Long-Term Stock Market Volatility Datapoint of the Day

By Felix Salmon
March 29, 2009

Warren Buffett, take note:

Although mean reversion makes a strong negative contribution to long-horizon variance, it is more than offset by the other components. Using a predictive system, we estimate annualized 30-year variance to be nearly 1.5 times the 1-year variance.

The subject is the stock market, and the paper in question, which Mark Hulbert writes about in the NYT today, could well give the Sage of Omaha some sleepless nights, since Buffett famously accepted a $4.5 billion bet, very near the top of the market, that stocks would go up in the long run and not down.

There’s been a lot of debate surrounding the bset way to mark Buffett’s losses on that bet: while the base case is to use Black-Scholes, a vocal contingent of Buffett supporters has said that it’s silly to use today’s elevated volatility to price long-dated European-style options which can only be exercised on one specific date. Over the long term, they say, stock-market volatility is much lower than we’re seeing right now.

Well, it has been in the past. But how much reason do we really have to believe that the future of the US stock market is going to resemble the past of the US stock market, rather than simply wending its way, in a necessarily volatile fashion, towards zero? Empires do fall, after all, and one of the co-authors of the paper, Robert Stambaugh, points out that the probability of global warming proving catastrophic for the stock market, while it can’t be calculated with any specificity, is surely non-zero. Stambaugh’s co-author, Lubos Pastor, generalizes:

Professor Pastor emphasized that the last two centuries could easily have been less hospitable to the United States, most likely lowering the stock market’s returns. An investor couldn’t have known in advance that the United States would win two world wars, for example, or emerge victorious from the cold war. In any case, he said, there is no guarantee that the next two centuries will be as kind to the domestic equity market as the last two.

This is exactly why an unknown set of counterparties paid Warren Buffett $4.5 billion: for his triple-A-rated guarantee that over a very long time horizon, something catastrophic and unexpected wouldn’t happen to US equities. If you couple that guarantee with some credit protection written on Berkshire Hathaway, you come close to having a very powerful insurance policy against black swans. You can’t clip tails outright. But clearly there are some people trying their hardest to minimize their tail risk. Maybe they put more stock in Bayesian analysis than Buffett does.

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