strategy for the option. The expected return of the underlying is irrelevant to this strategy. The only distributional property of the underlying that is used in the BSM model is the volatility. A hedged position will, on average, make a profit proportional to the difference between the volatility implied by the option market price (by inverting the BSM model) and the subsequent realized volatility. The choice of the option structure and hedging scheme can change the shape of the PL distribution, but not the average value. These choices are far from immaterial, but successful option trading depends foremost on finding situations in which the implied volatility is mispriced.
Summary
Arbitrage-free option pricing models do not include the underlying return. BSM includes only volatility.
Inverting the pricing model using the option's market price as an input gives the implied volatility.
The average profit of a hedged option position is proportional to the difference between implied volatility and the subsequent realized volatility.
Practical option hedging is designed to give an acceptable level of variance for a given amount of transaction costs.
CHAPTER 2 The Efficient Market Hypothesis and Its Limitations
A lot of trading books propagate the myth that successful trading is based on discipline and persistence. This might be the worst advice possible. A trader without a real edge who persists in trading, executing a bad plan in a disciplined manner, will lose money faster and more consistently than someone who is lazy and inconsistent. A tough but unskilled fighter will just manage to stay in a losing fight longer. All she will achieve is being beaten up more than a weak fighter would.
Another terrible weakness is optimism. Optimism will keep losing traders chasing success that will never happen. Sadly, hope is a psychological mechanism unaffected by external reality.
Emotional control won't make up for lack of edge. But, before we can find an edge, we need to understand why this is hard and where we should look.
The Efficient Market Hypothesis
The traders' concept of the efficient market hypothesis (EMH) is “making money is hard.” This isn't wrong, but it is worth looking at the theory in more detail. Traders are trying to make money from the exceptions to the EMH, and the different types of inefficiencies should be understood, and hence traded, differently.
The EMH was contemporaneously developed from two distinct directions. Paul Samuelson (1965) introduced the idea to the economics community under the umbrella of “rational expectations theory.” At the same time, Eugene Fama's studies (1965a, 1965b) of the statistics of security returns led him to the theory of “the random walk.”
The idea can be stated in many ways, but a simple, general expression is as follows:
A market is efficient with respect to some information if it is impossible to profitably trade based on that information.
And the “profitable trades” are risk-adjusted, after all costs.
So, depending on the information we are considering, there are many different EMHs, but three in particular have been extensively studied:
The strong EMH in which the information is anything that is known by anyone
The semi-strong EMH in which the information is any publicly available information, such as past prices, earnings, or analysts' studies
The weak EMH in which the information is past prices
The EMH is important as an organizing principle and is a very good approximation to reality. But, it is important to note that no one has ever believed that any form of the EMH is strictly true. Traders are right. Making money is hard, but it isn't impossible. The general idea of the theory and also the fact it isn't perfect is agreed on by most successful investors and economists.
“I think it is roughly right that the market is efficient, which makes it very hard to beat merely by being an intelligent investor. But I don't think it's totally efficient at all. And the difference between being totally efficient and somewhat efficient leaves an enormous opportunity for people like us to get these unusual records. It's efficient enough, so it's hard to have a great investment record. But it's by no means impossible.”
—Charlie Munger
Even one of the inventors of the theory, Eugene Fama, qualified the idea of efficiency by using the word good instead of perfect.
“In an efficient market, at any point in time, the actual price of a security will be a good estimate of its intrinsic value.”
—Eugene Fama
There is something of a paradox in the concept of market efficiency. The more efficient a market is, the more random and unpredictable the returns will be. A perfectly efficient market will be completely unpredictable. But the way this comes about is through the trading of all market participants. Investors all try to profit from any informational advantage they have, and by doing this their information is incorporated into the prices. Grossman and Stiglitz (1980) use this idea to argue that perfectly efficient markets are impossible. If markets were efficient, traders wouldn't make the effort to gather information, and so there would be nothing driving markets toward efficiency. So, an equilibrium will form where markets are mostly efficient, but it is still worth collecting and processing information.
(This is a reason fundamental analysis consisting of reading the Wall Street Journal and technical analysis using well-known indicators is likely to be useless. Fischer Black [1986] called these people “noise traders.” They are the people who pay the good traders.)
There are other arguments against the EMH. The most persuasive of these are from the field of behavioral finance. It's been shown that people are irrational in many ways. People who do irrational things should provide opportunities to those who don't. As Kipling (1910) wrote, “If you can keep your head when all about you are losing theirs, … you will be a man, my son.”
In his original work on the EMH, Fama mentioned three conditions that were sufficient (although not necessary) for efficiency:
Absence of transaction costs
Perfect information flow
Agreement about the price implications of information
Helpfully for us, these conditions do not usually apply in the options market. Options, particularly when dynamically hedged, have large transaction costs. Information is not universally available and volatility markets often react slowly to new information. Further, the variance premium cannot be directly traded. Volatility markets are a good place to look for violations of the EMH.
Let's accept that the EMH is imperfect enough that it is possible to make money. The economists who study these deviations from perfection classify them into two classes: risk premia and inefficiencies. A risk premium is earned as compensation for taking a risk, and if the premium is mispriced, it will be profitable even after accepting the risk. An inefficiency is a trading opportunity caused by the market not noticing something. An example is when people don't account for the embedded options in a product.
There is a joke (not a funny one) about an economist seeing a $100 bill on the ground. She walks past it. A friend asks: “Didn't you see the money there?” The economist replies: “I thought I saw something, but I must've imagined it. If there had been $100 on the ground, someone would've picked it up.” We know that the EMH is not strictly true, but the money could be there for two different reasons. Maybe it is on a busy road and no one wants to run into traffic. This is a risk premium. But maybe it is outside a bar where drunks tend to drop money as they leave. This is an inefficiency.