The Beauty of Option Theory

This past weekend, I cloaked myself in the robe of imposter syndrome and gave a talk to a small group of sophisticated investors. I don’t consider myself a great investor, my core portfolio is a simple asset allocation model in the vein of a permanent portfolio. The point of it is to preserve wealth so I have the slack to take shots using my human capital which I have more faith in than the meanderings of a drunk market.

That wasn’t going to be interesting to a group like this (although it’s a topic worth plenty of discussion for the average saver). Instead, I decided to talk about the beauty of options. It fails the test of giving a directly actionable investment idea, but if it helps extend an investor’s mental toolbox it would at least be worthwhile. Plus, I’m a hedgehog. Options are probably the only thing I’m justified to pontificate on. A pathetic, dull boy in 99% of contexts, but hopefully value-added here.

I started with the practical before wandering into the aesthetic.

A Practical Option Consideration

  1. The directional use of options is trivial because most of the work is upstream of the option expression. If you have a divergent view of an asset’s distribution from what the volatility surface implies, trade expressions are often obvious. Any decent option broker or junior level option trader could probably help.

  2. So-called “vol trading” is irrelevant to 99% of the investing world  — it’s a low-margin business relying on the law of large numbers while also being capacity-constrained. In the bigger picture, it’s chess-boxing — nerds fighting. If you want to be really rich, find a way to get paid on beta.

  3. If directional trading is the most common use of options, then covered calls and hedging are the next most common. We can use a “replication mindset” to understand that even when you sell covered calls (or hedge) you are, regardless of how promoters sell the idea, engaging in a volatility trade. Consider my logic:

    • The alternative to selling a 20d call monthly: you can sell 20% of your position instead.

      1. Call selling: You get called away on your position about 1 in 5 months

      2. Selling the stock: you are out of your position in 5 months

    • The false accounting that the call seller uses to rationalize: “I get called away on my position less than 20% of the time so actually selling the calls is better”

    • Reality: You are failing to account for the times when the stock dives where you don’t get assigned on your short calls, but you would have been better off to have sold 20% of your position.

      The spread between the false accounting and reality is a function of the volatility that was realized vs the IV you sold¹

      When you sell covered calls, whether it was a better choice than just selling the equivalent fraction of your position depends on what vol is realized vs what vol you sold.

      If you sell calls too cheap you are better off just selling a fraction of your position and that’s why you shouldn’t sell calls indiscriminately for “income”. You need to consider whether the price is right.

Stop thinking of options through the lens of directional trading — you are still just trading volatility.

The Beauty of Options

I don’t actively encourage investors to trade options. In “Do You Even Trade Bro?” I offer a framework for deciding if you should bother. That said, learning about options and portfolio theory is worthwhile in both an appreciative sense — options are a “bicycle for the mind” and because it’s a useful lens for decision-making. Decisions are options.

The beauty of options theory and arbitrage pricing, in general, is in its replication mindset. Pricing derivatives is an exercise in finding and valuing a portfolio that would mimic the derivative’s payoff. If we combine the derivative with its replication, we have constructed a risk-free portfolio. The Black-Scholes formula prices an option by showing (under faulty but useful assumptions) that its cost should be equal to a trading strategy that rebalances a mix of cash and underlying shares until expiration. The rebalance between cash and shares depends on the probability of the underlying going through the strike price and by how much. That probability depends on the volatility of the asset and its distance from the strike, all normalized by time.

By studying the concept of replication (ie arbitrage pricing theory) you gain a new mental tool for approaching decisions.


  1. In How Much Extra Return Should You Demand For Illiquidity?, I provide an options-based approach to thinking about how much extra yield you might require to hold a bond (like an EE bond or annuity-type investment) that you cannot sell. The key is to price the illiquid asset like the liquid version of the investment (ie Treasury bond) as the illiquid plus the option to rebalance. The higher the volatility, the more the rebalance option is worth. This confirms your intuition — the more volatile the world becomes, the more we should value liquidity.

    If there is a large discount to buy an illiquid version of an investment, you are being offered a “deal” to effectively short volatility by abandoning the option to rebalance. When illiquid investments (ahem PE) argue that the illiquidity is an advantage for behavioral reasons (”protect yourself from selling during periods of stress”) they are standing in defiance of financial theory.

    If you understand options conceptually, you can inoculate yourself from such motivated sales pitches. As an investor, if the stock market drops 25% and PE is not marking itself down, then you’d want to liquidate your PE investment at the nonsense mark and rebalance into the public markets. Of course, you can’t do that because the PE mark is not tradeable and you have forgone your option to rebalance. By not understanding options, you are the mark.

  2. Understanding when a typical situation now has an option embedded

    In Options on USO when oil went negative, I show how a popular oil ETF became an option. It began trading at a significant premium to its NAV — but thinking this was wrong was a fool’s trade. USO had turned into an option instead of a futures or “delta one” equivalent and the premium to NAV represented the volatility value of the option. (An easy way to see that USO had turned into an option is to realize you could have bought USO and shorted CL oil futures to structure a riskless trade — USO cannot go below zero but futures can!)

  3. A final example comes from portfolio theory in general.

    Portfolio theory shows us that if we have 2 assets that are only loosely or perhaps negatively correlated, a portfolio comprising a mix of both assets can have a better risk/reward than either of the components. In You Don’t See The Whole Picture, I give a simple math example to demonstrate this principle.

    This principle has a deep implication — it means you don’t get paid for taking diversifiable risks. If I own a sunglasses company, I am the most “efficient bidder” for an umbrella company because I can diversify my weather risk. If markets are liquid, transparent, and the world transmits information cheaply then I should only expect to get paid for risks that are systematic, not idiosyncratic. Idiosyncratic risks are the types that can be diversified by being held by a party who owns the opposite type of risk (like the sunglasses/umbrella example).

    A real-world example of this is the vol premium in oil puts when Pemex conducts its annual “Hacienda” hedge. Pemex, Mexico’s national oil company, hedges its forward production by buying puts and put spreads on oil futures. Typically this increases the value of the puts, enticing risk capital and arbitrageurs to sell the puts at a price that they believe exceeds their replication value.

    However, I remember a year when Delta Airlines sold them the puts at a relatively fair price. This was a win for both Pemex and Delta. Delta is happy to sell the puts because they are “natural buyers” of oil via jet fuel (Delta also owns a refinery!)

    This is a great example of markets doing their job. A risk that could be diversified was paired off between natural counterparties. However, from another perspective, this is bad news for investors who expected to earn the “sell expensive puts” risk premium. If a risk premium exists but it diversifies another party’s exposure, then that party can afford to pay more for it than the standard speculator. So the efficient frontier for speculators is just the set of investments that contain systemic risks that cannot be hedged.

The most obvious example is the equity risk premium in general — the corporate world is levered to financial growth. Corporations are owned by people in the population. Once all risks are netted, there is no stakeholder remaining who benefits from economic collapse. Therefore the only carrot to entice someone to invest in corporations, effectively doubling down on their reliance on economic growth, is a yield in excess of the risk-free rate. That’s an undiversifiable risk premium.

I’ve given more examples in *Why You Don’t Get Paid For Diversifiable Risks, but like any model or theory it’s not water-tight. It’s useful. This one is a reminder to consider if the risk you are being asked to underwrite should command a premium. If it was hedgeable by someone else more cheaply, why did it show up on your doorstep labeled “excess return”?


  1. technically it’s that spread times your dollar gamma which is mathematically how path-dependency expresses itself in the p/l

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