Berkshire Hathaway - Chairman's Letter

I was much closer then Gary Ransom.  

Me: 

Therefore the liability is going to increase by about $2 billion. (note: This was only the index puts, my estimate for total derivative losses was $3 billion.)

Gary:

That means Berkshire could take a fourth-quarter hit on the options, as much as $12 billion, says Fox-Pitt Kelton analyst Gary Ransom.

It looks like the total (index puts, CDS's, misc) is closer to $5 billion.  The index put liability was slightly over $3 billion.  I'm not going to bother trying to get more precise until the 10k comes out. Gary was close on the overall decline in book value, so he gets points on that.

However, the figures imply that Buffett decided to increase the volatility assumption in Black Scholes. This is significant for a couple of reasons. My thinking is that he should be using a figure that is roughly fixed -- or a 15 year rolling average. He said the following:

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. This metric is simply irrelevant in estimating the probability-
weighted range of values of American business 100 years from now. (Imagine, if you will, getting a quote every day on a farm from a manic-depressive neighbor and then using the volatility calculated from these changing quotes as an important ingredient in an equation that predicts a probability weighted range of values for the farm a century from now.)

Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens. In my opinion, the valuations that the Black- Scholes formula now place on our long-term put options overstate our liability, though the overstatement will diminish as the contracts approach maturity. Even so, we will continue to use Black-Scholes when we are estimating our financial-statement liability for long-term equity puts.

Therefore, Buffett INCREASED volatility, even though he believed it was already too high, from an economic perspective.

One other factiod regarding the index puts. When Buffett originally booked them, he thought they were grossly over valued. However, he booked them with no initial income impact. In order to do this, he had to "back into" Black-Scholes parameters that would produce this result. Therefore, the fact that the parameter adjustments will be much lower then others have suggested, one reason is that they started on the high side.