Primer #2: The Nature Of Options
moontower.ai Primer #2
As promised, moontower.ai includes a primer which is being dripped 1 post a week right here on substack.
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Markets are like democracies in the sense that they are decision-coordinating mechanisms. They are people-driven. They can be wise or mad. They learn and adapt.
But markets are also critically different from democracies. A market’s price outputs are not equally weighted by votes. They represent dollar-weighted preferences.
I say preference not prediction because they are biased.
To illustrate the point, imagine a contract that settles to $1.00 based on a fair coin flip turning up heads. You’d expect it to trade for $.50. That represents an unbiased expectation. And we’d expect it to trade at the unbiased price because if it traded for any cheaper price you could buy the contract and diversify the risk by placing bets on many coin flips. The law of averages over a large sample would make your “theoretical” profit a reality.
However, if you bought every asset in the world, effectively diversifying like the multiple coin example, you’d still be exposed to the systematic risk of something like a global slowdown in economic activity. Therefore, the price must offer the buyer a risk premium in excess of the risk-free rate.
As a rough heuristic, you can think of investing in the SP500 as a proposition which offers say 3-7% excess return above the risk free rate in exchange for about 20% annual volatility and the possibility of a steep drawdown. The argument feels a bit circular — “the risk premium exists because if it didn’t nobody would take risks beyond the risk-free rate”. It’s also common sense. You would prefer a guaranteed 10% return over a 10% expected return.
A market is a weighted voting mechanism reacting to a mix of expectations and risk preferences.
What is a "complete" market?
Consider 2 stocks:
a) A biotech stock whose business relies on single medical innovation being approved
b) A diversified conglomerate
Assume:
The risk-free rate is 0
Investors are indifferent between a risky and riskless outcome
The biotech stock has a 10% chance of being worth $1000 and a 90% chance of going to zero.
The conglomerate has a 50/50 chance of being worth $120 or $80
The fair value of both stocks today is $100 representing the weighted expectation of the outcomes.
But this $100 price feels "flat" or 2-dimensional. It obscures reality — these stocks have completely different distributions and risk-profiles. If you knew the distributions were so different you would size them differently.
Hold that thought, as you read this definition:
A complete market is one in which the complete set of possible bets on future states of the world can be constructed with existing assets… goods are state-contingent; that is, a good includes the time and state of the world in which it is consumed. For instance, an umbrella tomorrow if it rains is a distinct good from an umbrella tomorrow if it is clear.
Welcome to Options!
Options help complete the market. They give you more choice. In the previous example, the 200 strike call option on the conglomerate is worthless. But it’s worth $80 for the biotech stock (10% chance of being $800 in-the-money).The call is almost worth the price of the stock itself!
The call options have vastly different values even thought the stocks are the same price.
The beauty of options is they are priced for specificity.
Options will:
1) Fine-tune your bets
Pay only for the risks you want, for the time period you want. Discard the risks you don’t want. This allows you to paint with fine brushes instead of a roller. It is a creative unlock! You can even make bets that have nothing to do with the direction of the stock but on a changing perception of the stock’s risk or distribution.
2) Highly leverage the bet to whether its right or wrong
If you are correct on your idea and the timing/volatility you get paid extra. Loosely similar to a parlay. If you are right on one and not the other, your outcome may be ambiguous. Wrong on everything and, well, knowledge will be the only thing you gain.
The focus of moontower.ai is options
This bears clarifying a misunderstood idea:
Options are actually not zero-sum in a practical sense.
It’s true that options are zero sum in dollar space. Assuming an option is unhedged, the buyer and seller of an option cannot both win.
But options are not zero sum under 2 possible conditions:
1) The option is hedged.
If I buy a call option 10% out-of-the-money and the stock goes up 20% then I will win at expiration. The option seller who hedges by purchasing the stock can also win if the stock rallies slowly. The losers are the counterparties who sold the hedger that stock. This is not a revelation but simple accounting.
2) Options are not zero-sum if we measure “utility”
Utility is a nebulous economics term that can be appreciated by analogy:
A voluntary decision to buy home insurance means by definition that both buyer and seller are better off. The insurance company makes actuarial profit and you sleep better at night knowing a fire doesn’t destroy your nest egg. The story of finance itself is the efficient pricing and transfer of risk. A zero-sum transaction in “dollar space” is positive sum in “utility space” because the most efficient holder of a given risk is the highest bidder to warehouse it.
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