Berkshire Hathaway Letters to Shareholders: 1965-2024

by Warren Buffett

It’s often useful in testing a theory to push it to extremes. So let’s postulate that we sell a 100-year $1 billion put option on the S&P 500 at a strike price of 903 (the index’s level on 12/31/08). Using the implied volatility assumption for long-dated contracts that we do, and combining that with appropriate interest and dividend assumptions, we would find the “proper” Black-Scholes premium for this contract to be $2.5 million. To judge the rationality of that premium, we need to assess whether the S&P will be valued a century from now at less than today. Certainly the dollar will then be worth a small fraction of its present value (at only 2% inflation it will be worth roughly 14¢). So that will be a factor pushing the stated value of the index higher. Far more important, however, is that one hundred years of retained earnings will hugely increase the value of most of the companies in the index. In the 20th Century, the Dow-Jones Industrial Average increased by about 175-fold, mainly because of this retained-earnings factor. Considering everything, I believe the probability of a decline in the index over a one-hundred-year period to be far less than 1%. But let’s use that figure and also assume that the most likely decline — should one occur — is 50%. Under these assumptions, the mathematical expectation of loss on our contract would be $5 million ($1 billion X 1% X 50%). But if we had received our theoretical premium of $2.5 million up front, we would have only had to...