I disagree with Warren Buffett on a point about his stock option trading. There, I said it (or wrote it). It’s rare that I disagree with anything Buffett writes. In fairness, it’s not that I think he made a poor investment. It’s just that I think the real explanation of why his investment is a good one is different from his justification.
Buffett’s eagerly anticipated 2008 letter to shareholders of Berkshire Hathaway arrived on Saturday. It contains his usual brilliant financial insights expressed clearly. Any number of reporters will summarize its contents, but those interested should consider reading the original letter as well.
One aspect of the letter that caught my attention was the discussion of Buffet’s option trading. He believes that certain long-term put options are mispriced, but his explanation of why they are mispriced leaves out the dominant reason.
Buffett has sold put contracts on the world’s major stock indices. These contracts amount to bets between Buffett and other parties on the value of a stock index at some future point in time called the maturity date. I can’t improve on Buffett’s explanation of these put options:
“To illustrate, we might sell a $1 billion 15-year put contract on the S&P 500 when that index is at, say, 1300. If the index is at 1170 – down 10% – on the day of maturity, we would pay $100 million. If it is above 1300, we owe nothing. For us to lose $1 billion, the index would have to go to zero. In the meantime, the sale of the put would have delivered us a premium – perhaps $100 million to $150 million – that we would be free to invest as we wish.”
Buffett has sold a total of US$37.1 billion in put contracts on the world’s major stock indices: the US S&P 500, the UK FTSE 100, the Euro Stoxx 50, and the Japanese Nikkei 225. To take on the risk of possibly having to pay some fraction of this $37.1 billion, Buffett has collected $4.9 billion in option premiums.
The accepted way to value stock options is with a formula called Black-Scholes. This formula predicts that he is expected to pay out $10 billion on his put option contracts. If this turns out to be right, he will pay out $5.1 billion more than he collected in premiums.
Obviously, Buffett doesn’t believe the Black-Scholes formula or he would never have entered into these contracts. He explains that “if the formula is applied to extended time periods, however, it can produce absurd results.” Buffett continues:
“The ridiculous premium that Black-Scholes dictates ... is caused by the inclusion of volatility in the formula and by the fact that volatility is determined by how much stocks have moved around in some past period of days, months or years. This metric is simply irrelevant in estimating the probability weighted range of values of American business [many] years from now.”
Problems with estimating volatility are a factor, but the real reason why the formula fails for long-term options is much simpler. Black-Scholes denies the existence of a risk premium. You don’t need to understand the formula to see that it has no input for the expected return of the equities.
Black-Scholes assumes that the expected return of stocks is equal to the risk-free return of short-term government debt such as US treasury bills. However, historical data tell us that stocks give better returns, on average, than government debt. This failing of the formula doesn’t significantly affect calculations of the premium for short-term options, but gives absurd results for multi-decade options.
An easy way for Buffett to see that risk premium is a major factor is to look at long-term call options. If volatility were the main reason why he finds selling long-term put options profitable, then he should find selling call options to be profitable as well. After all, overestimating volatility drives up the premiums of both puts and calls.
However, I’m confident that Buffett would find long-term call options much less attractive than long-term puts due to the risk premium.