Path, VIX, & Hit Rates vs Expectancy
Friends,
The CBOE’s VIX index interpolates 30-day implied volatility based on options struck on the SPX index.
A VIX future settlement price is based on the prevailing VIX index at the future expiry date. It’s a bit of a confusing concept. A future that expires to a VIX index level that looks ahead 30 days.
There are ETFs and ETNs that reference VIX futures (VIXY, VXX). They also come in levered and inverse forms (UVXY, SVXY).
Despite the abstract nature of trading “a level of volatility”, these are popular products. There is 2-way interest in them. SPX returns are inversely correlated to implied volatility making long VIX positions a natural hedge. At the same time, the upward-sloping term structure of SPX implied volatility means implied volatility in the future trades at a premium to volatility today. Many traders will short VIX futures and ETFs to capture the downward drift they expect if the market remains calm as the futures will “roll down” to converge with spot VIX by expiration.
Quant finance geeks about these volatility term premiums. Term structures recognize that volatility is mean-reverting. Historically, SPX realized volatility bounces around 15% give or take a couple percent over long periods. Implied volatility typically trades at a risk premium. The premium also bounces around but 16% IV on a 15% realized vol (ie 1% premium) is in the right ballpark.
The averages mask the distribution. VIX is bounded by zero. It’s rare for it to get to about half its average. It’s rare to double but less rare than halving from 15%. But it’s even possible to triple or quadruple (Covid and Aug 5th 2024 for recent examples). It’s also more common for VIX to go to 12 than 18, at least in recent years.
This low-res farmers almanac description paints a picture of a lognormally distributed index. VIX futures will drift lower frequently but occasionally spike and sometimes those spikes are very high (and fast).
It’s natural for us to think in terms of averages. This habit persists despite witnessing price moves that would be impossible if normal curves were in charge (and despite the warnings from cranky Lebanese deadlifters). The nasty side effect of Gaussian-brain is when it creates the illusion that something is massively mispriced when prices are just properly reflecting a skewed or fat-tailed distribution.
In the 2 min read, The Benefit Of Betting Culture, you can see how the price of a futures-style bet vs an over-under style focuses your attention on the distinction between probability and expectancy. This is the heart of the matter. Investors confuse hit ratios with expectancy constantly.
I field emails and calls too often that are basically retail traders saying “I was doing great selling options for 6 months then I lost it all in month 7”. The reasons for these mini-blow-ups vary from oversizing because they’ve been winning to naive pricing but the universal mistake is in the epistemology.
Some traders are executing without understanding the nature of the proposition. It’s not that selling options is a mistake (there’s a price for everything). It’s that you shouldn’t be surprised by the shape of the payoff. Roughly speaking, if I sell a 10-delta option every month and I win 6 months in a row, I haven’t learned anything about whether my strategy has an edge. I should expect to win most of the time. That says nothing about the expectancy. The person is thinking in terms of 50/50 averages, ie win or lose. But the proposition if it’s fair is more like win $1 9 times and lose $9 one time. If you have an edge, then you either win more often for the same payouts or the payouts are not as far apart but the hit ratio is the same. But most retail traders don’t have large enough sample sizes to infer anything from such skewed results. The track record is nothing but a statistically underpowered study.
Unlike rolling dice or flipping coins, it’s hard to learn anything about the distribution of prices from direct experience. Historicals help but you only have to look at acute incidents in markets over the past 5 years alone to appreciate the challenge of calibrating what’s improbable.
But we can strengthen our conceptual understanding to hopefully be a little less blind to hit rate vs expectancy (or median vs mean) illusions. Option surfaces themselves are great teachers in this regard. In a deeper understanding of vertical spreads, we’ve seen how call and put spreads are a rich source of information about a distribution.
In the remainder of this discussion, we’ll get some mileage towards internalizing the difference between hit rate and expectancy from a non-technical discussion about the price of a VIX future.
Pricing a VIX future (via arbitrage)
If you are a professional trader who just heard me say “price a VIX future” and “non-technical” in the same sentence, you feel like you’re at a Houdini act…” How’s this mf gonna pull this off?”
[cracks knuckles, bends neck side-to-side, deep breath]
Ok, a little background for the uninitiated.
The VIX complex of futures, ETFs, vanilla options and VIX options is one of the more technical areas of options trading. There are arbitrage triangles between these things.
They’re not exactly clean though.
Replicating a variance swap also isn’t clean (not every strike exists and even for the ones that do transacting entire strips is not economical). Neither is dispersion. Neither is isolating forward vol.
But all of these things lend themselves to a fair value that can be F9’d in Excel if you ingest the real-time bid/asks for the building blocks. Every large vol desk has a group that computes a fair value for VIX futures that is derived from SPX options and VIX options. You can trade around that fair value by being better bid on the building blocks that are relatively cheap and vice versa. Manage the residual risks and over time you make money.
I’ve never worked out a model for VIX futures fair value myself as I’ve never traded the SPX complex. But we can still step through it conceptually.
Imagine you are short 100,000 shares of VXX at $16.
*VXX references VIX futures. Just to avoid computing position ratios let’s just pretend VXX and the VIX futures trade for the same price.
You are short 100,000 vega because your position vega by definition is “change in p/l per 1 point change in volatility”.
If vol (ie the VIX future) drops by 1 point, you will make $100,000.
Arbitrage pricing comes from replication. If I can construct a portfolio with a cash flow of 0 in every state of the world, then I have a risk free position (and if I get paid to hold that portfolio I have an arbitrage profit).
To offset my VIX futures risk, I must therefore buy 100,000 vega via SPX options.
[This is conceptual, so we are hand-waving important details like what strikes, expires, weights and managing the deltas.]
At this point we are vega-neutral. Long SPX options, short VXX.
What happens if vol suddenly doubles?
You’re going to make a lot of money.
Why?
Because you lose linearly on your VXX short (-$1.6mm or 16 vol points on 100k shares) but you win more on your SPX option longs.
The reason: you are long not just ATM options but OTM options too. OTM options pick up more vega has vol increases. It’s like being long “vol gamma” (it’s literally called volga). Remember how a long gamma position gets longer delta as a stock goes up and shorter delta as a stock goes down. Well, this is the same effect but for vega via vol.
💡See Finding Vol Convexity for a full explanation.
The fact that you make money because your are long “vol of vol” means you aren’t quite replicating the VIX future though. That’s a problem.
[There’s a cost to being long “vol of vol” so we can deduce that vol never changed and expiration arrives that this so-called hedged position would have lost. There has to be a flip-side to the fact that if vol makes a large move that portfolio wins.]
Conveniently there is an instrument that’s a pure expression of “vol of vol”. You guessed it — VIX options.
The conceptual algebra:
VIX future = SPX options - VIX options
In our example, you can short VIX future, buy SPX options, and then sell VIX options to neutralize this long volga exposure.
This identity is loaded with insight.
If I’m long VIX futures and short SPX options, I’m synthetically shorting “vol of vol”.
If I’m short VIX futures and long SPX option, I’m synthetically long “vol of vol”.
If I’m short VIX futures and long VIX options, I’m short vol but long vol of vol which is similar to be being short SPX straddle but long strangles.
You can envision how looking at the VIX complex you can see which leg stands out as cheap or expensive relative to the others. Layer in implied correlation which relates index vols to single stock vols and suddenly you’re Neo in the matrix.
A day in the life of a vol arb desk is market-making all the flows with an axe. Based on the price of the various parameters like vol, skew, convexity, term structure and correlation you might be:
Selling VXX
Buying 1-month VIX calls
Selling 1-month single stock OTM calls
Buying weekly SPX calls
Selling SPX 6-month straddles
Buying 9-month single stock downside puts
Like a chess player chunking their position, you look at this and think:
“I’m short SPX call spreads and vol near-dated, long upside implied correlation near dated, long a 6 month/9month time spread with a dispersion kicker.
I’m long gamma, short vega, long tons of volga, paying theta”
[Note: the greeks will vary based on the ratio of position sizes. If you’re playing along at home you can try to map the positions to the first line of the summary. And for the greeks you can try to imagine what position sizes are required to make the sign of the greeks make sense]
You do this not because these positions are inherently right or line up with some macro view. You do this because the prices are “right”.
You take what the market gives you. Everyone who’s out there trading on their opinions is moving the price of these parameters around. You are agnostic. Pick up the edge, manage the risk.
All you care about is others having strong enough opinions to move prices around and that you can find contradictions in the matrix.
To quote the closing line in Pacino’s speech in Any Given Sunday:
“That’s football folks. That’s all it is.”
Pricing a VIX future (like an option)
The fact that a VIX instrument has a fair value in a similar manner to how an ETF has a NAV has always kept me away from it. Just like I wouldn’t trade an ETF if I didn’t know its premium/discount. If a box has a dozen donuts I don’t want to buy it for a price that implies a baker’s dozen. Negative edge.
That said, lots of people trade VIX products with a belief that they have an edge based on a relative value lens rather than an arbitrage framework. I’m guessing this leads them to selling VIX futures (which is probably the right side from the arbitrage perspective as well.)
[I’ve often thought that if I were to build a VIX or SPX suite in moontower.ai I’d want to “do it right” which is to use the arbitrage lens rather than extending the in-place moontower analytics to VIX as if it applied. I’ll leave it to you to decide if other platforms do it right or if they’re like children playing house pretending to be grown ups. By the way I have similar opinions about 0DTE. I’d use a totally different framework than the one we currently use in moontower.ai to deploy a 0DTE suite.]
Since a proper VIX complex treatment is prohibitively scarce for retail, it’s additive to think about another way to price VIX. I think it’s intuitive to consider VIX itself an option.