Primer #10: Trade Expressions & Structures
Implementation Unit #4
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The moontower.ai Primer is divided into 2 units: Conceptual and Implementation.
To review, the Conceptual Unit which includes:
The Implementation Unit thus far:
Trade Expressions & Structures
The chief motivator behind any trade or position is either speculation or hedging. The beauty of options is they are priced for specificity. By explicitly incorporating the dimension of time, you can fine-tune the expression of a trade to better match your goal.
The prospecting funnels are invaluable tools whether you:
1) start with a cross-sectional funnel to identify a speculative trade or
2) proceed from a spontaneous idea or desired exposure, and then filter for the most attractive prices for that exposure
The output of your prospecting funnel is your “axe”.
For example:
“I want to buy near-dated TLT volatility” or
“I want to sell long-dated oil put skew”
You've concluded that a particular parameter is cheap or expensive. You must now turn that view into an explicit trade. That’s what we mean by “expression”.
The expression should take into account two considerations:
1) Isolation
The trade should profit as the mispricing goes away. The point of the trade is to be exposed to that trade. In the case of hedging, on balance you might still lose but the profit on the specific trade should leave you with a smaller net loss.
On the subject of "noise"
It’s important to be aware that there is always noise in the result stemming from path dependence and randomness. However, the fact that options are priced for specificity means there will be less noise than blunt expressions like simply buying or selling an underlying stock.
We can demonstrate this with a stylized example:
Consider a stock that is fairly priced at $100 because in the next year the market believes there is a 20% chance it goes to $500 and an 80% chance it goes to zero. In such a scenario, the 500-strike call will be valued at zero.
Suppose you believe the stock is fairly priced but the distribution is more skewed. There’s a 10% chance it’s worth $1,000 and a 90% chance it’s worth $0. Although the value of the stock is unchanged, the 500-strike call is now worth $50! [There’s a 10% chance of it going $500 in-the-money]
The option market offered you an opportunity to make a finer-tuned bet that the underlying market did not. Your bet is that the volatility and skew of this stock are both higher than consensus. These are the mispriced parameters. Buying the call instead of the stock is the right expression of the bet.
The noise comes from the fact that you cannot know the true distribution even after the stock makes its move. That’s a single draw from many possible futures. The existence of many counterfactuals suggests that drawing conclusions from individual outcomes is a fool’s errand. But noise is unavoidable no matter what type of investing you are doing. But the ability to fine-tune the bet with options is undisputable.
2) Suitability
The trade expression should make sense with respect to your general constraints. If you are selling options to capture an excessive VRP, a form of carry, then you would delta hedge to isolate the p/l to the difference between realized and implied volatility (at least to a first approximation).
If you do not dynamically hedge, the delta p/l will swamp your volatility p/l. The tradeoff is that hedging is a direct cost comprising of fees and slippage. These costs are not noise — they will deterministically cost you expectancy (since your source of edge is not in predicting direction). By sterilizing directional risk, the costs allow the trade expression of “being short a straddle” to be mostly exposed to the option prices being expensive.
If hedging costs are prohibitive you can choose alternative expressions. For example:
spread trades that have less directional exposure
you may simply accept noise but let diversification via a large quantity of trades smooth the results.
A variance swap is the purest expression of a VRP trade but it is not easily accessible, and therefore unsuitable for the typical investor.
As we proceed with a taxonomy of trades that express the investor's "axe" or attempt to monetize a mispriced parameter, we will discuss how they fare on both dimensions of isolation and suitability.
Taxonomy of Trade Expressions Based On P/L Driver
Repetition is good. I’ll reiterate — the funnel process works in 2 ways:
1) It decants option surfaces to separate what's normal or fair from possible mispricings.
2) It helps you drilldown into where on the option surface the “view you woke up with” is mispriced.
In both cases, after your discretion adds a layer of restraint, you target a trade expression to monetize the mispricing. This is true whether you are speculating or hedging.
We categorize 3 sources of P/L that drive monetization of the mispricing:
Distributional (driven by the realized destination of the underlying)
Carry (driven by realized volatility)
Surface re-pricing (driven by changes in the implied volatility surface)
It is useful to think in these categories because it frames the management of the position. The categories bleed into one another but the way a position is managed can dramatically alter which driver dominates.
Having a clear understanding of what your expression is trying to monetize will:
a) keep you from drifting into a driver that you didn’t have an opinion on
b) save you from overtrading
Distributional Trades
These are trades driven by the stock’s destination
Unhedged vertical spreads
Examples:
1) Buying or selling a call spread or put spread.
A stock is $50 and you pay $2.00 for the 55/60 call spread. You risk $2 or make as much as $3 if the call spread expires worth $5.
2) Buying or selling a butterfly
You pay $.50 for the 55/60/65 call fly. If the stock expires exactly at $60 the fly is worth $5! The most you can lose is the $.50 outlay.
Description
A vertical spread is a “model-free” bet on the stock’s distribution by expiration. We say “model-free” because the structure is immune to modeling assumptions about the underlying distribution. Why? Because you buy and sell an option within the same month. The closer the strikes, the less sensitive the trade is to assumptions. It’s a pure probability bet. The call spread example can be reframed as:
"I’m getting paid 3-2 odds on the stock expiring $60 or higher". If you think the probability is greater than 40% then this is a positive expected value bet. This is less complicated than understanding if a single option is being priced for say $5 because it has a 10% chance of expiring $50 in-the-money or a 50% chance of expiring $10 ITM. We can focus on the probability without being highly sensitive to the magnitude.
Aside on over/under vs futures style bets: the role of expected value
Suppose the median time to drive to work is 10 minutes. Consider these bets:
a) Over/Under Bet: If you get to work in 10 minutes or less you get paid $1, otherwise $0.
The contract will trade for $.50. The median data suggest it’s 50% to be worth $1 or $0
b) Futures-style Bet: the payoff is exactly how many minutes it takes drive to work. (If the commute takes 9 minutes it settles at $9)
This contract will not trade for $10. Because the average time to get to work is higher than 10 minutes. There’s a lower bound on how fast you can get to work, but traffic or any unforeseen problem (you realize you left the garage door open) will delay your commute time. So there’s positive skew to your commute time. The median time might be 10 minutes but the average time might be 15 minutes because of those random bad days. The futures-style contract will trade closer to $15 because it is based on expectancy — probability times magnitude.
The value of the contract is highly sensitive to the length of the right tail.
Outright options share this sensitivity. Vertical spreads cut the tails off reducing the bet to one of probability alone.
Vertical spreads are best used when you have a directional view for speculation or hedging.
Your fundamental or upstream analysis handicaps a probability that is mispriced or fairly priced (getting a fair price on a hedge is a great deal. If you can buy life or car insurance for its actuarial fair value, you’d be thrilled to cut the risk for no cost in expectancy).
Suitability
An unhedged vertical spread is a clean trade. If you hold until expiration, the potential risk and reward are perfectly defined.
Isolation
If you have a nuanced view on the probability of certain moves, the trade expression embodies “get paid for the risk you want, discard the rest”.
The decision to sell (buy) options that are expensive (cheap) is based on an expectation that the implied volatility will revert or expand towards a more “fair” relationship either to its own history, its realized volatility, or its relationship with implied volatility in other assets.
Carry/VRP Trades
These trades are driven by realized volatility
Examples
Hedged options, straddles, strangles
Hedged vertical spreads
Description
Since you are explicitly trying to sell (buy) options that are expensive (cheap) compared to how the stock is moving you either:
delta hedge to sterilize your exposure to the asset’s direction, isolating your bet on volatility
do lots of trades and let the directional risks cancel out
When your lens is that the option is cheap or expensive compared to the realized volatility you will typically choose options that are:
relatively near-dated (1-month or less as a heuristic) because that’s where the gamma and theta (the cost of gamma) is highest
at-the money
Suitability
Straddles are most suitable for trading VRP because they are:
approximately delta-neutral (at least at the start)
only sensitive to first-order changes in volatility which drives a VRP thesis
Strangles are suitable if you have a view on normalized skew as well as volatility.
Delta hedged vertical spreads embed a view on realized skew. For example, buying an ATM put and selling a downside put on a delta-neutral is a complex trade. The delta required to hedge the trade is difficult to calibrate for the further OTM option because it depends on the correlation of implied volatility to underlying price. For example, if the downside put vols expand rapidly on a sell-off the option is acting as if it has a higher delta than an off-the-shelf model predicts. This type of trade is only suitable for dedicated, experienced volatility traders.
Isolation
Straddles are the most direct expression of VRP trades. If they are relatively near-dated, the vega attribution of the p/l will be swamped by the interaction of gamma vs theta. The longer-dated the option, the less dependent the expression is on realized volatility.
The more you hedge the delta, the more closely you “sample” the realized volatility and the less noise there is in the final p/l. The less noise the more the p/l reduces to the interaction between the implied vol you traded and the realized volatility. The trade-off to isolating the expression by hedging is the increased transaction cost (fees + slippage).
⚠️Caution: Vanilla options are never pure bets on VRP because of path dependence. As the stock moves around, the gamma exposure of the option changes. An option that is 10% out of the money has less gamma and theta than an ATM option. Its value is less dependent on the daily moves (even net of the delta which is presumably hedged). Another way of appreciating this is to recognize that your option position doesn’t “re-strike” every night back to the new ATM price.
Surface Re-pricing
These trades are driven by changes in the implied volatility surface
Examples
Buying/selling straddles or outright options on a delta-hedged basis
Description
The decision to sell (buy) options that are expensive (cheap) is based on an expectation that the implied volatility will revert or expand towards a more fair relationship either to its own history, its realized volatility, or its relationship with implied volatility in other assets.
Suitability
Longer-dated options or short-dated options where the implied volatility is itself highly volatile are suitable for expressing bets on IV.
Why?
A long-dated option has a large vega, or sensitivity to implied volatility. The vega profits will swamp the p/l due to realized volatility (ie the interaction between gamma and theta)
A short-dated option with an implied volatility that has large changes can generate meaningful p/ls despite having lower vega sensitivity. A $2.50 option with a vega of $.03 per vol point can move $.30 cents in one day if the volatility changes by 10 points (all else equal). Think meme stocks. If the implied volatility trades in a tight range, short-dated options don’t have enough vega to make them suitable for betting on implied volatility.
Isolation
If you are betting on implied volatility then ideally you should delta hedge. You are trying to isolate the p/l to changes in volatility, not stock direction.
Path dependence is less of a concern with long-dated options since the options have less gamma and critically the gamma profile is more smooth (versus a short-dated option where suddenly your exposure can flip from lots to negligible amounts of gamma or vice-versa).
If you trade lower delta (ie out-of-the-money instead of straddles or at-the-moneys) options, the vega profile can change with the vol level. Your position’s sensitivity to volatility can rise or fall as volatility itself rises and falls. If you don’t have a view on normalized skew, then isolate your strike choices to options closer to .50 delta.
It’s useful to mentally frame your source of edge while recognizing that the categories of trade contain overlap. This section gives special treatment to a class of popular trades that have a strong overlap between distributional and carry drivers.
Thoughts On Popular Trade Expressions
Because they are popular, they are also poorly appreciated because they are typically promoted by marketers rather than explained with depth. We’d rather give consumers credit for caring about the drivers of the p/l.
The following examples have significant overlap between destination and realized volatility.
Covered Calls & Cash Secured Put Selling
These trades are driven by realized volatility
Covered calls are still bets on volatility. Think about it. You are disappointed by extreme moves in the stock in either direction. If the stock has a giant rally you forgo profits and if it tanks you own the entire downside minus the fixed premium you collected.
If the logic is “I'm going to hang on forever, even if it goes down anyway” you have chosen a strange p/l asymmetry — pre-commitment to cut winners and let losers ride. You have confessed that when you bought the stock you would never sell for a loss.
If logic is to hedge, it's a peculiar choice to want the hedge for small moves as opposed to large ones.
The covered call seller’s implicit logic is they are trying to generate yield by monetizing a volatility premium (VRP). This is an acceptable and honest framing. With that established, we can proceed.
Let’s treat covered calls way they should be treated — as a volatility trade. It’s a VRP carry trade. The price of the volatility should drive the decision to execute it…or not.
Employ the same lens we used above for funneling VRP trades. The fact that you already own the shares should not influence the decision process.
Cash-secured put selling is a symmetrical problem. If the stock moves far away from the strike to the upside you have forgone buying it in exchange for a fixed premium and if the stock tanks far below the strike you have lost the chance to buy it much cheaper.
“Stock Replacement” Call Buying
These trades are driven by realized volatility and stock direction.
Description
“Stock replacement” is a strategy where you liquidate your holdings of a stock and use a portion of the proceeds to buy call options.
The P/L is straightforwardly dependent on the stock direction and volatility, as you might expect from any outright trade in a single option. But the framing is worth mentioning as a foil to selling covered calls.
If you replace your long shares with a long call position you do significantly better on extreme moves.
In the case of a rally, your return is levered
In the case of a sell-off, your loss is limited to the premium.
The nature of put-call parity, is evident. By owning a call option and losing far less in the event of a sell-off, you can prove that the payoff was algebraically equivalent to owning the stock plus a put as insurance.
A stock-replacement strategy is suitable if you want to maintain a long position but have bearish concerns.
Your worst-case scenario is a real loss — the case where the stock continues to rally up until the strike and stops. You have:
forgone the limited profit between the share price you sold (in the case of an out-of-the-money call) and the strike
lost the call premium
Calendar Spreads
These trades are driven by relative changes in implied volatility between the strikes and the realized volatility.
Description
A calendar spread or roll is the purchase (sale) of an option in a deferred month vs a sale (purchase) of an option in a nearer month. The strikes are the same in each month.
If you buy a calendar spread (pay premium to buy the deferred month and sell the near-dated) the most you can lose is the premium if you do not delta hedge. If you consider an extreme scenario where the stock goes to zero, both options will be worthless and you’ll lose the premium.
Considerations when purchasing a calendar spread without hedging the delta:
You win if the implied volatility of the second month increases faster than the near month or even if there is a parallel shift higher in the volatility term structure. Because you own the longer-dated option your position is net long vega. However if the near-dated volatility increases much faster than the deferred month, the value of the calendar spread can fall resulting in a loss.
If you construct a calendar spread trade on 2 deferred options, the net theta will be smaller. This is a purer play on forward volatility (the relative implied volatilities between the 2 months). It’s not a perfectly pure trade because of path dependence. As the stock moves away from the strike, the sensitivity of the options to volatility (ie the vega) shrinks and the delta spread between the options increases leading to greater exposure to directional moves.
The major risk is the stock makes a large move. Again if it went to zero, the calendar spread would go to zero. If the stock doubled, both calls would be deep-in-the-money and likely trade for the same price as they would both be comprised of only intrinsic value. Take note — the calendar spread has a maximum loss equal to the premium paid and benefits from the stock standing still.
🦋The calendar spread behaves similar to buying a butterfly! If the stock is unchanged we expect the price of the calendar spread to increase by the net theta of the 2 options overnight. This makes sense because the spread is short the faster-decaying option, so the structure is collecting theta.
Verdict
Calendar spreads can be messy implementations of realized volatility or relative implied volatility expressions. But forward volatility analysis is still highly useful for choosing where on the term structure you find the most value in expressing your desired trade even if you don’t take an offsetting position in another month.
References
In The Laws of Trading by Agustin Lebron, rule #3 states:
Take the risks you are paid to take. Hedge the others.
This principle emphasizes the importance of isolating your bets to align as closely as possible with your original reason for wanting the exposure. It's about focusing on the risks that are part of your strategy and hedging or eliminating the ones that are not.
Structuring
Straddles
Vertical Spreads