Monday, March 2, 2009

Buffett’s Justification of Option Trading Misses the Mark

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 U.S. 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 U.S. 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.


  1. Yes, I agree these derivatives are unlikely to result in losses because the stock market has a bias for going up over time, for the reasons Buffett mentioned: retained earnings and inflation. The longer term the call, the less likely they will pay off.

    Reminds me of Buffett's opposition to non-indexed stock options. A company retaining earnings will likely go up in value over time, similar to a bank account with compounding interest.

    I think his point about volatility causing mispricing is more applicable to the quarter to quarter changes in the value these derivatives are carried at on the books. Of course, the past six months or so have been extraordinarily volatile.

    His example of a one-hundred year derivative contract being affected by the volatility in the first year is valid, as is your argument about the low risk of loss.

  2. Gene: I agree that Buffett's argument about using Black-Scholes with recent volatility figures is the cause of quarter-to-quarter fluctuations in the accounting value of the put portfolio. However, the following statement of his is misleading:

    "The ridiculous premium that Black-Scholes dictates in my extreme example 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."

    Black-Scholes tends to heavily overvalue long-term put contracts because is uses a risk premium of zero. Volatility measures at any given time will cause put premiums to be overvalued by more or less, but sufficiently long-term put contracts are always overvalued.

    It's possible that Buffett understands all this perfectly well and has adjusted the Black-Scholes formula to compensate, but it's hard to give him credit for this from what he wrote.

  3. Quite right, Michael James. After I wrote my comment, I realized I was probably putting words in your mouth. What do they call it in debating? A straw man? Inadvertent on my part, I apologize.

    I suspect Buffett doesn't think volatility deserves a spot in valuing options, since he considers volatility to be noise, especially on long-dated derivatives. But, yes, I agree with your thinking he wrote these puts based on it being mis-priced risk, not mis-priced volatility.

    To go off topic a bit, I thought his letter was pretty mild mannered this year. I suspect he will be more critical and outspoken at the annual meeting.