of people don’t have that. They don’t have a trade or a skill or anything they can honestly call expertise. If you asked them, ‘What are you an expert at?’ they wouldn’t have an answer. You could name several — UFC, mixed martial arts, jiu-jitsu, podcasting, standup, whatever it is.

You could learn another language or master an instrument. But so many people never find that thing. They never develop a skill they can own. And because of that, they walk around in this heightened state of insecurity.”

This is an insightful point: once you start getting good at something, and it can be almost anything, you can build from there. You now have something to talk about, something you know more about than most people. And if you can make it even mildly interesting, you can speak about it at length.

But many people spend their free time on social media or binge-watching TV. It is strange now: if you talk to younger guys and ask what they’re interested in, they’ll tell you about a Netflix show, or getting high, ordering Uber Eats, binge-watching, and maybe sports gambling.

If your life is dull and uneventful, and most of your free time is spent scrolling social media, it will be hard to hold anyone’s interest.

I think Henderson and Corolla are broadly correct. You start with some kind of actual skill but I think it’s important to match well to the skill so it is compatible with your talents. Then you can be more than an enthusiast. I play guitar and bass, but I’m not a talented musician. These are hobbies. They bring me joy. They are among the things I think about and do when I have free time. But I don’t really feel that any of the skills I have in them make me more confident. If anything, they are a source of insecurity. I’ve been playing for decades and routinely see 14-year-olds who are better (and guitar is rarely started as young as say piano).

Again, if the goal is to build confidence through competence then the word “skill” needs to meet standards that go beyond hobbyist. Having hobbies is great, I just doubt they directly address insecurity. It might be a nit-pick, but in a time where comparison and competition furnish all the insecurity one could bear, I find it a bit of a stretch to put Joe Rogan’s passion for archery, which I have no doubt is sacred soulcraft, on par with the skills that get him paid.

Of course, there are a lot of ways to express skill that don’t necessarily lead to getting paid, while still building confidence. But I suspect they have something in common… they make people’s lives better. Skills that only nourish ourselves might be satisfying, meditative, or rejuvenating. They might be necessary for our well-being. But unless they rise to the standard of helping others, it’s unlikely they will address insecurity since insecurity is entangled with our social selves. Status through usefulness.

The ability to fight might seem like an exception since one of its primary payoffs is a sense of security. But this ability is addressing the most literal form of insecurity — “a lack of safety” rather than security as self-worth. The ability to protect one’s loved ones, however, does scale the ability to a broader sense of security.

Survival skills are an interesting case whereby one can achieve an empowering sense of self-reliance with a decent but not all-consuming commitment. An Eagle Scout might not be special forces, but proving to yourself that you can persevere through a long-term challenge is a key ingredient in affirming self-efficacy.

In a similar vein, I wonder if running a marathon or other hard-earned achievement scales one’s sense of self-worth or does that sense remain siloed in the domain which it was accomplished, since, unlike survival skills, the task itself is, in pragmatic terms, useless.

Anyway, the tweet caught my eye because I do believe that the cure for insecurity is usefulness, but usefulness and skill aren’t equal (being great at Madden football vs being able to cook for your family).

I’m totally being pedantic, but this comes from wanting to understand insecurity better. Relieving insecurity is a giant lever for reducing hate and suffering. How much trash behavior, people rooting against one another, and destructive envy trace back to wounded pride and social fears.

Reducing insecurity by telling people that they are enough doesn’t cut it versus offering every reasonably healthy person a path to mutual benefit, which is a more stable requirement of nature than some faith-based notion of equality. If you try earnestly to be useful, regardless of your ability, I believe that’s enough to project a dignity that can be reflected back to you.

Napoleon Dynamite thought nunchuck skills would get him the babes. Corolla would say it’s a start and I’d like to believe it, but insecurity is such a glaring source of anguish amongst our kind that its remedy demands more than skills.

🔗 You Nerds are Still Hiring for Experience! | 3 min read

Jon Matzner argues that “MUST have 3+ years of [weird industry software]” was always lazy thinking but it used to at least be safe. He claims six months from now you can replace that software with a cheap agent such that the experienced hire is starting from scratch alongside the smart-hungry-coachable kid you passed on, except the kid would’ve taught themselves the new tool Saturday morning for fun.

I don’t know enough about software development and the pace of AI to judge this, it certainly sounds presumptuous for the better developers out there. But as we expand time to see this as the intersection of opposing curves where skills expire faster, while attributes compound, it seems feasible. Speculation aside, I appreciate the sentiment that I have shared even before these AI days:

You can’t teach curious, resourceful, or gives-a-shit.

It’s like the train problem from the SATs. It might start the journey later, but at the speed it’s traveling, it won’t take long to overtake the uninspired plodder.

Another pair of related reads

🔗Agency is for sociopaths | 3 min read

Cate Hall has a book coming out called “you can just do things” and I appreciate this short essay which serves as a preemptive strike that needed to be written since I’ve noticed the same things she has.

Yes, many bad people are high in agency, and a lot of the people most obsessed with agency kind of suck. In fact, stop for a moment and call to mind the worst person you can think of. Odds are, they’re the kind of person liable to embrace the mantra “you can just do things.”

This correlation makes sense if, like me, you think of agency as the capacity to see and act on options that others overlook. It’s a combination of inventiveness and courage that most people lack, very often due to social conformity. Bad people don’t feel social conformity as strongly, given that they don’t view the welfare or opinions of others as important. This frees them to indulge in vicious creativity.

It would be a mistake, however, to draw from this a conclusion that agency itself is the problem. It’s more accurate to think of agency as a general-purpose, morally neutral tool, like physical strength or intelligence. And it’s a tool we should be very wary of warning people off of developing, just because there’s some population-level correlation between agency and Dark Triad traits.

🔗 How to walk through walls | 9 min read

The difference between Bloobiebla & MrGrunz and me is not, primarily, that they are faster than I. It is, Gwern points out, that they see the game differently. When I played Zelda, I saw “villages” and “hen.” But they have a hacker mindset, so they know that there aren’t actually any villages and hens…

Most systems can be viewed at multiple levels. There is a superficial system which pretends to be made of one thing (walls, hens). But actually, it is really made of something else (bits, memory allocations). And if you learn to understand that underlying system, you can find ways to use the lower-level details to steer the system in a way that looks incomprehensible to those who only see the more superficial system.

Robert Rodriguez’s classmates must have experienced a bewilderment of this kind when they saw him go down to Mexico with $7,000 dollars and return with a film showing in cinemas across the US. That was not a move that was part of how they’d been told the game that is the film industry works; but it was a move that was perfectly compatible with the facts of cameras, lights, and Hollywood deal-making if you understood them at a deep enough level.

Rodriguez could speedrun a film career, walking through proverbial walls, because he saw through the game to its underlying mechanics. He had the hacker mindset. He was willing to get his hands dirty and learn the practical realities. He saw that a lot of what the other film students took for reality were just fictions they’d been taught at school.

This is a bit vague. Let me give some concrete examples…

Stay groovy

☮️

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I re-print this post a commencement post at this time every year. It’s a great set of reminders with an awesome delivery. It’s a no-brainer to pass along to the grads amongst your family and friends. But you’ll find it rejuvenating too.

Today is a short one. We are in Reno for 3 days of hoops with our son’s 13U team. Enjoy your Memorial Day weekend! And if you’re roadtripping in CA, you’ll understand this one:

Inspiration Season

In Dazed and Confused, Wooderson is the creeper who hangs around the HS crowd years after he’s graduated. Guessing he didn’t pay much attention to the commencement speech. And here’s irony coming around the corner — my favorite all-time commencement speech is by the guy who played Wooderson, Matthew McConaughey.

Presidents, great scientists, Steve Jobs. I can’t imagine the pressure of having to deliver timeless wisdom in the tradition of such minds and achievers. And yet McConaughey, at ease, perched on a barstool, delivers the best commencement speech of all time.

It’s best via video but you can find my favorite excerpts below.

#1: Life’s not easy…don’t try and make it that way.

“It’s not fair, it never was, it isn’t now, it won’t ever be. Do not fall into the entitlement trap of feeling you are a victim, you are not. Get over it and get on with it. And yes, most things are more rewarding when you break a sweat to get em.”

#3: The difference between happiness and joy.

“Happiness is an emotional response to an outcome — If I win I will be happy, if I don’t I won’t. An if-then, cause and effect, quid pro quo standard that we cannot sustain because we immediately raise it every time we attain it. You see, happiness demands a certain outcome, it is result reliant. If happiness is what you’re after, then you are going to be let down frequently and be unhappy much of your time. Joy, though, is something else. It’s not a choice, not a response to some result, it is a constant. Joy is “the feeling we have from doing what we are fashioned to do,” no matter the outcome.”

#4: Define success for yourself.

“How do I define success? For me, it’s a measurement of five things — fatherhood, being a good husband, health, career, friendships. These are what’s important to me in my life. So, I try to measure these five each day, check-in with them, see whether or not I’m in the debit or the credit section with each one. Am I in the red or in the black with each of them?”

#5: A roof is a man-made thing

“You ever choked? You know what I mean, fumbled at the goal line, stuck your foot in your mouth once you got the microphone, had a brain freeze on the exam you were totally prepared for, forgot the punch line to a joke in front of four thousand graduating students at a University of Houston Commencement speech? Or maybe you’ve had that feeling of “Oh my God, life can’t get any better, do I deserve this?” What happens when we get that feeling? We tense up. We have this out-of-body experience where we are literally seeing our self in the third person. We realize that the moment just got bigger than us. You ever felt that way? I have. It’s because we have created a fictitious ceiling, a roof, to our expectations of ourselves, a limit — where we think it’s all too good to be true. But if we stay in the process, within ourselves, in the joy of the doing, we will never choke at the finish line. Why? Because we aren’t thinking of the finish line, we’re not looking at the clock, we’re not watching ourselves on the Jumbotron performing the very act we are in the middle of. No, we’re in the process, the APPROACH IS THE DESTINATION… and we are NEVER finished. Bo Jackson ran over the goal line, through the end zone and up the tunnel — the greatest snipers and marksmen in the world don’t aim at the target, they aim on the other side of it. We do our best when our destinations are beyond the “measurement,” when our reach continually exceeds our grasp, when we have immortal finish lines. When we do this, the race is never over. The journey has no port. The adventure never ends because we are always on our way. Do this, and let them tap us on the shoulder and say, “hey, you scored.” Let them tell you “You won.” Let them come tell you, “you can go home now.” Let them say “I love you too.” Let them say “thank you.” TAKE THE LID OFF THE MAN MADE ROOFS WE PUT ABOVE OURSELVES AND ALWAYS PLAY LIKE AN UNDERDOG.”

#12. Give your obstacles credit.

“Instead of denying your fears, declare them, say them out loud, admit them, give them the credit they deserve. Don’t get all macho and act like they’re no big deal, and don’t get paralyzed by denying they exist and therefore abandoning your need to overcome them. We’re all destined to have to do the thing we fear the most anyway. So, you give your obstacles credit and you will find the courage to overcome them or see clearly that they are not really worth prevailing over.”

The speech Scott Alexander would give

The other graduation speech I share each year is one that was never actually given. Slatestarcodex refers to it as a fake graduation speech. It’s better than most of the real ones.

These excerpts capture the gist of the “speech” that I want to retain. It ends with my favorite lesson. The first in our household coat of arms.

It takes a peircing look at the cost of education throughout our youth and while all of that is interesting, my favorite section is later in the post with affirmations for individuals depending on the story they tell themselves.

To the one who says:

I am the 3.3%! I know who Euclid was and I understand the sublime beauty of geometry. I don’t think I would have been exposed to it, or had the grit to keep studying it, if I hadn’t been here surrounded by equally curious peers, under the instruction of enthusiastic professors.

• to you, my advice is: if you’ve sacrificed everything for knowledge, don’t forget that. When you are a paralegal in Brooklyn, and you get home from work, and you are very tired, and you want to curl up in front of the TV and watch reality shows until you are numb, remind yourself that you value knowledge above everything else, that you will seek intellectual beauty though the world perish, and read a book or something. Or take a class at a community college.

my education was worth it….because of the friends, I made here

• my advice is similar: if you’ve sacrificed everything for friendship, don’t forget that. When you are a paralegal in Brooklyn, or a market analyst in Seattle, or God forbid an intern in Michigan, and you get home from work, and you are very tired, and you want to curl up in front of your computer and check Reddit, remind yourself of the friends you made here and give them a call. See how they’re doing. Write them a Christmas card, especially if it is December. Anything other than declaring friendship your supreme value and drifting out of touch.

my education was worth it…because of the connections I made

• If you’ve sacrificed everything for ambition, be ambitious as hell. When you are a paralegal in Brooklyn or whatever, claw your way to the top, stay there, and use it to do something important. If you’ve sacrificed everything for ambition, don’t you dare stop at middle manager.

my education was worth it… because it helped me learn civic values, become a better person who is better able to help others.

• If you’ve sacrificed everything to help others, don’t let it all end with donating a tenner to the OXFAM guy on the street now and then. Join Giving What We Can or go volunteer somewhere. If you’ve sacrificed everything for others, make sure others get something good out of the deal!

my education was worth it because formal education in the school system taught me how to think.

• Sorry, one second, HAHAHAHAHAHHAHAAAHAHAHAHHHAAHAHA…I’m sorry. Ahem. To you my advice is, again, similar. If you’ve sacrificed everything to learn how to think, learn how to think. When someone says something you disagree with, before you dismiss a straw man and call that person names and slap yourself five for your brilliant rebuttal, take a second to consider it fairly on its own terms. Go learn about biases and heuristics and how to avoid them. Read enough psychology and cognitive science to figure out why your claim might kind of inspire hysterical laughter from people even a little familiar with the field. Just don’t sacrifice everything to learn how to think and end up only rearranging your prejudices.
  
  

For those who feel fleeced…

Finally, some of you will say, wait a second, maybe my education wasn’t worth it. Or, maybe it was the best choice to make from within a bad paradigm, but I’m not content with that.

To you, I can offer a small amount of compensation. You have learned a very valuable lesson that you might not have been able to learn any other way. You have learned that the system is Not Your Friend. I use those last three words very consciously. People usually say “not your friend” as an understatement, a way of saying something is actively hostile. I don’t mean that.

The system is not your friend. The system is not your enemy. The system is a retarded giant throwing wads of $100 bills and books of rules in random directions while shouting “LOOK AT ME! I’M HELPING! I’M HELPING!” Sometimes by luck you catch a wad of cash, and you think the system loves you. Other times by misfortune you get hit in the gut with a rulebook, and you think the system hates you. But either one is giving the system too much credit.

To you I don’t have very much advice…if I knew how to fix the system, it’s a pretty good bet other people would know too and the system would already have been fixed. Maybe you, armed with a degree from the University of [mumble], will be the one to help figure it out.

On the other hand, someone a lot smarter than I am did have some advice for you. Poor Kurt Vonnegut never did get to give a real graduation speech, but one of his books has some advice targeted at another major life transition:

Hello babies. Welcome to Earth. It’s hot in the summer and cold in the winter. It’s round and wet and crowded. On the outside, babies, you’ve got a hundred years here. There’s only one rule that I know of, babies-“God damn it, you’ve got to be kind.”

I don’t know how to fix the system, but I am pretty sure that one of the ingredients is kindness.

I think of kindness not only as the moral virtue of volunteering at a soup kitchen or even of living your life to help as many other people as possible, but also as an epistemic virtue. Epistemic kindness is kind of like humility. Kindness to ideas you disagree with. Kindness to positions you want to dismiss as crazy and dismiss with insults and mockery. Kindness that breaks you out of your own arrogance, makes you realize the truth is more important than your own glorification, especially when there’s a lot at stake.

This Week In The Options Trench

The market for box spreads has been growing and becoming 2 sided beyond just market makers funding. This will get you up to speed if you haven’t been following.

Stay groovy

☮️

Moontower Weekly Recap

• the phantom zone rant

• stacking carry: an inflation hedge you get paid to own

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US bond yields are rising as inflation re-enters the conversation. The 10-year yield is up to 4.65% and 30-year bonds have just crossed 5%, a nearly 20-year high.

This isn’t surprising. 6 weeks ago, in Trading As A Sudoku Puzzle With Prices As The Given Numbers, I talked about how 1-year gasoline futures were trading at a 1/3 discount to prompt pricing, but if gasoline prices remain high, this will roll up. If spot prices stay high for a year, those back-month futures will converge to current prices. Even though energy is only about 5% of CPI, the size of such a sustained move would easily transmit 1.5% to inflation indices and that is just due to direct energy effects and ignoring indirect effects on food, construction, and transport.

We’ll switch the conversation to crude oil just because it’s more widely tracked and the specifics of the contracts aren’t critical to where we’re going. Prompt oil is roughly in the same place vs 7 weeks ago, but the contract that was 12-months out and is now 11-months out has rolled up >6%. Meanwhile, another month of sustained high oil prices has pushed the 10-year yield up 30 bps from 4.3% to 4.6% with IEF price returning about -1.6% a bit better than what’s expected by its duration.*

*There’s some leeway since I’m using an index for the yield which may have a different set of weighted maturities than IEF holds. Also, IEF total return is closer to -1.1% because you earn interest for 7 weeks.

So far, so good. The reaction function in bonds makes sense. But my Sudoku post claimed that an inflation-induced yield bump would transmit to real equity risk premiums. In other words, I would expect equities to sell off with bonds, or heck, at least not have such a sharp rally.

This is not quite the puzzle it appears to be. The equity exuberance is actually quite limited if you look under the hood of the index.

From Shannon’s substack:

The internals are doing something the people who watch this for a living have never seen. The S&P is up 4.2% month-to-date with 209 stocks up and 295 down. The NASDAQ is up 8% month-to-date on a near-even split (51 up, 50 down). The index is 9% above its 50-day moving average while only roughly half the components are above their own 50-day; at that distance you’d normally expect 80% breadth. Four days running, more S&P stocks hit new 52-week lows than 52-week highs, with the index at all-time highs and up 30% year over year. Yesterday 9% of the index hit new lows. None of this happens together in a healthy tape.

I’ve noticed many market people interpret these “internals” as bearish. I’m not sure this is bearish for the index. It just is. A few companies are eating everything else. We get it. At this point, the low cross-correlation of the components is common knowledge (isn’t this what managers call a “stock pickers market”?).

Rather than use the term “bearish” which has a predictive slant I can’t justify, we can just accept that the sustained oil price, inflation jitters, and rise in yields are being reflected in prices broadly. SMH (semis ETF) is near 1-year highs while XHB (homebuilders) are near one-year lows.

The AI story is in a parallel vacuum, indifferent to relics like discount rates or identities such as spending = income, but stocks overall are not being indiscriminantly bid. SPY has returned nearly 2x RSP, the equal-weighted SP500 index, over the past year. So the loving arms of our cap-weighted benchmarks hold us tight, shielding our eyes from the turmoil within. Trepidation over supply-side inflation is confirmed by bond and non-AI stocks alike.

Concerned with inflation, I dust off some old posts, like What I Learned About TIPs which I wrote when I bought when breakevens shrunk to about 2.2% (green box).

(When breakevens are skinny, TIPs are relatively cheap compared to nominal bonds, and when they are fat, they are relatively expensive. The way to think of that is if you buy TIPs at say 2% breakevens, then you are better off with the TIPs if CPI realizes more than 2% and vice versa.)

Breakevens are currently matching 3-year highs so TIPs don’t look attractive on a relative basis, but that’s only one lens. The real driver of my decision to buy TIPs in Oct 2023 was the absolute real rate which was ~2.45% which still stands as the peak for most investors under age 40’s working life.

Remember that’s 245 bps of return above inflation for no risk and if you hold them in an IRA, no tax drag. Historically speaking, equity real returns have been in the range of 3-6%, but recent years have been quite a run of heads. Whether the coin is biased now is a question for someone smarter than I. But I digress.

The point is I’ve started once again to consider inflation-aware trades. 10-year TIPs don’t stand out as a bargain relative to nominal bonds. I’m wary on gold and silver because of how well they’ve performed recently, but also historically, they have not been great to own when real rates increase and we can see from the absolute TIPs rate that, despite breakevens not breaking out, real rates are crawling higher, approaching an 18-month high.

So I dust off yet another post, this one from 2 years ago: Inflation Replicator. I show how a portfolio of oil futures plus nominal bonds mimics the behavior of inflation-indexed bonds like TIPs. I constructed it in Composer using USL, which holds a strip of oil futures maturing within the next 12-months, plus TLH, a bond ETF holding bonds with 10-20 year maturities. The portfolio is inverse-vol weighted, rebalanced quarterly.

This is the out-of-sample performance since I published the post (green line).

That portfolio is a set-and-forget inflation hedge if you don’t like TIPs.

[Speaking of “tips”, here’s a general one. If you have a portfolio that rebalances, it is often selling winners to re-invest in losers. This keeps you diversified and avoids the volatility tax that comes from concentration, but it’s not tax-friendly unless you do it in a sheltered account. To do it in a regular account, you can consider a tax-loss overlay where instead of buying more of the losing position, you actually sell the losing position and another ETF that has a highly correlated exposure. So, for example, if TLH is the losing side and you need to add more on the rebalance, you actually tax-loss harvest the TLH and replace it with TLT length. It’s a similar exposure, but you can now use the TLH capital loss to offset the gain on the USL win you trimmed.]

The specific inflation replicator I composed was TLH + USL. But if we abstract it to “bonds + oil”, it invites us to think about risk premia that exist in both asset classes in the current market.

In the remainder of this post, I’ll narrate layering a couple of edges onto a core portfolio idea. By following along, you’ll get concrete ideas for measuring and managing risk and open your mind to the different Legos available to build the portfolio and ultimately express the trade while targeting the carry embedded in the asset’s pricing complex.

Read more

This is a straight-up rant.

If you are anywhere near financial or tech twitter you’ve seen Deedy’s tweet and the reactions to it. Here’s a reprint:

The vibes in SF feel pretty frenetic right now. The divide in outcomes is the worst I've ever seen.

Over the last 5yrs, a group of ~10k people - employees at Anthropic, OpenAI, xAI, Nvidia, Meta TBD, founders - have hit retirement wealth of well above $20M (back of the envelope AI estimation).

Everyone outside that group feels like they can work their well-paying (but <$500k) job for their whole life and never get there.

Worse yet, layoffs are in full swing. Many software engineers feel like their life's skill is no longer useful. The day to day role of most jobs has changed overnight with AI.

As a result,
1. The corporate ladder looks like the wrong building to climb.
Everyone's trying to align with a new set of career "paths": should I be a founder? Is it too late to join Anthropic / OpenAI? should I get into AI? what company stock will 10x next? People are demanding higher salaries and switching jobs more and more.

2. There’s a deep malaise about work (and its future).
Why even work at all for “peanuts”? Will my job even exist in a few years? Many feel helpless. You hear the “permanent underclass” conversation a lot, esp from young people. It's hard to focus on doing good work when you think "man, if I joined Anthropic 2yrs ago, I could retire"

3. The mid to late middle managers feel paralyzed.
Many have families and don't feel like they have the energy or network to just "start a company". They don't particularly have any AI skills. They see the writing on the wall: middle management is being hollowed out in many companies.

4. The rich aren’t particularly happy either.
No one is shedding tears for them (and rightfully so). But those who have "made it" experience a profound lack of purpose too. Some have gone from <$150k to >$50M in a few years with no ramp. It flips your life plans upside down. For some, comparison is the thief of joy. For some, they escape to NYC to "live life". For others still, they start companies "just cuz", often to win status points. They never imagined that by age 30, they'd be set. I once asked a post-economic founder friend why they didn't just sell the co and they said "and do what? right now, everyone wants to talk to me. if i sell, I will only have money."

I understand that many reading this scoff at the champagne problems of the valley. Society is warped in this tech bubble. What is often well-off anywhere else in the world is bang average here.

Unlike many other places, tenure, intelligence and hard work can be loosely correlated with outcomes in the Bay. Living through a societally transformative gold rush in that environment can be paralyzing. "Am I in the right place? Should I move? Is there time still left? Am I gonna make it?" It psychologically torments many who have moved here in search of "success".

Ironically, a frequent side effect of this torment is to spin up the very products making everyone rich in hopes that you too can vibecode your path to economic enlightenment.

The speed and magnitude of the wealth creation is like a black hole. The envy and accompanying anxiety that AI will devour future paths to wealth for anyone who doesn’t already have it has a gravitational pull in the Bay Area from which no light can escape. The metaphor writes itself. The event horizon is the singularity moment where capital is the only thing that matters.

Stanford senior, author Theo Baker’s recent NY Times editorial What A.I. Did to My College Class indicates the black hole is growing at one of the world’s leading universities. Pardon another long excerpt, but it’s worth it:

Cheating has become omnipresent. I don’t know a single person who hasn’t used A.I. to get through some assignment in college, yet the school was at first slow to realize how widespread this would become. As freshman year went on, some professors suggested that the “nuclear option” might be called for: allowing faculty to proctor in-person exams, a practice banned at the university for over a century to demonstrate “confidence in the honor” of students.

In our tech-enabled, newly A.I.-powered world, students were increasingly fudging just about everything. They would embezzle dorm funds to spend on their friends and lie about having Covid to get the UberEats credits that the school offered to those in quarantine. Some kids I knew published a paper that claimed a groundbreaking new A.I. advancement. Online sleuths quickly pointed out that it appeared to be just a stolen Chinese model, to which the two Stanford co-authors responded by blaming the plagiarism on the third author.

In junior year, 49 percent of the 849 computer science majors who responded to an annual campus survey said they would rather cheat on an exam than fail. A friend of mine captured the school’s ethos while we were discussing the tech hardware and other items our student club neglected to return to corporate sponsors. It was all, I recall her saying, “just a little bit of fraud.”

About halfway through freshman year, some coding classes started requiring students to sign a declaration — “I did not utilize ChatGPT” — to submit each assignment. During the first term these attestations began to appear, I watched a freshman I knew sign the declaration that he’d done his homework without A.I. as ChatGPT was still open in the next window — while on the deck of a yacht party financed by venture capitalists. The incentive structures were not aligned toward honesty. One could get ahead, quickly, by cutting corners, by focusing on self-presentation.

The money is a big part of it. A.I. has merely accelerated a trend that was already underway at Stanford and has been reflected by many of the country’s most corporatized universities: Education itself can be seen as a secondary goal to enabling future success, frequently defined as a future windfall.

The article then goes on to talk about the student body's fascination with getting rich as they watch peers and recent alum hit the equivalent of the lotto in this hockey-stick environment. And even if it’s not the lotto, there’s the constant reminder that any obsession not having to do with money is carrying an increasing opportunity cost:

Next to me, one student scribbled on a branded notepad from Hudson River Trading, a quantitative trading firm where fresh graduates can earn upward of $600,000 a year.

This is scrambling people’s brains. Here’s :

I would think that tech people have had plenty of practice coping since this has been going on for awhile even if the numbers are bigger now. Being in finance and watching more than a fair share of idiots get rich has given me plenty of perspective. But it’s exactly to not think of the idiots getting rich, but of all the great people who didn’t.

Think of the people you know who haven't had your luck and who you know are better than you. This immediately shifts your mind to gratitude. There are a million moments in a day to recognize how lucky you are. If you’re so f’n “agentic” why are you unable to choose to see that reality.

I wouldn’t be surprised if the most anxious people, the ones described in Deedy’s post, are the ones who are the most imposter. The ones who massively outperformed and in their hearts know it. They are not as self-reliant as they outwardly show and they hope their bank account will save them from ever having to face the truth that they are stunted in broad ways. They are less adaptable than they appear. They are specialized and therefore hostage to an environment that may well be artificial and, feeding their deepest fear, fleeting.

The deranged psychology in Deedy’s description isn’t about greed. Maybe for a few. It’s really about being fragile. These are rich but fragile people. And it’s even more twisted than this. The permanent underclass meme isn’t a nightmare. It’s a fantasy. If you’ve lucked into being “post-economic” by age 30, where even the most conservative compounding assumptions mean being able to throw out your alarm clock forever, you’ve secured never having the discomfort of testing your character and resilience.

But this fantasy is just that. A fantasy. And a poorly thought-out one. What’s a world where the United States has a permanent underclass? That’s what Egypt is today.

How do you get from where we are today to that arrangement?

1. We really do achieve capital singularity and pre-existing wealth becomes the only meaningful input to flourishing and class mobility. This might be a foregone conclusion to many, but I also think it’s short-term profitable to promote this view so it’s not a fully honest position.

2. This new order becomes common knowledge. The government and its wealthy owners use media and propaganda, supercharged by the tech they own, to pacify the unwashed (ie most of us.)

3. The dam eventually breaks. You know the scene already: The powerful will be ripped from their decadent nests and cast into the cold world the rest of us have known and endured.

4. This aggression will not stand, man. The oligarchs respond. The ensuing authoritarianism in this country is unprecedented. Welcome to Egypt’s corrupt system of favor-trading and hopelessness, except it’s secured by the most dystopian sci-fi technology.

So let’s see, you're rich but not as self-reliant as you want others to believe, and this world is your salvation? What you’ve secured is a boot-licking future. At least you’ll still be able to afford DoorDash.

If you’re going to be a piece of shit, at least be evil and accountable instead of swallowing and boosting anxiety-porn because you either lack the imagination to see why either it’s wrong or how little your bag will matter in the world where it’s not.

Get over yourself. Show some gratitude. Do you hear what you sound like? If you’re fucked, then everyone else is dead. Do you really believe this? If so, while not redirecting your energy towards a remedy, is to admit being a rich coward. Enjoy your enclave while it lasts. It’s a life raft to nowhere.

I find being in finance and from NY, but building a life and family in the Bay Area makes it hard to avoid comparing the locations. The Bay Area really struggles to reconcile its identity with profound wealth. It’s not surprising given the velocity of change. The legacy of hackers, iconoclasts, and nerds who happened into insane riches bred a more institutionalized capital formation ecosystem. Like the kind that NY has always been known for.

But the cultures cannot thoroughly mix without paradox. The unabashed but honest avarice of NY capitalism meets the idealism of artists who, at some point, cannot resist turning in their bicycle for a Pagani and fuel-guzzling jet. But they also don’t wanna see themselves as “that guy”. So we endure this moralizing hypocrisy. Watching them strain to serve a master they haven’t checked in with since the days of eating ramen in a garage.

I kind of appreciate the Stanford story. For most kids, school was always about “is this gonna be on the test?” not skill-building. It’s a place to demonstrate the “right” mix of aptitude and conformity to keep the “right” options open. The “right” options being a white-collar gig with either enough prestige to please your parents or enough money to shut them up.

Instead of “Is this gonna be on the test?”, it’s ”Is this gonna make me rich?” It sounds crude, but given the cost of college and its role for many people as a way to break out of the lower class, it is what many people are already thinking. It’s the next logical step in the progression because money is prestige and prestige without money ain’t gonna get you into a Great Schools 10 zone to perpetuate the cycle with your own kids.

If there’s a devil, he doesn’t want to kill you. He wants you to live, but be obsessed with yourself. That scales. That is a cycle that goes deeper than the radiation from a one-time nuclear cloud. To stay alive, with your insecurity trapping you in a 2-D rhombus projecting its phantom zone on your bloodline for eons.

The upper bound of being obsessed with yourself is survival. That’s a strange peak ambition for people who are free of material constraint.

Perhaps they are anything but free?

Stay groovy

☮️

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In this issue:

• racing to a mountaintop or just another “collection of tradeoffs”

• how high implied vol can work against you or for you

• the greatest intern class of all time?

Thursday’s post what I want my kids to know struck a nerve with readers for different reasons. A close friend noted that it seemed pretty male-centric. Having grown up with only a brother himself, he probably wouldn’t have noticed if it wasn’t for raising a daughter now. He wrote me a thoughtful email about it, analogizing between seeing the world as a mountain to climb (male-coded lens) vs a more sea-like horizontal interconnectedness where you are bombarded by both supportive and punishing waves. A line he wrote that resonated:

women are more in-tune or more impacted by the reality there may not be a peak to this mountain. That the mountain itself is just a projection of a higher-dimensional reality and the “peak” is really just a collection of tradeoffs.*

*You can find my immediate response to this further below but it’s secondary to the message front-and-center

I think seeing a “collection of tradeoffs” does several things.

First of all, it immediately flattens the idea of a peak or at least places them as narrow spires on a plateau. You can be the greatest in the world at XYZ, but you haven’t conquered life. Elite performers don’t usually sugar-coat the cost of these conquests. Sometimes the public sees the price they pay when their lives crumble and wonder if it’s because they are stunted in every other domain than the one they dominate. The self-aware ones are effusive in acknowledging the support of their families in enabling what is ultimately a pursuit of glory and even posterity.

Secondly, seeing a “collection of tradeoffs” loosens the creativity muscles. If you view life as a race to some mountaintop, you will restrict the routes your life can take. That artificially narrowed menu will be written by your immediate surroundings, which is already a skinny slice of human experience.

I want to pause on that for a moment. The narrowness of the menu we choose flows from the most tyrannical source: random path dependence. Where you were born, in what time, and to whom? It’s probably adaptive to ignore that perspective and trudge forward, but I admit it’s a thought that intrudes just enough to bug me.

I was watching videos of people covering songs I like on YouTube the other night. I will often wander to the long tail of videos that have very low view counts. It feels like you are watching something vulnerable and isn’t really intended for your eyes except for that they posted it publicly. I watch and I wonder. Who is this person? What’s their life like? I’m getting an energy from their performance but they have no idea who I am, where I am, and that I’m watching this a decade after they posted it.

I’m several of the 34 views of this vid:

It’s not a nice voice. The man looks unwell. But it’s extremely expressive. The way he performs it. The instrumentation he chose. The fact that he looks enigmatically young and old at the same time.

Futurism and space travel represent adventure and vastness. Sheer wonder reminds us how small we are. But I see vastness in a simple video like this. This individual is made of the same stuff I am, but we are aliens to each other. Maybe or maybe not. But that’s the point. The mystery creates a sense of vastness. It is the wonder, that right here on Earth, the lyrics of the song hold:

See the animal in his cage that you built
Are you sure what side you’re on?
Better not look him too closely in the eye
Are you sure what side of the glass you are on?
See the safety of the life you have built
Everything where it belongs
What if everything around you
Isn’t quite as it seems?
What if all the world you think you know
Is an elaborate dream?
And if you look at your reflection
Is it all you want it to be?
What if you could look right
Through the cracks?
Would you find yourself
Find yourself afraid to see?

Shortly after that vid, the YT algo served me Trent Reznor’s speech when he inducted The Cure into the Rock and Roll Hall of Fame. He eloquently transmits the idea that their music and way of being spoke to so many people who didn’t feel like they belonged. People who likely saw something besides life as a “mountain”. When Trent first heard The Cure he thought they were making music directed at him.

Trent is gesturing at the thing every great artist or artisan understands. The skeleton key is to connect with others authentically. To give people something they deeply want because you understand the yearning yourself. Artists express and artisans solve. One has fans, the other has clients. Sometimes the artisan is so good the clients are fans. In both cases, the relationship is deeply empathetic. I call it a skeleton key because that thing is different for everyone but it unlocks the same door.

The door to thriving.

*As promised, this was my reply back to my friend:

I see what you mean and yes I agree its gendered. I think underneath it all, my sense of how the world operates is probably from a biological place -- women are default valuable (their overt subjugation in much of the world is a demented response to this...like a male attempt to take back power that biology confers) whereas a man is entire worth depends on what he can provide. Modernity changes the calculus to a meaningful extent (in doing so trades off against novel considerations) but I don’t think it has created a new calculus. At the end of the day, there is a competition and as with any competition, there are niches that will provide a better harbor for some individuals to strive within based on their unique traits and views.

Insofar as my writing is narrow, it is written from the perspective of being subsumed by one of these niches. I’m swimming in the “water” in the David Foster Wallace sense of the word. But of course, the audience is self-selected and therefore assumed to be in the same water.

The beauty of travel is to be able to look back home and see the water for what it is. Something that has a particular pH balance that nourishes parts of our souls and sickens other parts.

Money Angle

🔗 How to Short a Bubble | 10 min read

Outstanding post. Alexander Campbell on why shorting the thing going vertical is the worst possible expression of being bearish. As something goes parabolic your exposure grows with it (I have a collection of posts on why shorting is complicated).

The vol that accompanies a bubble renders the puts useless (more on that in the Masochists section). Instead, Campbell proposes a better risk-adjusted approach by identifying:

• the wedge: the thing that kills it the bubble. He suggests if AI is the bubble, rates are the wedge, and inside every bubble there’s a weakest link that needs the bubble to keep accelerating just to survive a pause

• the victim: the cheap-vol neighbor that gets dragged down such as airlines pre-COVID, BAC instead of housing CDS in ‘08.

• confirmation: wait for a trend to break then press specific shorts

🎙️PTJ on Invest Like The Best | podcast link

Patrick O’Shaugnessey interviewed legendary macro trader Paul Tudor Jones. It’s self-recommending, but here are the 2 parts that stayed with me:

From contraction to expansion on the issuance side

PTJ: If I think of some really, really big accidents, most of them have the same underlying reason, the same underlying foundation, which is some too much leverage somewhere. Most of the leverage, most of the time – if I think of the big ones – were derivatives inspired. Either futures or options.

1987, that crash was 100% portfolio insurance. A hundred percent. Had they had limits, which they didn’t, it would’ve been 10%, maybe 15% max. But that was a hundred percent derivatives. If I think about 1998, Long-Term Capital, big derivatives. They had a huge balance sheet with a lot of derivatives they were offsides on.

2000 was a little different. 2000 was the easiest bear market I’ve ever seen in my whole life. It’s got so many similarities to right now, in the sense that the bear market of 2001 and 2002 were a consequence of all the IPOs in ’99 and 2000. And then as they unlocked, you just had this never-ending cascade of selling, that’s a great way of putting it. And we’re getting ready – I want to say that the contemplated IPOs for next year are going to be five or six percent of market cap. So why are we where we are right now? Because we’ve been retiring two or three percent of market cap, probably a little less than 2% of market cap, every year without fail for the past 10 years [through buybacks.]

And so now all of a sudden, you’re gonna completely reverse that math. And so, I don’t think it necessarily happens instantaneously with the IPOs, but then there’ll be the unlocks. So you can see a situation where, okay, maybe we go through some kind of rolling top. And then 18 months from now – six months, we’ll have to look at the unlock schedule. But you’re going to want to watch those because that’ll just be adding equity supply. And you’ve already gonna be diminishing the buybacks because of all the commitment to capex from the hyper-scalers. They’re already gonna be eating into their cash flow.

This one sticks with me because I’m a “the market is just positions and flows”. There’s nothing magical about historical rates of return, margins and so forth. You have tradeable capital in the form of stocks and bonds. Issuance is the supply. Demand comes from savings. If savings increase faster than paper prices go up. And this is not linear because the marginal propensity save one’s millionth dollar is higher than one’s thousandth dollar.

Prices have gone up a lot so it makes sense for a narrow base of supply owners should dump it on the wider marketplace. I’m quite curious if the public markets will value these companies as highly as the illiquid private markets do, but since the issuance was be low float, I assume the owners share my curiosity and wanna feel things out before trying to realize their god-wealth.

Life advice

At the end of the interview PTJ (emphasis mine)

We can humbly devote ourselves to finding the kindness within ourselves and the goodness within ourselves, and transmit that to somebody else during that day.

I think that’s the secret to happiness. You don’t have to worry about yourself. You have to worry about, “How am I going to brighten someone else’s day?” And with that attitude, one, you’ll always be happy. I’m just gonna spend this one day doing this one outward act. And if you repeat it enough pretty soon you take “I should” and they will become “I ams”.

So if you take that mentality, that I want to do this wonderful act of kindness for someone else, pretty soon you become an incredibly kind person. It becomes natural. It becomes instinctive and organic. And it’s gonna brighten your day. You’ll have such a positive outlook on life.

I’m in the camp that happiness is a self-effacing end. You never get it if you aim at it. You’ll probably get more mileage from the definition of humility that it’s not about thinking less of yourself but thinking about yourself less (I don’t know who said that. There’s debate over whether it was C.S. Lewis. For all we know it was Mark Twain. Either way, it’s public domain.)

Money Angle for Masochists

Here’s how high vol works against you

This echoes Campbell’s thought about using puts to trade directionally once an asset has already made a giant move).

When you are 100+ vol, it’s not surprising the market puts your odds of getting cut in half at 1 in 3 proposition.

It’s hard to make money in a reasonable risk-adjusted away once an asset is already high vol since it's hard to size it without risking your neck.

It is well within the meat of the distribution for SNDK to get cut in half this year. That’s just a good baseball player’s chance of getting a hit or a typical NBA player hitting a 3 in a game (or missing a 3 in practice).

How high vol works for you

The high vol is a gift to the natural holders. Millennial employees can lock in their unborn grandkids' inheritance.

A non-technical way to appreciate how high vol creates this opportunity in upside call vs downside put differentials:

Imagine a stock starts at $100. It gets to $125. From $125 to $150 is only 20%

But if the stock fell to $75 the distance from $75 to $50 is 33%

Both $50 and $150 are 50% from the initial price, but in a compounding sense 150 is much “closer” to the starting value than $50. The higher the vol the less “distance” a fixed dollar move represents. As implied vol increases OTM calls grow faster in value than OTM puts. This is the source of the attractive pricing you see in the risk reversal (ie option collar).

That tweet comes from Dean Curnutt of The Alpha Exchange Podcast. He's a partner in an option brokerage firm I’ve known for a long time. I told him he needs to buy an SF realty company, since risk reversal-financed $10mm SF Victorian pipeline is unmanned!

Speaking of, if you wanted to bet on AI without access to private shares, real estate on leverage would have worked. See Redfin economist Daryl Fairweather’s Is the Bay Area in an AI Housing Bubble?. I hear from locals who own a bunch of SF RE that the bid is mostly in single-family and multi-family rental units are not getting the hockey stick treatment. The rents have been exploding higher, however. And to think coming out of COVID, you couldn’t give away an SF condo. Super high vol asset. They need options!

Interestingly, home prices locally in the burbs have been dead money since around 2023 although having a step-function increase from the Covid era. I can think of at least one person who rebalanced, selling their burb home, moving to a cheaper state but plowing some of the proceeds of the sale into a depressed SF condo.

Geniuses

This is just fun.

My son is in 7th grade. This is Scott Wu in 7th grade. But it doesn’t matter what grade. Tough day for the genius girl standing next to him. It’s just a 1 minute vid, watch it before you read ahead:

I just wanted to share the trick I think Scott did to do 255² - 245² so quickly.

You have to immediately recognize that a difference of squares is the same as the sum of the 2 numbers times their difference. You’ve all done this in school:

a²-b² = (a+b) (a-b)

My guess is Scott quickly reasoned:

255 + 245 = 500

255 - 245 = 10

500 x 10 = 5000

If you are regularly practicing math I’d guess converting “difference of squares” which is a canonical form into its factored form is quite natural.

From there, the particular numbers chosen make this problem quite easy to compute but yea he’s fast as hell. And for the final question, you witness insane reading speed.

This Week In The Options Trench

We talk about greeks in understandable ways (I hope!)

Stay groovy

☮️

Moontower Weekly Recap

• turning a Jane Street interview question blunder to a lesson

• what I want my kids to know

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I went to Catholic school for K-12. Public schools were less than good where I grew up. My kids go to public school. The K-8 schools here are fine. Better than where I was raised but still nothing special.

The biggest difference is demographics. This is an upper-class area, the student body on average has a natural head start academically. You can attribute it to nature or nurture but it’s true. The mean OLSAT scores, which determine if your kids get into gifted programs, are a full standard deviation higher than the CA mean. Since the test is approximately an IQ test, that places the mean public school student at around 115 in this area. You need to be somewhere around 1.5-2 standard deviations higher than that mean to make the gifted programs here.

There are children of founders, scientists, artists, doctors, lawyers and athletes. Several are legit famous (Steph Curry lived here at the start of his career and there are a number of NBA, MLB, and Olympians who call our area of the East Bay home. Alanis Morrissette lived a few blocks away from the first house I lived in here, but has since moved, and the Chevron CEO’s house is on the best block for trick-or-treating. I think he’s not here anymore either, though). There are many more famous in their fields. But it is a deeply understated area as I can think of at least 3 billionaires in town and probably 2 dozen centimillionaires, but you are not going to find a 30k sq ft house anywhere in the vicinity. It is the opposite of Miami. It is what my friend Jason Buck calls, “stealth wealth”.

Beneath the fancy folk, there’s a thick sedimentary layer of unmemorable overachievers (like yours truly) ranging from white collar workers to the type of entrepreneur who calls themself a businessperson, not a founder. You own a construction company or a few burger joints that sell boozy shakes.

And then there’s the strata of wage earners with the honest jobs. The kind you find in Richard Scarry books. Nurse, firefighter, teacher, cop. They almost all grew up here. Nobody subjects themselves to the financial punishment of moving here if they make their money the hard way.

Finally, there are the villains of CA. Retired boomers living in $2mm houses, paying $2k a year in property taxes with 2 vacant bedrooms plus a 3rd for their golden-doodle. As an abstract class, I understand the venom, but also these are my neighbors who I mostly get along great with. If I went on Nextdoor maybe I’d feel differently but I choose not to look.

[Everything I said above is likely taken up 1 to 10 notches, depending on if you are in Marin or the peninsula. The East Bay, for all its unrelatability to much of the U.S., is still the most relatable. Much of my surrounding area towns remind me of where I grew up, but parallel shifted higher simply because CA cost-of-living and incomes have a higher Y-intercept. The slope of experience is likely very similar. For Mother’s Day my wife’s extended family of ~50 people visited from various parts of the East Bay and I feel like this is the normal I grew up around, except everyone has straight hair and knows how to use their indoor voice when they're 12 inches from your face.]

Back to public school. The system itself is incrementally better than home, but the kids are generally pulling from a more talented, competitive, and driven baseline. Life’s not fair and it’s indifferent to your pleas otherwise. I tell my kids this.

On Monday, on the way home from track, I took the 7th grader to Safeway. We were in there for odds and ends. Bagels, sunflower seed butter, milk, berries. 2 paper bags worth of stuff. There was a $30 tub of protein. All-in, $120.

I gave Zak a lecture he didn’t ask for or see coming. “Did you see how little stuff we just bought? 120 bucks, including about 10% sales tax. If you work as that check-out person in the grocery store for $15/hr, that haul is a day of work.”

Then I go on my dad rant about not getting fooled by your surroundings. What school says is an A is nothing but basics. The basics of showing up and executing on what they told you to do. If inflicted by an uninspiring teacher, it’s compliance training.

[I’m not saying everyone should feel this way, you know your own kids. The only way I would not have gotten As growing up was if I were negligent and that certainly happened sometimes, but again, the bar of not being negligent is ground zero executive functioning. If you can’t do that, then it makes sense to track down the reason and decide what the cost/benefit of trying to remedy it or not is. These are personal battles to choose.]

The gears were turning. Both he and his 4th-grade brother were taking this in. I’ve explained this to them before but they were listening now. We chatted for about 45 minutes meandering through several related topics. One question took me off guard because it’s a sharp reminder that their frames of reference are so different that their minds go to places that surprise me. They asked if I had that paper they give people when school is over.

A diploma?

Yes. They asked if everyone gets one if they finish school or if you have to go to a “good” school? A bit of a strategic moment here. I need to simultaneously encourage education without tricking them into placing it on a pedestal. Education at its best is useful knowledge and deep inquiry, but at its worst, the exact opposite — propaganda and conformity (I hate using the “—” but I assure you that was me).

I told them I had a diploma. In fact, it’s framed, a gift to me from their grandma. They asked why I don’t hang it up like the orthodontist does. It was time for real talk.

I explained that I’m not especially proud of my degree. But take full responsibility for my disappointment. I took a non-technical econ degree. It was an easy 4.0 because it relied on me writing persuasive-sounding bullshit on blue-lined pamphlet paper. This didn’t push me to grow.

Then I found myself in a technical career where I wish I had studied what I tried to study at first but gave up on. Computer science. It would have empowered me to go faster. But even more important is the confidence. I was always insecure about not applying myself growing up and therefore having no real skills. Attached to what I was told about my potential for longer than maturity should permit.

Possessed by the ghost of my adolescent guile, I asked Zak if he thought he was actually good at the tasks given to him at school or if he was good at guessing the teacher’s password. By whose standards is your grade an A?

My correction (overcorrection?) now is that I tell my kids the world doesn’t need nor give a smouldering turd about another smart person. Dime a dozen. What you need is nerve. Courage. What’s the point of smart if you can’t get what you want out of life? In fact, nothing is more embarrassing than watching a person who thinks of themself as smart complain. If you’re so smart, figure it out. If you can’t, then your smarts are either not useful, not real, or a party trick. If they are a party trick, find a way to get the trick rewarded so you have less to complain about.

So what is school good for? What can you salvage from the private school or the better school district? It’s a hard question. And I’m at least a little concerned that my impulsive but deeply sincere reply below represents the bulk of my answer.

I’m not trying to manufacture contempt in my kids for their smuggest peers, but I assure you I’m going to look the other way while their mom does.

The excerpt below from author Devon Erikson articulates a phenomena we all see. It’s also deeply related to trading which I’ll explain afterwards.

There are two types of intelligence tasks: answer tasks and result tasks.

A result task is graded by the reaction of the environment to your work. Either your software runs, or it doesn't. Either your rockets fly, or they don't. Customer buy millions of your product, or none.

You have unlimited tries unless you run out of money, but there's no partial credit, and you can't talk the universe into accepting your answer if it doesn't.

Result tasks typically require a lot of work, are data-intensive, and have lots of sub-problems, because the ones that didn't are already solved.

Result tasks are why we care about smart at all. Because smart people are the ones who can do this. And every human advancement or achievement ever was a result task.

Answer tasks are quite different. They are artificial problems created by a human being for another human being, whose goal is to produce the known answer.

Tasks like this have useful features. They can be tightly calibrated for appropriate difficulty. They are easy to grade. They can be used to teach particular subjects or skills.

But there are certain things they don't teach.

How to do the boring parts that don't impress anyone with how talented you are.

How to fail and try again.

How to change the question instead of answering it, because the question itself was wrong.

How to absorb from others what they had to learn the hard way, instead of reinventing the wheel.

How to deal with problems that have no solutions, only tradeoffs.

How to work with others and pass the ball.

How not to adapt instead of freezing when the universe gives the exam before the lesson.

How to substitute the adequate you can afford for the ideal you can't.

How to prioritize what is needful over what is elegant or cool.

Without this learning, and other similar lessons, the talent child turns into an adult with an unbalanced intellectual development, like a bodybuilder who skipped far too many leg days.

You'll find a lot of men like this in academia because it provides them with a sheltered, tightly controlled environment, where the problems are abstract if not utterly fake, and the persuasiveness of a solution trumps its workability.

They tend to scorn achievers, especially achievers with modest academic credentials or none, and this invites scorn in turn from people with real jobs.

But really what they are is victims. Entire campuses and networks full of what was potential greatness, crippled in it youth by bureaucracies that claim to serve it.

Homeschool your children.

Give them projects, not puzzles.

Teach them to build things.

The bridge to picking better advisors, doctors and agents in life

Read more

The genre led me to this game. It’s tongue-in-cheek but has real questions too.

I got an interview question wrong, which in itself isn’t bothersome, as they are designed to trip up smarter people than me. But the one I got wrong is in the realm of questions I should get right, which I do find compulsively bothersome.

I looked at the answer, but I know looking at answers doesn’t mean you necessarily learned. I wasn’t confident I could reproduce the answer or the answer to questions in a similar vein with twists.

So, I prompted Claude to teach me to answer it, but in a Socratic way. Then, for 2 days as I was drinking the morning coffee, I would rederive the identities and restate the meanings of the identities in words. Finally, do a couple of practice problems (like the dice version further below).

After 2 days, I felt like I got the idea, so I’ll continue on to a related topic, but I wanted to consolidate what I learned. I regurgitated my pen-and-paper effort to Claude to validate my work. Then, based on how I internalized this, I had Claude write an explainer emphasizing the points that I latched onto the most.

Between the process of generating the explainer and my editing of the post, this is a centaur (half-man, half-machine) article that helps you move frontwards and backwards between the concepts of simple multiplication, variance and expectation. A bonus of this approach is that you internalize volatility drag and Jensen’s Inequality by accident.

Variance Is Just A Difference Of Squares

There’s a piece of grade-school arithmetic everyone has done:

The difference of squares. You probably learned it as a parlor trick for multiplying numbers that sit symmetrically around a round number.

47 × 53?

That’s 50² − 9 = 2,491.

98 × 102? 100² − 4 = 9,996.

It turns out this same identity is the variance formula.

Once you see the connection, it makes one of the most important identities in probability feel obvious instead of memorized.

This post walks through the connection slowly, builds the variance identity from first principles, and ends with a clean drill set you can come back to.

The interview problem that started it

I flip a fair coin 100 times. What is the expected value of (number of heads) × (number of tails)?

The naive answer is 50 × 50 = 2,500. Heads and tails each average 50, so just multiply.

The naive answer is wrong. The right answer is 2,475. Off by 25.

Where does the 25 come from? It’s the variance of the number of heads. What is going on?

Setting up

Let H be the number of heads, T the number of tails. Every flip is one or the other, so:

H and T are not independent. They are perfectly negatively correlated.

Once you know H, T is fully determined.

So we can rewrite the product:

Take the expectation of both sides.

Expectation is linear, so it distributes over the subtraction and the constant 100 pulls out:

E[H] is easy. 100 fair flips, expected heads is 50. So 100 · E[H] = 5,000.

The interesting term is E[H²].

The trap: E[X²] is not (E[X])²

Squaring and averaging do not commute. Square first then average gives a different number than average first then square. Always.

Tiny example. X is either 0 or 100, each with probability ½.

• E[X] = 50, so (E[X])² = 2,500

• E[X²]: square the outcomes first (0 and 10,000), then average. That’s 5,000.

Different answers. 5,000 vs 2,500.

Squaring punishes deviations asymmetrically.

Going from 50 to 100 adds 50 to the input but adds 7,500 to the square. Going from 50 to 0 subtracts 50 from the input but only subtracts 2,500 from the square. The high side balloons faster than the low side shrinks. When you average the squared values, the ballooning wins.

This gap between E[X²] and (E[X])² has a name. It’s the variance.

In words: variance is the average of the squares minus the square of the average.

Where the formula comes from

The standard definition of variance is the average squared distance from the mean:

Expand the square:

Take the expectation of each term but keep in mind that μ = E[X] and μ is a constant, not a random variable. We computed it once and froze it. Constants pull out of E[·] freely.

Now substitute μ = E[X] everywhere it appears:

The two E[X]² terms collapse from −2 + 1 = −1. Done.

Two lessons from the derivation:

1. Whenever you see E, just think average. Probability-weighted, but average.

2. The mean is a number, not a random variable. Once you take E[X], the result is frozen.

Closing out the coin problem

Back to the interview question. We have:

Use the identity:

What’s Var(H)?

H is the sum of heads from 100 independent flips.

The variance of one flip is 0.25

Why?

• 2 equally likely outcomes of 0 and 1, so the mean is .5

• deviations from the mean are .5, therefore the squared deviation is .25

Variances of independent flips add, so:

Therefore:

The answer falls short of the naive 2,500 by exactly Var(H)!

The product H · T peaks when H = 50 and pays a penalty whenever H drifts away from the mean (think of the extreme where H = 1, H · T = 99, meanwhile when H=50, H · T = 2500)

Averaged over the distribution of H, that penalty is exactly the variance. In investing contexts, that penalty on the expectation is volatility drag.

Numerical drills

Computing variances

Drill 1 — Two-outcome warmup

X is 0 or 10, each with probability ½.

• E[X] = 5

• (E[X])² = 25

• E[X²] = average of 0 and 100 = 50

• Var(X) = 50 − 25 = 25

Sanity check: deviations are ±5, squared deviations are both 25, average is 25. ✓

Drill 2 — Uniform on three values

X is uniform on {1, 2, 3}.

• E[X] = 2

• (E[X])² = 4

• E[X²] = (1 + 4 + 9) / 3 = 14/3 ≈ 4.67

• Var(X) = 14/3 − 4 = 2/3

Drill 3 — Asymmetric (lottery ticket)

X is 0 with probability 0.8, 10 with probability 0.2.

• E[X] = 2

• (E[X])² = 4

• E[X²] = 0 · 0.8 + 100 · 0.2 = 20

• Var(X) = 20 − 4 = 16

Standard deviation is 4 — bigger than the mean. Signature of a skewed payoff. Lottery tickets, insurance claims, venture returns all look like this.

Drill 4 — Single die roll

X is uniform on {1, 2, 3, 4, 5, 6}.

• E[X] = 3.5

• (E[X])² = 12.25

• E[X²] = (1 + 4 + 9 + 16 + 25 + 36) / 6 = 91/6 ≈ 15.17

• Var(X) ≈ 15.17 − 12.25 = 2.92

Computing E[X²]

Drill 5 — Going backwards

This is the direction you’ll actually use most often, because in practice you usually know the mean and variance of something and you need E[X²] to compute something else (a covariance, a portfolio variance, the second moment of a return distribution).

If E[X] = 6 and Var(X) = 9, then E[X²] = 36 + 9 = 45.

If E[X] = 0.10 and Var(X) = 0.04 (a stock with 10% expected return and 20% vol), then E[X²] = 0.01 + 0.04 = 0.05.

Drill 6 — Locked-together products

The original problem in disguise. X has E[X] = 10 and Var(X) = 4. Y = 20 − X.

• 20 · E[X] = 200

• E[X²] = 100 + 4 = 104

• E[X · Y] = 200 − 104 = 96

Naive answer (treating X and Y as independent): 10 × 10 = 100. Real answer is 96. Gap is 4, which is Var(X). Same pattern as the coin problem.

The connection to 43 × 37

We can link this to multiplication as I have shown before in how I explained vol drag to a 12-year-old.

Imagine a “random variable” with two outcomes: 43 with probability ½, and 37 with probability ½.

• Mean: 40

• Deviations from mean: +3 and −3

• Squared deviations: 9 and 9

• Variance: 9 (it’s the average of 9 and 9, which is just 9)

What’s the product of the two outcomes?

43 × 37 = 1,591.

And what does the difference-of-squares identity say it is?

The product equals mean² − variance.

Same shape as the coin problem, where the answer was 50² − 25 = 2,475.

[Note: The difference-of-squares identity gives you mean² − deviation². The variance identity gives you mean² − variance. They’re the same equation when your random variable has only two outcomes that are equidistant from the mean, because in that special case variance is the squared deviation. There’s only one squared deviation to average, so the average is itself.

For a more spread-out random variable like H (which can be 0, 1, 2, ..., 100), variance is still “average squared deviation from the mean” — it just averages over many outcomes instead of being a single squared distance.

The product of any two numbers is mean² − deviation²:

• 47 × 53 = 50² − 9 = 2,491

• 98 × 102 = 100² − 4 = 9,996

• 17 × 23 = 20² − 9 = 391

• 195 × 205 = 200² − 25 = 39,975

The grade-school arithmetic trick is a special case of variance.

Revisit Jensen

This explainer will make more sense now:

Jensen’s Inequality As An Intuition Tool

What to keep from this explainer

Three things, in order of importance.

E[X²] = (E[X])² + Var(X). Average of squares equals square of average plus the spread. E[X²] is always the bigger one. The gap is the variance.

Whenever you see E, think average. Probability-weighted average of whatever’s inside the brackets. Linearity makes E distribute over sums freely. Constants pull out. The mean of a random variable is itself just a number once you’ve computed it.

Locked-together products lose the variance. Anytime two things sum to a constant (H + T = 100, X + Y = 20), the expected product equals the product of the means minus the variance. The product peaks at the mean and pays a penalty for spread. That penalty, averaged over the distribution, is exactly Var.

A coda: covariance is just variance with two variables

There’s one more layer here, because it gives a clean name to the phenomenon driving the whole interview question.

We said the expected product H · T comes up short of the naive 2,500 by exactly Var(H) = 25. Why?

Because H and T move opposite to each other. When H is above its mean, T is below. They’re locked together by H + T = 100.

The quantity that measures this kind of co-movement is covariance:

The average of the product of deviations. Think about the sign of that product on a typical outcome:

• X and Y both above their means → positive × positive = positive

• X and Y both below their means → negative × negative = positive

• X above, Y below (or vice versa) → positive × negative = negative

• X and Y unrelated → product is sometimes positive, sometimes negative, averages to zero

So covariance is positive when they move together, negative when they move opposite, zero when they’re unrelated.

The computational identity

Apply the same FOIL-and-take-expectations trick we used for variance. Multiply out:

Take expectations term by term, remembering that μ_X and μ_Y are constants and pull out of E freely:

Substitute μ_X = E[X] and μ_Y = E[Y]:

Three copies of E[X]E[Y] with coefficients −1, −1, +1 collapse to a single −E[X]E[Y]:

Same shape as the variance identity:

Average of the product minus the product of the averages.

And if you set Y = X, this collapses back to Var(X). Covariance of a variable with itself is its variance:

Variance is the special case. Covariance is the bigger object.

Diagnosing the missing 25

Rearrange the covariance identity:

The naive answer to the interview question assumed Cov(H, T) = 0. Plugging in what we actually know:

So Cov(H, T) = −25.

The missing 25 was negative covariance.

That’s not just numerically equal to −Var(H). It is −Var(H), and it has to be, by the structure of the problem.

Why Cov(H, T) = −Var(H)

Let’s prove it directly.

We need one new property of covariance: it’s linear in each argument. Constants pull out, and sums split apart. Same as expectation.

Specifically:

Cov(X, A + B) = Cov(X, A) + Cov(X, B)

You can prove this in two lines from the identity we just derived (FOIL the product, use linearity of E).

We also need one tiny fact: covariance with a constant is zero.

Look at the definition. If Y is a constant c, then (Y − μ_Y) = 0 always, because a constant equals its own mean. Zero times anything is zero. Constants don’t co-vary with anything, because they don’t vary at all.

Now the calculation.

T = 100 − H. Treat that as a sum: the constant 100 plus the random variable −H.

Split the sum:

The first term is Cov of a random variable with the constant 100, which is zero. For the second term, pull the −1 out the same way you’d pull a constant out of expectation:

But Cov(H, H) = Var(H).

So:

There it is:

Whenever two variables sum to a constant, their covariance equals the negative of either’s variance!

The H + T = 100 constraint forces them to move one-for-one in opposite directions, which is the most negative covariance the structure can produce.

The whole problem in one sentence

The answer falls short of E[H] · E[T] by exactly Var(H), because Cov(H, T) = −Var(H) when H and T sum to a constant.

Today we got ETFs, a volatility observation, and math.

Income ETFs

Off the back of my review of the ISBG and ISSB, Marcos from ETF Academy, invited me for a chat on income-based ETFs which are all the rage. People love yield. I got opinions. This one is a mix of spice and nutrition. Bon apetit.

Appreciating what high volatility means

SNDK is up ~40x in a year. The vol has justifiably exploded. If you want to bet on it halving by December (ie up 20x from where it was a year ago), the put spreads offer only about 2-1 odds.

When you are 100 vol, getting cut in half is a 1 in 3 proposition.

The ricochet thought that should occur to you:

It is tough to make money in a reasonable risk-adjusted way once an asset is already high vol since it’s hard to size it without risking your neck. After all, it is well within the meat of the distribution for SNDK to get cut in half this year. That’s just a good baseball player’s chance of getting a hit or a typical NBA player hitting a 3 in a game (or missing a 3 in practice).

Math

If you ask Grok for threads about Jane Street interviews, a lot of people are sharing their war stories, but it’s also turned into a hilarious copypasta art form (example).

The genre led me to this game. It’s tongue-in-cheek but has real questions too.

I got an interview question wrong, which in itself isn’t bothersome, as they are designed to trip up smarter people than me. But the one I got wrong is in the realm of questions I should get right, which I do find compulsively bothersome.

I looked at the answer, but I know looking at answers doesn’t mean you necessarily learned. I wasn’t confident I could reproduce the answer or the answer to questions in a similar vein with twists.

So, I prompted Claude to teach me to answer it, but in a Socratic way. Then, for 2 days as I was drinking the morning coffee, I would rederive the identities and restate the meanings of the identities in words. Finally, do a couple of practice problems (like the dice version further below).

After 2 days, I felt like I got the idea, so I’ll continue on to a related topic, but I wanted to consolidate what I learned. I regurgitated my pen-and-paper effort to Claude to validate my work. Then, based on how I internalized this, I had Claude write an explainer emphasizing the points that I latched onto the most.

Between the process of generating the explainer and my editing of the post, this is a centaur (half-man, half-machine) article that helps you move frontwards and backwards between the concepts of simple multiplication, variance and expectation. A bonus of this approach is that you internalize volatility drag and Jensen’s Inequality by accident.

Variance Is Just A Difference Of Squares

There’s a piece of grade-school arithmetic everyone has done:

The difference of squares. You probably learned it as a parlor trick for multiplying numbers that sit symmetrically around a round number.

47 × 53?

That’s 50² − 9 = 2,491.

98 × 102? 100² − 4 = 9,996.

It turns out this same identity is the variance formula.

Once you see the connection, it makes one of the most important identities in probability feel obvious instead of memorized.

This post walks through the connection slowly, builds the variance identity from first principles, and ends with a clean drill set you can come back to.

The interview problem that started it

I flip a fair coin 100 times. What is the expected value of (number of heads) × (number of tails)?

The naive answer is 50 × 50 = 2,500. Heads and tails each average 50, so just multiply.

The naive answer is wrong. The right answer is 2,475. Off by 25.

Where does the 25 come from? It’s the variance of the number of heads. What is going on?

Setting up

Let H be the number of heads, T the number of tails. Every flip is one or the other, so:

H and T are not independent. They are perfectly negatively correlated.

Once you know H, T is fully determined.

So we can rewrite the product:

Take the expectation of both sides.

Expectation is linear, so it distributes over the subtraction and the constant 100 pulls out:

E[H] is easy. 100 fair flips, expected heads is 50. So 100 · E[H] = 5,000.

The interesting term is E[H²].

The trap: E[X²] is not (E[X])²

Squaring and averaging do not commute. Square first then average gives a different number than average first then square. Always.

Tiny example. X is either 0 or 100, each with probability ½.

• E[X] = 50, so (E[X])² = 2,500

• E[X²]: square the outcomes first (0 and 10,000), then average. That’s 5,000.

Different answers. 5,000 vs 2,500.

Squaring punishes deviations asymmetrically.

Going from 50 to 100 adds 50 to the input but adds 7,500 to the square. Going from 50 to 0 subtracts 50 from the input but only subtracts 2,500 from the square. The high side balloons faster than the low side shrinks. When you average the squared values, the ballooning wins.

This gap between E[X²] and (E[X])² has a name. It’s the variance.

In words: variance is the average of the squares minus the square of the average.

Where the formula comes from

The standard definition of variance is the average squared distance from the mean:

Expand the square:

Take the expectation of each term but keep in mind that μ = E[X] and μ is a constant, not a random variable. We computed it once and froze it. Constants pull out of E[·] freely.

Now substitute μ = E[X] everywhere it appears:

The two E[X]² terms collapse from −2 + 1 = −1. Done.

Two lessons from the derivation:

1. Whenever you see E, just think average. Probability-weighted, but average.

2. The mean is a number, not a random variable. Once you take E[X], the result is frozen.

Closing out the coin problem

Back to the interview question. We have:

Use the identity:

What’s Var(H)?

H is the sum of heads from 100 independent flips.

The variance of one flip is 0.25

Why?

• 2 equally likely outcomes of 0 and 1, so the mean is .5

• deviations from the mean are .5, therefore the squared deviation is .25

Variances of independent flips add, so:

Therefore:

The answer falls short of the naive 2,500 by exactly Var(H)!

The product H · T peaks when H = 50 and pays a penalty whenever H drifts away from the mean (think of the extreme where H = 1, H · T = 99, meanwhile when H=50, H · T = 2500)

Averaged over the distribution of H, that penalty is exactly the variance. In investing contexts, that penalty on the expectation is volatility drag.

Numerical drills

Computing variances

Drill 1 — Two-outcome warmup

X is 0 or 10, each with probability ½.

• E[X] = 5

• (E[X])² = 25

• E[X²] = average of 0 and 100 = 50

• Var(X) = 50 − 25 = 25

Sanity check: deviations are ±5, squared deviations are both 25, average is 25. ✓

Drill 2 — Uniform on three values

X is uniform on {1, 2, 3}.

• E[X] = 2

• (E[X])² = 4

• E[X²] = (1 + 4 + 9) / 3 = 14/3 ≈ 4.67

• Var(X) = 14/3 − 4 = 2/3

Drill 3 — Asymmetric (lottery ticket)

X is 0 with probability 0.8, 10 with probability 0.2.

• E[X] = 2

• (E[X])² = 4

• E[X²] = 0 · 0.8 + 100 · 0.2 = 20

• Var(X) = 20 − 4 = 16

Standard deviation is 4 — bigger than the mean. Signature of a skewed payoff. Lottery tickets, insurance claims, venture returns all look like this.

Drill 4 — Single die roll

X is uniform on {1, 2, 3, 4, 5, 6}.

• E[X] = 3.5

• (E[X])² = 12.25

• E[X²] = (1 + 4 + 9 + 16 + 25 + 36) / 6 = 91/6 ≈ 15.17

• Var(X) ≈ 15.17 − 12.25 = 2.92

Computing E[X²]

Drill 5 — Going backwards

This is the direction you’ll actually use most often, because in practice you usually know the mean and variance of something and you need E[X²] to compute something else (a covariance, a portfolio variance, the second moment of a return distribution).

If E[X] = 6 and Var(X) = 9, then E[X²] = 36 + 9 = 45.

If E[X] = 0.10 and Var(X) = 0.04 (a stock with 10% expected return and 20% vol), then E[X²] = 0.01 + 0.04 = 0.05.

Drill 6 — Locked-together products

The original problem in disguise. X has E[X] = 10 and Var(X) = 4. Y = 20 − X.

• 20 · E[X] = 200

• E[X²] = 100 + 4 = 104

• E[X · Y] = 200 − 104 = 96

Naive answer (treating X and Y as independent): 10 × 10 = 100. Real answer is 96. Gap is 4, which is Var(X). Same pattern as the coin problem.

The connection to 43 × 37

We can link this to multiplication as I have shown before in how I explained vol drag to a 12-year-old.

Imagine a “random variable” with two outcomes: 43 with probability ½, and 37 with probability ½.

• Mean: 40

• Deviations from mean: +3 and −3

• Squared deviations: 9 and 9

• Variance: 9 (it’s the average of 9 and 9, which is just 9)

What’s the product of the two outcomes?

43 × 37 = 1,591.

And what does the difference-of-squares identity say it is?

The product equals mean² − variance.

Same shape as the coin problem, where the answer was 50² − 25 = 2,475.

[Note: The difference-of-squares identity gives you mean² − deviation². The variance identity gives you mean² − variance. They’re the same equation when your random variable has only two outcomes that are equidistant from the mean, because in that special case variance is the squared deviation. There’s only one squared deviation to average, so the average is itself.

For a more spread-out random variable like H (which can be 0, 1, 2, ..., 100), variance is still “average squared deviation from the mean” — it just averages over many outcomes instead of being a single squared distance.

The product of any two numbers is mean² − deviation²:

• 47 × 53 = 50² − 9 = 2,491

• 98 × 102 = 100² − 4 = 9,996

• 17 × 23 = 20² − 9 = 391

• 195 × 205 = 200² − 25 = 39,975

The grade-school arithmetic trick is a special case of variance.

Revisit Jensen

This explainer will make more sense now:

Jensen’s Inequality As An Intuition Tool

What to keep from this explainer

Three things, in order of importance.

E[X²] = (E[X])² + Var(X). Average of squares equals square of average plus the spread. E[X²] is always the bigger one. The gap is the variance.

Whenever you see E, think average. Probability-weighted average of whatever’s inside the brackets. Linearity makes E distribute over sums freely. Constants pull out. The mean of a random variable is itself just a number once you’ve computed it.

Locked-together products lose the variance. Anytime two things sum to a constant (H + T = 100, X + Y = 20), the expected product equals the product of the means minus the variance. The product peaks at the mean and pays a penalty for spread. That penalty, averaged over the distribution, is exactly Var.

A coda: covariance is just variance with two variables

There’s one more layer here, because it gives a clean name to the phenomenon driving the whole interview question.

We said the expected product H · T comes up short of the naive 2,500 by exactly Var(H) = 25. Why?

Because H and T move opposite to each other. When H is above its mean, T is below. They’re locked together by H + T = 100.

The quantity that measures this kind of co-movement is covariance:

The average of the product of deviations. Think about the sign of that product on a typical outcome:

• X and Y both above their means → positive × positive = positive

• X and Y both below their means → negative × negative = positive

• X above, Y below (or vice versa) → positive × negative = negative

• X and Y unrelated → product is sometimes positive, sometimes negative, averages to zero

So covariance is positive when they move together, negative when they move opposite, zero when they’re unrelated.

The computational identity

Apply the same FOIL-and-take-expectations trick we used for variance. Multiply out:

Take expectations term by term, remembering that μ_X and μ_Y are constants and pull out of E freely:

Substitute μ_X = E[X] and μ_Y = E[Y]:

Three copies of E[X]E[Y] with coefficients −1, −1, +1 collapse to a single −E[X]E[Y]:

Same shape as the variance identity:

Average of the product minus the product of the averages.

And if you set Y = X, this collapses back to Var(X). Covariance of a variable with itself is its variance:

Variance is the special case. Covariance is the bigger object.

Diagnosing the missing 25

Rearrange the covariance identity:

The naive answer to the interview question assumed Cov(H, T) = 0. Plugging in what we actually know:

So Cov(H, T) = −25.

The missing 25 was negative covariance.

That’s not just numerically equal to −Var(H). It is −Var(H), and it has to be, by the structure of the problem.

Why Cov(H, T) = −Var(H)

Let’s prove it directly.

We need one new property of covariance: it’s linear in each argument. Constants pull out, and sums split apart. Same as expectation.

Specifically:

Cov(X, A + B) = Cov(X, A) + Cov(X, B)

You can prove this in two lines from the identity we just derived (FOIL the product, use linearity of E).

We also need one tiny fact: covariance with a constant is zero.

Look at the definition. If Y is a constant c, then (Y − μ_Y) = 0 always, because a constant equals its own mean. Zero times anything is zero. Constants don’t co-vary with anything, because they don’t vary at all.

Now the calculation.

T = 100 − H. Treat that as a sum: the constant 100 plus the random variable −H.

Split the sum:

The first term is Cov of a random variable with the constant 100, which is zero. For the second term, pull the −1 out the same way you’d pull a constant out of expectation:

But Cov(H, H) = Var(H).

So:

There it is:

Whenever two variables sum to a constant, their covariance equals the negative of either’s variance!

The H + T = 100 constraint forces them to move one-for-one in opposite directions, which is the most negative covariance the structure can produce.

The whole problem in one sentence

The answer falls short of E[H] · E[T] by exactly Var(H), because Cov(H, T) = −Var(H) when H and T sum to a constant.

Stay groovy

☮️

• smart vs wise

• adverse selection when landing a senior role

• cost of carry as a conviction hurdle

• KenKen

Friends,

Happy Mother’s Day!

It’s a nice day for an enjoyable read. I loved this post from Adam Mastroianni:

Infinite Midwit | 12 min read

The essay is insightful and typical of Adam. It’s just so fun to read. Which is itself an exhibit of his thesis.

I stitched together these excerpts, but I encourage a full reading.

The opening

The better AI has gotten, the less anxious I’ve become.

A few years ago, when the computers first started talking, it was reasonable to believe that we would soon be in the presence of omnipotent machines. For someone like me, whose job is to produce words on the internet, it seemed like only a matter of time before I would have to fill my pockets with stones and wade into the sea.

Two intelligences

Some problems have clear boundaries and verifiable solutions, like “What’s the cube root of 38,126?”. These problems require objective intelligence. Other problems are vague and squishy and it’s not clear whether you’ve solved them, or whether they exist at all, like “How do I live a good life?”. These problems require subjective intelligence. Objective intelligence can be trained, reinforced, and validated. Subjective intelligence cannot.

[Kris: smart vs wise]

It’s unfortunate that people use one word to refer to both of these capabilities, when in fact they have nothing to do with each other. It is also, ironically, a case of objective intelligence overshadowing subjective intelligence: these skills are obviously and intuitively different, but a century of psychological research has “proven” that only one of them exists. Over and over again, psychologists have found that all intelligence tests correlate with one another, even when you ostensibly try to test for “multiple intelligences”. Numbers don’t lie, and they all say that there’s only one intelligence, the so-called g-factor.

The problem is that any test of intelligence is only ever a test of objective intelligence. “How do I live a good life?” is not a multiple-choice question. “Discovering” the g-factor again and again is like being surprised that you find the same patch of sidewalk every time you look under the same streetlight.

The Catan fantasy

The promise of artificial superintelligence is based on the idea that objective intelligence is the only intelligence. Or, even if there are multiple forms of intelligence out there, that they are fungible. To be an AI maximalist is to believe we are playing under Settlers of Catan rules, where if you have enough of any one resource, you can trade it for any other resource. If you have infinite objective intelligence, then you have infinite everything.

It’s not just that objective intelligence can’t be transmuted into “emotional” intelligence or social savvy or whatever we want to call it. It appears to be very difficult, if not impossible, to transmute objective intelligence into any other cognitive ability.

When you meet a human who can do quadratic equations in their head but can’t hold onto a job or a relationship, you know they’re missing something upstairs.

Nerds

When I was growing up, this paradox was an endless source of sitcom plot lines—if you’re so smart, nerds, why don’t you figure out how to make yourselves popular? The entrepreneur/essayist Paul Graham took up this question 20 years ago and came to the conclusion that the nerds must not want to be popular. They’re too busy with their Neal Stephenson novels and their D&D campaigns to spend a single brain cycle figuring out how to keep their heads out of the toilet.

I disagree. The nerds I knew in high school—myself included—were always hatching harebrained schemes to increase our social status. They just didn’t work. (”All the girls will want to go to the Homecoming dance with me once they see how many state capitals I’ve memorized!”) We couldn’t use our smarts to make ourselves popular because we had the wrong kind of smarts.

For example, I went to college with a guy who was super smart, but he also couldn’t do anything on time. He would be late to exams. His grades would tank because he would finish his essays but forget to turn them in. He would set meetings with his professors to sort everything out, and then never show up.

I always used to wonder: why doesn’t this guy just use his big brain to make himself more conscientious? Isn’t life one big role-playing game, and isn’t intelligence just experience points that you can assign to any of your Big 5 skills?

Why AI writing vaguely sucks

It’s cool that AI can fold proteins, create websites, fact-check journal articles, etc. but it can’t write anything that I am interested in reading. The problem isn’t that it hallucinates or makes mistakes. It’s that everything it writes vaguely sucks. I drag my eyes across the words and I feel nothing. That’s not quite right, actually—I feel like, “I would like this to be over as soon as possible.” …

Words themselves don’t contain feelings—they are a recipe for creating that feeling inside your own head, to assemble the right set of emotions out of the experiences you have at hand. If I do a good job, the subjective experience that results inside you might resemble the one that originated inside me, but it will never be identical, because we’re working with different ingredients.

The computer doesn’t know any of this. It can’t know any of this. It can only read the cookbook; it can’t taste the meal. Objective knowledge can make your sentences true, but it can’t make them alive. Without access to subjective knowledge, you quickly hit a wall. And unlike all previous walls that AI has surmounted, you can’t overcome this one by scaling—either in the literal or metaphorical sense—because it’s a wall with a width you cannot describe and a height you cannot see.

Money Angle

I unlocked this older post, which found a lot of agreement from senior professionals who have transitioned from a pure trading job to building a business or strategy for asset managers. The target audience is seasoned practitioners. It’s written specifically for option traders but the feedback is that its warnings extend well beyond that market.

We know that there is adverse selection when hiring but this is about avoiding a lemon when getting hired.

Enjoy:

Money Angle for Masochists

Brent and Alf have a regular macro podcast. This episode from late 2025 has a number of evergreen trading concepts.

On carry costs

Alf: In our fund, we’ve recently added an alert before you put a trade on. It looks at how much it’s going to cost you to own this position in a relatively vol-adjusted way if nothing happens for the next 30 days. It’s essentially like some sort of carry-to-vol screener.

[Kris: notice how naturally this forces a “thinking in bets” discipline on your opinions]

“Am I really sure this is going to happen or not?”

A Hungarian Forint Example

We had this example where we had all this theory on Hungary. We looked at Hungarian forint and said, “Okay, Orbán is going to go nuts, win the elections, spend money, and the market will punish the Hungarian forint.” Sure, you can be right. You can be wrong.

So how do you trade this? Well, you buy the euro and sell the Hungarian forint. You do the trade, then you look at the carry differential between the two currencies. It’s about 4% yearly carry differential in the forwards. That comes down linearly to about 30 basis points a month.

You think: “30 bips? That’s nothing. I can pay 30 bips in a month. No problem.”

But then you look at the monthly volatility of this thing. It basically doesn’t move. So at some point you realize: the static ex-ante Sharpe ratio of this thing for the next month is like -0.6 Sharpe against me. Holy crap. I need to be not only right—I need to be right with a high Sharpe ratio just to start offsetting the negative carry adjusted for volatility in this trade.

Analogizing to options where the costs are framed more explicitly

A lot of trades are very expensive to own. With options, I think sometimes you fool yourself because you pay for the vol once, and then you say, “Okay, I paid for the vol. That’s what it is. Now I can go long, and this thing can drop to zero, but I did pay for the vol.”

But if you buy 50 options in a year, you pay for the vol 50 times. In options, people do it very lightly but in linear trades, people don’t sometimes think about this, but I think it’s important.

[Kris: I’d broaden this discussion to be a reminder that the cost of carry in addition to opportunity cost is hurdle that your conviction must clear. If it’s not explicit in your in your process consider making it so]

Extending to Hard-to-Borrow Stocks

Brent: It’s a different but similar situation where normally you’re dealing with a very high-vol instrument, but you’re paying a crazy amount of money to borrow the stock.

There’s quite a bit of research showing that hard-to-borrow stocks do tend to go down—they’re hard to borrow for a reason. Someone knows a secondary is coming, or it’s a really bad company. There’s usually a reason why it’s hard to borrow and why everyone’s short.

But functionally, the cost to borrow negates the negative return of the stock almost perfectly in aggregate. If you short all the hard-to-borrow stocks, you’ll make money on the shorts and lose about exactly the same amount on the borrow.

A CoreWeave Example

Take CoreWeave—there’s no borrow right now, but there has been off and on, and the borrow was like 150%. Even if you catch a pretty decent move, if you’re not catching it instantaneously, you’re probably not making money.

One simple thing I’ve been doing: when there is a borrow, just selling it at 9:30 AM and buying it back at 4:00 PM. You actually made more money being short that way than holding it—not even counting the borrow—because CoreWeave has a little bit of positive drift in the overnight session.

Extending to currency roll costs

Even buying EUR/GBP today, I bought some at 0.8573 and rolled it to September 17th. It was 17 pips to roll it. For six weeks on a currency that’s moving 20-30 pips a day, you’re paying 17 pips of roll. That’s not very fun.

Spurious Correlations: When Copper Takes Down Silver

Here’s something huge: spurious correlations. Copper tariffs were actually removed. All of a sudden there are no tariffs on copper, and copper goes down like 30% in two days.

Then, do you know what happens to any other high-beta metal? Doesn’t matter what it is—palladium, silver, you name it—goes down 3-4-5 percent. It’s just cascading risk and basically some exogenous event hitting you, not even directly, but laterally, and you lose money.

The Sympathy Trade Strategy

Brent: Generally, I feel like there’s a lot of good trades like that. Being short silver when copper collapses—but these sympathy trades tend to be very short-lived.

For me, it’s always like: if you’re looking at AppLovin and The Trade Desk, they’re similar companies. When AppLovin craters 50 bucks on earnings, you can sometimes sell The Trade Desk and make four bucks in 20 hours.

But like you said, there’s really no economic reason for the correlations a lot of the time. Sometimes with earnings there is, but with copper and silver, it’s just that a lot of the same people who have that sort of inflation and debasement trade are long copper, long silver, long gold, long Bitcoin. When one part of the portfolio gets a nuclear bomb, they’re forced to liquidate the other stuff.

I do those trades as sympathy trades, but I go in knowing: most of the time, there’s no economic sense to this. It’s more of an endogenous unwind story. So you got to be quick.

This Week In The Options Trench

Erik has a soft spot for GME so in light of Ryan Cohen’s bid for eBay, we talk about GME options. A fun thing about this casual weekly podcast format is, while we have a loose calendar of discussion topics, we might just talk about whatever grabs our attention. This week was one of those.

📺GameStop and eBay Acquisition What the Options Markets Say

From My Actual Life

My 4th grader loves the KenKen puzzles his teacher gives. KenKen is a Sudoku-style puzzle invented in the early 2000s.

In this 4x4, grid each row and column must contain each of the digits 1,2,3,4.

The digits in the bold cages must satisfy the arithmetic operation in the cage’s upper left. For example, in the cage with “5+”, the only valid combinations are (4,1) and (3,2).

In this example, I know the bottom right corner must be a 2 because the 7+ cage must include (3,4). 2 is the missing number in the column.

We got the kid a KenKen book for his birthday and my mother saw it while visiting and got addicted herself so we sent her a copy as well.

The puzzles can range from easy to hard and they can have larger grids (ie 6x6 or 7x7). My son likes to make them as well. At first, that sounded difficult but brain fart. I asked him how he did it and he said he just fills out the grid so the row/column rules are satisfied and then you simply cherry-pick your cages and display the operation and target that makes the cage work.

Again Happy Mother’s Day, may the simple pleasures pamper.

Stay groovy

☮️

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If you reside in the quark-sized intersection of people who read this letter but don’t follow the market, I’m informing you that shares of corporations are up sharply in the past 5 weeks.

The magnitude and speed of the rally have been “hellacious” to use a mentor’s favorite way to describe the face-ripping bear market rallies. Not that this is a bear market rally. As you know, bears are extinct and all the degeneracy you see is their normal diet flourishing without a natural predator.

Now, about that face-ripper…my turn to cherry-pick. It turns out selling calls that carry a high implied vol but were in the 0th percentile of skew wasn’t really “income”.

The green line is a portfolio of 75% SPY, 25% cash rebalanced monthly which is a more proper comparison to JEPI which sells OTM calls. Rough month for the home team.

If curious here is 75% SPY vs JEPI since it launched:

The rally has people confused. What about the war? What about oil? What the f is happening in this chart:

Read more

Before a few links, here’s a quick, embarrassing story I got reminded of because of this tweet:

A few years ago when my eldest was in 4th grade we were talking about his class number being “2“. Class numbers are assigned alphabetically by last name.

I said oh there must be an “Aaron” or something but my son said no then proceeded to tell us #1’s last name.

When I heard it, I said, “Wow, you have another Egyptian kid in your class”.

Son: “Who’s the other one?”

Wife looks at me: “That’s on you dad”.

Me: 🫠

To be fair, we live in the Bay area, it’s Hapa central where we are. We live near my wife’s family and my Vietnamese MIL has lived with us since the month before my eldest was born. The boys understand Vietnamese and can speak it, although it’s quite broken. In Arabic, they know their numbers and some swear words, but that’s it.

We have taken them to both Vietnam and Egypt in back-to-back years which helped them relate to their very different heritages a bit better. Looks-wise, my eldest looks Asian but with big eyebrows and a mustache that’s more than a few strays. He could style his hair in a spiky Street Fighter way if he wanted (although today having these fluffy mops appears to be the trend and he’s taking his hair powder game seriously).

The younger one just looks Mexican. No Asian features, darker skin, and hair that resists straightening.

Growing up, I wanted to blend in with “the American kids”. I hid my ethnicity because it only served as insult fodder. The culture supplied kids with stereotypes. The WWF had a bad guy known as the Iron Sheik and a black guy who was supposed to be a bum called “Bad News Brown”. Spoiler alert: the audience did not root for him either.

(If you browse X today, you're quite likely to encounter entire online personas that are basically racism or anti-semitism as a service. Both the far right and left get to make Elon bucks from their phone.)

My own relationship to ethnicity is a bit weird and possibly insulting to general sentiment (that’s a conversation for another day), but I don’t let any of that leak to my kids. We can show them what we can of the world, which is quite limited in the grand scheme, encourage curiosity, and generally demonstrate our reasoning in all things and let that be the nest from which they will incubate their own views.

Links

Legibility: When insider trading becomes a national security issue | 7 min read

Andrew Courtney on prediction markets and the double-edged nature of price legibility. The story starts with the US soldier who traded on plans to attack Maduro, risking ~$33k for $400k+ in profit. In financial terms, the money is small but it leaks critical information.

The nature of this information is that it is highly “legible” which is very different from the information prices generate in traditional capital markets.

Stocks have low legibility in that we cannot easily map price changes to their cause. The ”more buyers than sellers” sounds like a snarky response to “why did the market go up?” but it’s most truthful. Andrew says options have medium legibility and prediction markets have high legibility since the claims are so specific. Oil markets allow you to bet on “US attacks Iran” indirectly since a long oil position encompasses a bundle of views, but “US attacks Iran” contracts on prediction markets are, well, targeted bets.

Here’s Matt Levine on a recent episode of the Money Stuff podcast (emphasis mine):

Apparently somewhere within Charles de Gaulle Airport in Paris, there’s a sensor that gives you the temperature for Paris. And Polymarket takes quite a lot of bets on the weather in Paris. At two points this month, the reported temperature in Paris — by which I mean the temperature at this one sensor in the airport — spiked by four or five degrees Celsius in the space of a few minutes, causing very long-shot bets on this temperature to pay off to the tune of tens of thousands of dollars. The French meteorological service is investigating, and their tweets are basically: someone took a hair dryer to Charles de Gaulle and made thousands of dollars trading these weather derivatives…

There’s market manipulation in the world, right? There’s some underlying stuff trading, and there are derivatives on the underlying stuff, and people can manipulate the stuff to cause the derivatives to go up. I’ve written about dozens of cases over the years. But what prediction markets have done is create a sort of infinite surface for market manipulation. Anything you can think of, there can be a prediction market on it, and the outcome of anything you can think of might be manipulable.

[Kris: this part echoes Andrew’s legibility argument]

If you’re buying grain futures, the weather in the Midwestern United States is an input to the price of those grain futures — but a liter of air in the Midwestern United States is not a material input. But if you’re buying the Polymarket bet on the weather in Paris contract, one tiny little spot causes the bets to pay off or not. There’s always going to be market manipulation, but prediction markets have created this vast new possibility of things to manipulate.

Andrew’s post also talks about a new manipulation vector he calls a “tail wags the dog attack”:

The liquidity in “Will US attack Iran” is tiny vs that of oil futures or equities. If traders in traditional finance see prediction market prices as a good information source… a bad actor could first put on a position in oil futures, then buy up a huge amount of a geopolitical contract that has an effect on oil prices. But there’s no attack and no inside information — it is simply an attempt to convince traders to incorrectly incorporate this legible probability from the thin prediction market into a more liquid security. Oil spikes, they sell their position, having incinerated a few hundred thousand dollars to manipulate the prediction market, and made millions in the futures market.

[Kris: This is a classic manipulation scheme where you exploit the fact that 2 related market signals are given similar weights despite the fact that one is far less liquid than the other. Think of Jane Street trading in India, where sloppy orders in the illiquid underlying basket could be used to get the far more liquid options markets to react or how VIX settlement is alleged to be manipulated. VIX settlement calculation is most sensitive to the price of very low delta puts, so by concentrating orders on those strikes, a MM who wants the index to settle higher for the benefit of a long cash-settled option position can efficiently (ie burn not too much money in negative edge) bid for teeny puts for a much larger option position to profit.]

Andrew sums the problem up simply:

The legibility prediction markets bring to real-world events is their biggest strength compared to traditional financial products like stocks and futures. But this legibility has unique costs.

Trading Infrastructure, Trading Volatility | Byrne Hobart

Just sharing this blurb because it’s a good example of “options in the wild” where a deal isn’t articulated explicitly as an option but economically it is (emphasis mine):

SpaceX is buying an option to acquire Anysphere, maker of AI coding tool Cursor, for $60bn, or to pay them $10bn if they don't. You can rearrange the terms of this equation a little bit and say that SpaceX offered a $10bn note, maturing in a year, in exchange for an option to buy Anysphere, with a $50bn strike price.

The company was valued at $30bn in November. If we guess that their market value is somewhere in between the $30bn at which they last raised and the $60bn at which they agreed to sell (their valuation was rumored to be $50B just last week), you can plug these terms into the Black-Scholes formula and see that the implied volatility for this option is in the low 60s. Which, if you compare that to prices for listed options on public software companies valued in the mid tens of billions, is actually just about market rate.

You can even say the blurb is a good example of “put-call parity in the wild”. Fun stuff.

Stay groovy

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• The “three pitches” rule and a lazy man’s framework for getting in shape

• Things that popped from the Investment Beginnings Lesson #4 — Risk

• Made you an easy online tool to see how much diversification benefit you get from your holdings

Friends,

A couple of good articles that stood out before we get to Money stuff.

How to Apply Pixar’s “Three Pitches” Rule | 3 min read

David Epstein spent a lot of time with Ed Catmull in researching his recent book Inside the Box. He shares a neat practice from Pixar. Directors aren’t allowed to bring one idea, they must develop three. We often fixate on our first idea even though it’s usually not our best (the “creative cliff illusion”). Epstein applied this in writing the new book by writing three different openings for every chapter. Nine of twelve chapters ended up using attempt #2 or #3. He admits this is tedious, but leads to better quality. I’d add that LLMs can ease some of that burden or augment the process by asking them to consider more ideas beyond the 3 you generate yourself.

The Lazy Man’s Guide to Actually Getting in Shape | 60 min read

Jonathan doesn’t publish often these days, but it’s worth subbing; otherwise, you’ll miss a treatise like this. This is 16,000 words, but Jon tells you upfront that you can just read the bolded sentences for a fast version. It’s a moneyball lens on fitness with a decision process that generalizes to any wicked domain, wellness, of course being one of the most wicked. A lot of examples of “think in probabilities”, “make +EV bets with limited downside”, “via negativa”, and toggling confidence when multiple lenses validate an idea (ie personal experience, expert track record, math, what works empirically, science).

Money Angle

This week, I hosted class #4 of the Investment Beginnings for local kids aged 12+.

The series’ materials are here:

https://notion.moontowermeta.com/investment-beginnings-course

This is the specific material for class #4:

• Slides

• Spreadsheet Game (File:duplicate to have your own editable copy)

I also created a web version of the game:

☀️🌧️Sun/Rain Game

While I’ve been doing the series for kids, I think a lot of adults could even benefit. The overall arc of the presentation:

1. Last class’s game ended with a humbling but common result, hinting at a key pillar of investing.

2. We use a few facts to dispel the recency bias that all investors carry with them.

3. They learn what the fundamental nature of stocks predicts about their individual and group behavior.

4. We widen the meaning of diversification beyond stocks, which was extremely easy to do in light of March 2026.

5. We play a game that makes the implications for portfolios concrete.

While moontower readers span a wide range of investment experience (although overall quite interested in investing and money), here are a few ideas that I hope are presented in ways that might augment even your understanding or at least help you explain to learners in your life.

The most naive strategy is hard to beat

The kids spent Class 3 picking stocks based on a bunch of variables they could sift through, only for the equal-weight benchmark to beat everyone except the team that contrarily concentrated in the highest momentum company that is very much still an enigma to the market (TSLA).

The equal-weight strategy which I just called a monkey (although it’s not random, just dumb) beat 2/3 of the 15 individual stocks themselves.

The reason you shouldn’t be surprised that the naive strategy is hard to beat

Companies eventually die, but indexes shed them before they are in hospice.

Only 17% of the original S&P 500 companies from 1957 survived 50 years. The average company lifespan on the index was 33 years in 1964 — it’s now under 20. Kodak invented the digital camera in 1975 and buried it because of the innovator’s dilemma.

In a crash, stocks remember they’re all stocks.

Diversification works differently in good years than bad ones. In the class data, stocks spread widely in bull years. Then we looked at Jan 2022 to Jan 2023: 13 of 15 stocks fell together, the spread collapsed.

I didn’t want to lean into the word correlation, but I noticed a different way to convey the same idea. The inter-quartile range (IQR) of annual returns was smallest in the worst years. This chart is rich with insight. Notice the IQR’s visually but also how the equal-weight portfolio performed relative to the individual stock and median stock returns each year:

These observations are non-CAPM ways to arrive at the familiar language of diversifiable risk (company-specific stuff you can eliminate for free) and systematic risk (market-wide stuff you can’t diversify away but do get paid to carry). The crash revealed which was which.

If we zoom out from stocks alone, we see a race where the leaders change each year

The Novel Investor quilt shows 15 years of annual returns ranked best to worst across 9 asset classes. The diversified portfolio, that gray-ish bar, never wins a year nor comes in last. Note commodities, gold and BTC are absent from the series.

How do you think they would influence the gray portfolio?

The Sun/Rain Game

This leads to a game where we can build some intuition about the role of non-stock assets in a portfolio.

If you look at the sheet you can see how the kids actually did (I changed the kids names to letters):

• Spreadsheet Game

The game’s punchline is that owning the anti-correlated asset despite it having a worse expected return than the “good” asset leads to a better long-term portfolio.

But this is so unintuitive that I got a student’s question wrong during the discussion!

I’ll explain the mistake here.

A student asked if we played the game for 100 years instead of just 20 years, if owning the good asset ONLY would have led to the best return. I initially said no, then corrected myself and said yes because it has the higher expected return.

But I was right the first time. The answer is definitely NO.

It comes down to the fact that the good asset has an expected arithmetic return of +5%, BUT it has a negative expected CAGR or geometric return.

The math:

The company is 50/50 to return+40% or -30% in any given year.

.5 x 40% + .5 x -30% = +5%

But over 2 years, you expect 1 up, 1 down. Compounding math:

1.4 x .7 = 98%

You expect to lose 2% over a 2-year sequence of about 1% per year.

Formally, we compute the expected CAGR by multiplying (note how the arithmetic or single period return is added):

1.4^(1/2) * .7^(1/2) - 1 = .9899 -1 = -1%

[The exponents represent the probability of each outcome. If there were 3 outcomes, you’d have 3 terms and the exponents sum to 1.]

In the long run, the good asset destroys value. So you do not want to concentrate in it despite its superior expected arithmetic return.

The CAGR is being killed by volatility drag, which is the asymmetry of the fact that if you lose 30% you need to return 42.9% to get back to even, but the “up” years only return 40%. You are falling behind over time.

The bad asset returns -10% half the time and +8% half the time. It’s a "worse” asset, but it’s less volatile. Taking this quality to its extreme, isn’t this what cash is?

In arithmetic terms, our average return if we allocate to each asset equally is +2% (50% x 5% + 50% x -1%). But that portfolio is less volatile because one stock zigs when the other zags. The diversification cuts the volatility MORE than it cuts the expected return, leading to a better risk/reward!

If we rebalance each year back to an equal-weight portfolio, we “pull” the expected CAGR closer to the expected arithmetic return. It’s the only way we can get close to eating those expected arithmetic returns. Otherwise, they don’t really exist for you over time.

This table is worth staring at:

Here’s a message one of the dads sent me after the class:

Money Angle for Masochists

I made you a tool to compute your portfolio vol and see how much the cross-correlations between your holdings have been reducing total vol from the vol that the individual assets contain. You can tinker by adding ETFs of other asset classes to your equities (ie GLD or USO or TLT etc) to see how they affect the volatility.

If you just want inspiration for an idea, use the tool to compare the Mag 10 index (MGTN) realized volatility with the average realized volatility of its holdings. The index is conveniently equal-weighted, 10% in each name.

Two ways to try this on your own portfolio:

🌐To run in your browser

https://colab.research.google.com/github/Kris-SF/data-pipelines/blob/main/portfolio-vol/portfolio_analysis.ipynb

⚠️Just push through the warning it spits off

The output will includes metrics and charts:

🖥️To run locally

git clone <https://github.com/Kris-SF/data-pipelines.git>
cd data-pipelines/portfolio-vol
pip install -r requirements.txt
jupyter lab portfolio_analysis.ipynb

Either way, edit the WEIGHTS dict and the START / END dates, then Run All.

An Explicit Solution to Black-Scholes Implied Volatility | Wolfgang Schadner

For the past 50 years, implied vols were calculated from option prices and other option inputs numerically. Simple versions use Newton-Raphson or bisection searches. The idea is to “guess” what the implied vol is, call that g*, see what option price that produces, split the difference, and repeat the recipe until you arrive at a price that is within a fraction of a cent of the market price. This method is used because there’s no closed form going from price → vol, only vol → price.

This SSRN paper came out this week and made the rounds quickly. It offers a closed-form approximation, alleging it recovers IV to machine precision ~3.4x faster than the current best-in-class. If it holds up under wider testing in the wild, it’s the kind of thing that ends up in textbooks.

From My Actual Life

My youngest turned 10 yesterday. I wrote him a letter just as I did for my eldest when he turned 10. It can be hard to remember what your kids are like at every phase. But also, it can be hard to remember where you’re at mentally at those ages. You hope the letter becomes a gift they cherish when they are older and can relate to being an adult writing to their child. But looking back at the letter myself will be a time capsule gift for my future self too.

This is an instance of a belief I have come around to as they’ve gotten older. A lot of what I think I do for them I really think is for me. I want to be around them selfishly more so than I think my presence is as important as I’d like to believe.

The possibility that kids do more for you than you for them is better left as a self-effacing end to having children rather than something to weigh before having them. Don’t tell the optimization maxxers.

This Week In The Options Trench

📺Convexity vs Leverage

This week Eirk and I disentangle the source of amplified profits and losses

Stay groovy

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Moontower Weekly Recap

• hard-earned trading wisdom

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I sold a house in the DFW area in 2022. Instead of a mortgage, the buyers financed the purchase via a margin loan against their stock holdings held in a Morgan Stanley account. A bit unusual. That was the year mortgage rates spiked so maybe the margin rate looked relatively more palatable. But there could be other reasons too. For example, getting a loan or HELOC is much harder these days without a fat W2 income, so maybe the buyer was an entrepreneur or retiree.

[I remember the aftermath of the credit crunch, an oil option trader I knew just had an 8-figure year as an independent trader, couldn’t borrow even $2mm of the $5mm loft he bought because his income was deemed so variable. I’m not saying bankers should use a sortino ratio, but damn that was broken. The contrast of today, when every risk gets underwritten with little premium, to that era when banks wouldn’t touch cash-good risks is stark. Do what you want with that.]

We are going to start construction on an ADU so I’ve been thinking about financing at a time when there are more options (a pun that doubles as foreshadowing). Last week, I wrote a guide to option margin. While a post like that was overdue, the timing of it was not an accident. It is deeply entwined with today’s topic of disintermediated borrowing.

Read more

Euan Sinclair needs no introduction from me.

I’ll cut straight to the gold.

He’s been a repeat guest on Erik’s Outlier Trading podcast a few times. His writing and interviews mince no words. Despite never sugar-coating the reality of trading, I found his most recent interview even bolder. It’s this witch’s brew of insight that is somehow both timeless and underreported.

I’ll start with an idea from the interview he did from late 2025 that always bears repeating before moving to the more recent chat.

The most common misconception about trading volatility

In Euan’s 2025 chat with Erik, he was asked “What is the most common misconception about trading volatility?”

He zoomed in on the mistaken logic that because volatility is mean-reverting, selling it when it’s high assures a profit since it always comes back down.

There are several facets to the mistake. One is with respect to how volatility can cluster based on a market regime.

Saying volatility’s mean reverting is true, but the means also change, you know? So, if you sold volatility in, I don’t know, March 2020, right? Volatility didn’t go back to 15 for about a year, right? Volatility had a new normal. So just because something’s mean reverting doesn’t mean you’ll make money because it comes back.

Another flaw is in understanding that you are exposed to both realized and implied vol.

The other thing that can be wrong is that you’re not directly trading volatility. You’re trading the spread between implied and realized. And that doesn’t have to be mean-reverting and it doesn’t have to be negatively correlated with the level of volatility either. So just because the implied V comes down, that’s not necessarily going to help you if the realized vol still is higher than the implied.

[Kris: I remember suffering through a short option position in nat gas in the expiry right before I got married. The V09 option cycle (expiry date was late Sep 2009). Implied vol got up to 110% but it realized more than implied for our entire holding period. We chopped ourselves up on the short gamma even though we had “positive vega p/l” on some of the marks.]

It’s easier to understand this when you scrap the concept of “vol” for a moment:

Forget about volatility, right? Volatility is just a way of turning option prices into another thing. It relies on a model. Forget about all that, right? Let’s say you’ve got a straddle and the straddle’s trading at five bucks and that straddle normally is trading at two bucks. So you’re like, “Oh, that’s really high. I’ll sell it.” And then as soon as you sell it, it moves by $10. You know, the stock moves by 10 bucks. You’ve just got hammered, right? But you know, the straddle drops down to a dollar. So you were right about the price of the straddle, but you weren’t really just trading that.

Finally the VIX chart illusion:

That’s one of the problems people get wrong is selling volatility spikes isn’t as appealing as it looks as when you look at the VIX graph over time and you’re like, “Oh, the VIX these spikes. It always comes down again.” Yeah, but you that’s not what you’re trading when you’re trading options.

See this post from the Liberation Day period if this is not clear: you can’t trade spot VIX.

The rest of these excerpts are from Euan’s 4/1/26 appearance on Outlier. Emphasis mine.

Where to start: known effects

Erik asked Euan where retail traders should start. Euan’s answer is a tour through what he actually believes works, why it works, and how to think about learning from past data without fooling yourself.

If you’re prepared to have low enough expectations that they’re realistic, and then really work at this, um, and it doesn’t have to be a full-time job, but you can’t just think this is my extra income. You know, this isn’t like driving for Uber.

Erik: Thinking a little more deeply then about the kind of things retail traders should look at — I went through an interesting exercise on my own, because people would ask me for ideas on places they might want to start looking, and I always struggled to give a good answer. There’s a million variables. But I’ve recently started directing people toward really well-known market effects — stuff you could go look at research papers on SSRN in mass, well-researched stuff. Something like time-series or cross-sectional momentum as a general market effect.

The reason I’ve been going that route is that there are so many things you have to do right as a retail trader. Even if you’re doing all the right things but it’s centered on an effect that isn’t really there but you think it is, that’s massively detrimental long term. Even though the returns might not be — as you talk about — stuff that would give you Lambo money this week, you’re at least building the infrastructure around something we know exists.

Are there effects or markets that you think are better suited for those first few repetitions for a trader?

Euan: It’s not so much about finding a market where you have an edge. It’s not like, “Oh, you’ve got to trade shitcoins,” or “You’ve got to trade options on pharmaceuticals.” The actual instrument and sector are of lesser importance than the concept of what makes this thing work.

There are a few things in finance that we know broadly are real. Momentum is one. The other one I’d say, if you’re just starting out and you want to set up what I’d call a real trading operation, would be carry.

If you really understand the concept of carry, particularly as it applies to futures basis trading — in theory, we know that a future is going to coalesce to the spot price at expiration. But that doesn’t tell you how it’s going to do it. It doesn’t say the future’s going to stay there and the spot’s going to go up toward it. It doesn’t say the other way around. But what actually happens most of the time is that the future moves toward the spot price. Naively, that’s exactly what you wouldn’t think happens — you’d think the future was an expectation of the future or whatever. But no. It doesn’t matter what you naively think. That’s a very strong effect.

If you know about that effect, you’ve now got lots of places you can look for ways to apply it. And if you understand the effect, you’ll know places that are better than others. You look for something with a big basis. You look for something with high volatility, because that also gives you more of a basis. And you want something to move a lot, because if nothing moves, you can’t make any money.

That leads you to something like the VIX. The VIX futures have a very high basis to the cash usually. If you look at the difference and you annualize it, if that entire basis is realized, that can be 100% a year. Are you going to get 100% a year? No, because lots of other things are going to happen, and you’re not going to realize all of that, and there’s volatility. But that’s now an effect where you can start saying, “Okay, now I know this. What can I do to harvest it?”

Then you start saying, “Well, clearly I want to be short the future if it’s above the cash. That’s risky. What do I do to hedge that risk until I’m happy?” And maybe you’re like, “Okay, I’ll do a future spread. I’ll be short the front one, long the back one. What ratio? What futures?” Eventually you’re going to come up with — and there are papers written on this exact effect, I haven’t just pulled this one out of nothing.

A lot of the stuff’s out there. People tend to have this idea that no one’s going to tell you anything that works, whereas literally there are thousands of pages written on stuff that works. The universe isn’t going to give you money the way you want it to necessarily, but this carry effect — once you understand it in the VIX, then you’re like, “Holy shit, this also works on a ton of other commodities. It works in bonds.” And then, “Okay, if it works in bonds, does it work differently in treasuries, credit, corporate bonds?” And the answer is yes. So now you’ve got spreads. So relative value is the next thing you start looking at.

Pick a bunch of carry situations, learn to put them on, learn to manage them. They largely take care of themselves, but you have to adjust, you have to understand the risks. It’s like when you fly a plane — you’re learning on a Cessna, learning slowly. You don’t just get into a MiG and blast off. But this is that Cessna. It’ll get you money, and it’s a real trading operation.

Then you move on to relative value. These spreads move around. Maybe I can scalp those spreads. How do they move around? What’s the range? And then, “Well, sometimes they don’t move around.” Okay, and that’s going to lead you to momentum. That’s your next one.

Everyone should read that book by Antti Ilmanen, Expected Returns. It breaks down — it’s about 400 pages long, that’s how detailed it is — and it talks about the volatility premium for about four pages. It goes into hundreds of things like this that work. Carry is a huge unifying feature. Relative value. Momentum. The variance premium and options — again, that’s there. I wouldn’t recommend people start with it. It’s kind of slippery and a good way to lose a ton of money unless you’ve got everything else sorted out. But it’s another one.

That’s where I’d start. I’d start with one thing, move to the next, keep adding. Once you got to three or four things, that’s probably all you can handle. You’re not going to be able to have 10 different strategies and keep things together. That becomes a major logistical operations issue.

Where to expect edge: the hard leg is where the money is

[Kris: My biz partner would say the “hard leg” is where the money is.]

Typically in the world, you get paid for doing something that makes the world somehow better. You provide a service, and typically there’s something unpleasant about that. Otherwise people will just do it themselves.

If you’re selling flood insurance, that’s a tough business because you make money, make money, make money, and then you get absolutely blitzed. That’s a tough thing to live through. Everyone thinks they can, but in reality it’s a lot harder than you think. We’re very bad at figuring out how we’ll feel when something bad happens. Similarly, the guy in the flood who’s cleaning out the sewers, he gets paid.

If you’ve got a clear idea of, say, the carry trade — why am I getting paid to do the carry trade? Largely because I’m providing a source of risk insurance for other people. I’m short those futures that are going to go massively up when the market — like a couple of weeks ago — when the VIX spikes from 18 to 30, those short front-month futures are going to hurt you way more than the long back months. And they have to. Because if you hedged that, then there’s not going to be any premium for you to take out of the trade. All of these things are risk premia. In order to get risk premia, you have to accept that risk. Over time you’ll be fine, but you’ve got that unpleasant nature of the payoff.

Another good rule of thumb: anything where you think this is a bad idea because the risk looks unpalatable — there’s probably edge in there somewhere. If you as a professional trader are like, “Yeah, this looks dangerous,” you’ve got to accept that most of the rest of the world also thinks it looks dangerous, and you get paid to manage that fear. You are the bomb disposal guy. That’s why you’re getting paid.

So if it’s like, “Ooh, there’s no way I’d sell options over the weekend, that’s dangerous” — all right, what side do you think the edge is on? The guy who is prepared to sell options over the weekend, or the guy who wants to buy options over the weekend?

Walking into danger — I’m not saying you always have to, and it’s a risk judgment; you don’t have to take every risk that’s out there. But if it makes you nervous, there’s probably edge in there somewhere. If you can get it to a point where you’re comfortable with it, or can diversify, manage, or hedge it, that’s a good place to start making money. That’s why you get paid for selling options. You don’t get paid for buying options.

Again, difficult thing to say, because for the last three or four years, retail made a ton of money buying 20-delta calls in the indices. By the way, historically, what’s the worst option to be long? Index 20-delta calls. If you think that’s your edge — no. Take that money and good for you. But that’s not the way the world has typically worked. It might work like that for the rest of my life, who knows. You’ve got three years where that worked really well, and 100 years where it didn’t. Just as long as you know that.

Look for any situation that legitimately makes you uncomfortable, and there’s probably something in there.

Learning from the past

Erik: Two follow-ons. I’ll give you both, and you can pick. The first is how to use past information to inform future projections or predictions. The second is pricing of convexity and some of the internals behind that. You pick whichever one sings to you.

Euan: I think the first one is probably more suited for a podcast format.

Basically, the only thing we have to predict the future is the past. And there are two things you can say: the future will be somewhat like the past, or it won’t be like the past. Of those, clearly the better one is to say it will be somewhat like the past. That just makes sense, and usually that’s the way it’s been.

The problem, particularly in finance, is it’s an adaptive system with people on the other side of, and everyone is going through this thought process to a certain degree as well. Everyone’s looking at the same information. Everyone’s saying, “This is the way it’s behaved.” Everyone’s trying to predict on the same thing. Largely coming to a spread, but broadly the same conclusions.

So using the past to predict the future is always going to be murky. And there’s an unfortunate tendency we have now. Like, 30 years ago, no one did backtesting, because you couldn’t. There was no data, no computers. Even before Excel — you’d have to write a program in Fortran. It was hard. No one did it.

Now, everyone does backtesting. The problem is that means most people do it wrong. They see backtesting as a way to find patterns, and they’ll test stuff, do cross-validation, test walk-forward, go out of sample, and they’ll find things. The problem is they look at so many things. Of course they’re going to find something. That’s the big problem with using the past — you think you’re doing statistics correctly, but really all you’re doing is looking at stuff over and over again until you find it.

You’ve also got to remember — and this is an Aaron Brown thing as well — as soon as you’ve looked at some data once, you’re done. That data is in sample forever. You can’t say, “Oh, I’ll try my trend-following system on the S&P. That didn’t work. I’ll try a mean-reversion system on the S&P.” The only reason you’re trying that mean-reversion system and think it might work is because your trend-following one didn’t. So you’re already overfitting. It’s not so much overfitting to the numbers. It’s applying information you’ve learned by looking at it already, even if you’ve looked at it for a different thing.

At this point, there is practically nothing I can do to study the VIX that’s going to tell me anything, because I’ve looked at the VIX for so long that I know what’s in there already. I’m not actually making any sort of new judgment. All I’m doing is applying what I know has worked in the past because I’ve looked at it so many times.

The way to address that is to start with something you believe first. Do you believe in carry? Yes. Do you believe in momentum? Yes. Cross-sectional momentum? Yes. Risk premia? Yes. And then you come up with an idea, and then you say, “Does this work in the past?” And you test it. If it works, great, you can make it better. If it doesn’t, you give up.

We see this with options particularly. People are like, “Well, I tried selling strangles on Monday and holding them all week and it didn’t work. But then I found if I sold straddles on Tuesday and got out on Thursday, it did work.” Both of those are driven by the same effect — they’re both variance premium plays. If one of them didn’t work and the other one did work, all it means is you got lucky picking the entry point for one and not the other. As soon as you’ve looked at that second one, you’ve just completely overfit the whole thing.

That’s one of the big problems people make by using past data. You use past data to come up with the overall belief. Carry means something. Credit spreads mean something. We’ve got, I don’t know, 5,000 years of stories about credit. Credit’s older than money. It’s a real thing.

Looking at numbers should be the last thing you do, and only to confirm something you’re already pretty sure works. My risk premia thing — I’m sure it works. I can test does it work better in a one-month option or a one-year option, but I should not be just blasting combinations in until I find something that is the best.

One of the most dangerous words that’s come out in quant finance is certainly “alpha drift.” This isn’t a retail problem either. I see this in quant firms all the time. They optimize and think they’re doing it out of sample, but they’re not, because they’ve already — this is the fourth model they’ve run on the same data because they keep looking at the S&P 500 or something.

Optimization is a horrific thing. It’s one of the worst things to ever hit the world of finance — that concept that you can make something better, or perfect, or optimal.

The other one, by the way, is theta. I can’t think of a thing that’s cost any more money than theta — this idea that options decay over time. That is literally not what the Black-Scholes equation is telling you. The Black-Scholes equation is literally telling you they don’t. If everyone knew an option was decaying over time, no one’s going to pay for it now — they’ll buy it tomorrow, it’ll be worth less. The number of people who’ve fallen into that “I’m harvesting theta” thing — and there’s plenty of influencer types who are peddling that story, typically also owning a brokerage at the same time.

The difficulty of learning from the past is that people think they can learn too much from the past. You have to discount everything you know based on how much you actually believe the thing. Show me an effect you found in the market — I don’t know what it is. A few years ago, “gold goes up on Fridays” was a big thing. Everyone looked at the data — look, gold went up on Fridays. Okay, why would that happen? “Well, it’s because fund managers are scared of risk and they go into gold on Fridays.” All right, find me one of those people. Not you, or some other person who buys gold on Fridays. I mean someone who runs an appreciable amount of money — doesn’t have to be Pimco, but people who run hundreds of millions or billions. Show me one of those people. No one’s ever managed to do that.

Does it go up on Fridays? Well, it looked like it did. T-stats, sure it did. Now how much do you actually trust that? On a scale of zero, which is candlestick charts, to 10, which is carry is a real thing — I’ll give gold on Fridays a three. Could it be true? Sure. But I don’t see a compelling reason. You look at enough things, you’re going to find that.

That’s the problem people get. They look at the t-stats and go, “Look, statistics, man.” All right — now how many other things have you looked at that didn’t work? Because you’ve got to include those.

The philosophical problem of what you can learn from testing

Starts with sound reasoning:

I’d like to start with the idea that people buy bonds at the end of the month because of window dressing and rebalancing of 60/40 funds. There’s an idea. If the stocks go up more than bonds in a given month, people rebalancing have to sell the stocks and buy the bonds. That should have an effect. That’s your hypothesis.

So let’s look for situations where that hypothesis has a market effect. Do you see it? Do you see it in situations where your hypothesis would tell you you should see it? Equally, do you not see it in situations where your hypothesis tells you you should not see it? If this also happens on the second week of the month, maybe it’s not what you think it is.

I’d always like to start with a reason and then test the reason.

…But there’s thousands of years of philosophers who pointed out all the contradictions in this stuff. Nothing in the world is out of sample. The only person in the world who’s out of sample is a baby who doesn’t know anything. That’s the great curse — the more you know. With me and the VIX, it’s not that I’m the greatest VIX person in the world or even close. I’ve just looked at it, I know it, I can’t be surprised by anything it does. That’s the downside of experience: nothing is out of sample…

The best you can do is find a situation that looks like it’s somewhat constant over time. If you look at the statistics of the VIX, the distribution is pretty constant. If you look at what it did in the ‘90s and in the 2000s, break it down in big blocks — it kind of looks the same. Whereas stocks tend not to. You can’t look at Tesla 10 years ago and Tesla two years ago. The business models were totally different, but in one case the stock was a dollar, and over the last two years it’s been between 200 and 400. These are different situations. Stocks are not stationary.

But really, one of the things you have to do is accept how little you know about the world. The good traders never say, “I’m right because of this, and this, and this.” The good traders are like, “I think I might be right because of this. But on the other hand, I could be wrong because of this and this and this.”

Aaron Brown, who’s probably thought more about this stuff than anyone I know, says that a bad trader is always saying “and furthermore,” and a good trader is saying “on the other hand.” A good trader is looking for holes in their argument. A bad trader is continually trying to find other reasons why they’re right.

David Hume — smart guy, all philosophers do is think about thinking — they were pointing out the problems of trying to learn from induction hundreds of years ago. There’s no answer. That’s the only information we have, but we can never really draw certain conclusions from it. So I always apply a big whacking discount to everything. And it’s not statistics. It’s a meta level above that. It’s like belief. I’m not just saying there’s a statistical rule for how you judge if this is good or bad. In fact, literally there isn’t. There’s an actual degree of belief that is independent from what the numbers are telling you.

Vibes vs quant is a false dichotomy — there’s vibes in everything

[The general construction of his portfolio isn’t] based on statistics. It’s based entirely on my degree of belief. Like that carry trade we talked about — how much do I believe that? A lot. Given what I know about its volatility — and I mean “things move around” volatility, not standard deviation of returns — given I know how much that is, given I know how scary it can be, but given I know the belief, I might give that 40%. Whereas there might be another trade where statistics are just as good, but I’m like, I don’t know, I don’t really believe in that one. That gets 20%.

That gives me my baseline, and then I go run all the statistics, and then I say, “Well, okay, I’m shrinking it to this vibes portfolio, because that’s the one I kind of wanted to be at in the first place.” There’s a lot of people who’d be like, “Well, that’s not quantitative. That’s not systematic.” Well, first of all, who gives a shit what they say? You don’t get a medal for being quantitative. You make money or you don’t. Being quantitative is seen as this kind of goal, and it’s not the goal. It’s a tool toward the goal.

Every time you make a portfolio or sizing decision, you are at some point applying that kind of thing. If you’re going to go through all the math, eventually you’re going to have a utility function, and that utility function is going to have a risk aversion parameter. So you’re going to go through all this math, and then at the end it’s going to say, “Oh by the way, what’s your risk aversion parameter?” You have to make that decision somewhere. I’m just doing it at the start. It’s much more of an exogenous thing that’s obvious.

It’s more a reflection of what I think I actually know than a mathematical statement. It’s not a mathematical statement. It’s an epistemological statement.

A lot of people get hung up on “insult found: the discretionary trader.” How is that an insult? Everything you do is discretionary at some level. Literally, you have chosen to do something. You have exercised your discretion to do something. Whether you do that in the math you choose, the problem you attack — you can’t go through life without exercising discretion. That’s actually called knowledge or experience. It’s a useful thing. If you don’t use that, you’re an idiot.

The cost of systematization

There’s certainly this whole idea that if you’re systematized, it’s emotionally easier to stay with things. I don’t think that’s true. I have operated completely systematic stuff when I’ve had jobs, and it loses money. It’s not easier. It just isn’t.

The reason I think you should systematize something is because you have to. Every time you’re removing yourself from interacting with the market, you’re removing yourself from an opportunity to learn. I think you should do things as manually as possible — and I mean it. If you can get away with writing stuff down on a legal pad, then that’s the way to go. If you need to use a spreadsheet, use a spreadsheet. But if you can do it on a spreadsheet, yet you choose to write some massive API call and do the whole thing in some language — you’ve done that because you wanted to, not because you needed to. That’s a mistake.

The places I’ve systematized things are because I wanted to avoid operational risk and key-man risk. If I’ve got a strategy I want to run for an ETF every day, it has to operate if I crash my car and go into a coma. That has to be systematized. But if I’m running something on my PA because I find it interesting and I’m still messing around with it — systematizing that, all I’m doing is removing the opportunity to learn.

It’s one of those things where retail look at institutional and go, “Well, it’s all systematized. I have to do that.” But they don’t think of the reason we systematize things. It’s not to make the strategy better. Honestly, it probably makes it worse, because you’ve locked it in. You’ve said, “This is it, I’m not going to be learning anything more about that now.” But it definitely removes operational risk. It makes it cheaper to run, because you can just let it run on its own. You don’t need a person doing it all the time.

People on the outside are making a judgment of how the things on the inside work, and they’re missing the point.

How do you avoid it? I don’t know. Hopefully if I pointed that out to you now, you’d be like, “Oh yeah, now I get it, this is the important thing.” Think about anything else you’ve ever learned. You’ve learned by doing, by the immersion in it. Trading now, the actual act of trading, is click, click, click, done. You don’t learn anything from that.

But what you do learn about — especially things like adverse selection and the ability to execute — like, “Oh, it looks like there’s plenty of volume. Oh, but every time I put a 100 lot in, all the bids disappear.” That’s the sort of thing you’ll learn so much about just doing it and interacting with it. You’ll never learn that if you automate the trades.

[Kris: To insert something here. I’m reminded by an interview with Agustin Lebron where he talks about getting ideas from just staring at an order book for ours. Seeing how it updates, how bids and offers change after trades, or in the absence of trades but while the rest of the market is doing things. He recommends doing this in medium or low-liquidity names where you can possibly see a story unfold in the order book. I agree with all of this. I mean I don’t think I never explained it quite like that because it’s just the water you swim in. If you trade something relatively illiquid, every movement matters. If some 20 delta put trades on the offer, you have to triangulate whether it’s skew expanding or volatility in general. See Mermaids, Fireflies, and the Bid-Ask Spread.

But there’s a corollary hidden in wisdom of learning from sparse order books: edge is inversely related to liquidity. The more liquid the market, the more whatever’s left looks like a risk premium. SPY is one of the most liquid markets in the world. If you had any edge in trading it, the edge would be so scalable your heirs would be set for an eon. Remind me to rant about this sometime.]

If you’re in a situation where you have to automate the trades, you’re probably playing in a game where you’re not going to win as a retail trader. You shouldn’t be trading, “Oh, I have to run this through the API so I can trade 15 times a day.” That’s one of those quant-envy things where you’re like, “I’m going to do this the way Citadel would do it.” Again, you’re playing basketball one-on-one with LeBron. Good luck. Don’t care how tall you are.

Inefficiency vs risk premia

There’s a split between inefficiencies and risk premia. With an inefficiency, price competition is going to drive it to zero. Nothing’s purely risk and nothing’s purely inefficiency, but market making in options has a lot of inefficiencies. It’s like, “I’m going to buy this option because I can sell this option. Those things should be worth the same. They’re off by a little bit.” That kind of thing. The act of providing liquidity is a risk premium, but the way you do it is looking at all these little inefficiencies.

If you look at the way equity market making has gone in the last 30 years or whatever, ever since the floors have gone and we’ve gone electronic, that has been driven to almost zero. It’s not at the point now where any sort of random person with an off-the-shelf piece of software is going to consistently make money making markets in equity options anymore. It’s gone from profit margins like Tiffany’s might have, and now it’s Walmart. Everything’s driven to zero.

Risk premia are different, though, because they’re there for legitimately a reason. It’s a different utility function. You’re doing something you know is wrong because you don’t want to deal with the risk. You’re buying insurance. You’re not buying insurance because you’re dumb, you’re buying insurance because you want insurance. And I’m selling it to you because either I can take the risk, or I can lay off the risk, or whatever reason — I’m doing it to maximize expected value. You’re doing it to maximize another utility function. We’re both happy.

That kind of thing has got more legs to it. If you look at the variance premium over time it’s been reasonably constant. Obviously it goes up and down. You’d think that after 2008 it would get wider; surprisingly, didn’t much. You’d also think that now, because of all these zero-DTE covered call funds, it would collapse. And it kind of has. But sooner or later people will realize a lot of these funds don’t make money, or some of them will blow up, and it will go back to where it was. All these risk premia are cyclical, but there seems to be a natural limit that doesn’t get driven to zero.

It helps to be able to say: is this an inefficiency that people can’t access, or is it genuinely a thing that everyone knows is there and people are doing it for different reasons? Because that’s the sort of thing you can build a trading life around. Inefficiency — if you find one, good for you, knock it out of the park as hard as you can. It’s not going to be there forever. If it is there forever, Citadel is going to come along and build a desk on it and crush you.

Adaptive markets, but not adaptive traders

Erik: The follow-on, though, even within something like risk premia that we know is there for a reason — an example you’ve given previously is there’s a $20 bill on a busy highway. If I’m standing on the sidewalk and there are five crackheads, and I say, “Hey, I’ll give you 10 bucks to go get that.” And then one of the other crackheads says, “I’ll do it for eight. I’ll do it for five.” And then at some point we get to a floor where the crackheads are like, “I am not going to risk my life for this anymore.” Do you think that with something like risk premia in index options, based on that consistency, we’re generally about at that level? Or do you think it’s likely to shift around more?

Euan: That’s difficult to say. But with your crackhead example — one crackhead might say, “I’ll do it for six bucks,” and he runs out there and he gets killed. And then the next crackhead’s going to come along and say, “Actually, I want seven now, because I saw what happened to this guy.” It’s not the same people all the time.

What we tend to see is a new cohort of traders come in and blow up doing the wrong thing, and then a bunch of other people come in and end up doing the same wrong thing. The market never completely adapts, because it’s never exactly the same group of people who learn. Markets learn, but traders as a whole don’t. For things like this, a lot of it’s propped up by new people coming along making the same mistakes as the old people. Adaptive markets, but not adaptive traders. In a lot of cases people think they’re the same thing. I don’t think they are. There were a ton of floor traders, good floor traders, and then everything went electronic, and they tried to do what they did on the floor on the screen. It just didn’t work. And I don’t know any of those guys who were like, “It’s not working, I’ve got to do this and this and this instead.” That didn’t happen. Instead, a whole bunch of other people — studied computer science at Cornell or whatever — came in. It was a whole different group of people who made money at that point.

Stay groovy

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