Berkshire Hathaway's Peculiar Volatility Numbers

I just got off the phone with someone who's been making good money shorting Berkshire Hathaway stock in the past few weeks; he pointed out to me something very peculiar in Berkshire's public statements.

First, look at the 10-Q for the second quarter, ended June 30. Have a look at page 24, where the company talks about its equity put options:

At June 30, 2008, the estimated fair value of these contracts was $5,845 million and the weighted average volatility was approximately 23%.

It then goes on to say that if volatility were to rise by 4 percentage points, the value of the contracts would rise by $1.124 billion, to $6.969 billion -- a rise of $281 million per percentage point.

It's not clear where Berkshire is getting its volatility numbers from, but the VIX volatility index, as of June 30, was at 24 -- which means that Berkshire's volatility number was pretty much in line with the VIX.

Now look at the 10-Q for the third quarter, page 25. Over the course of that quarter, the VIX rose substantially, from 24 to 39 -- so one would expect Berkshire's own volatility numbers to rise as well. But they didn't. In fact, they fell, slightly:

At September 30, 2008, the estimated fair value of these contracts was $6,725 million and the weighted average volatility was approximately 22%.

Stock markets fell by about 9% over the course of the third quarter, which would explain why the value of the put options rose even if volatility fell, as Berkshire seems to think that it did. But of course voliatility rose substantially during the quarter, and it looks as though Berkshire is using an improbably low volatility number here.

In the third-quarter 10-Q, Berkshire reckons that the value of its put options goes up by about $250 million for every percentage-point increase in volatility. The VIX is now at 80, but the VIX is much more short-dated than Berkshire's equity puts. But let's say that a reasonable volatility number for Berkshire would be somewhere around 50: that would mean the value of those equity puts going up by about $7 billion, before taking into account that the S&P has fallen by a good 35% since September 30.

Add it all up, and Berkshire's equity puts alone should probably have gone up in value (this is value to the holder of the puts, which means it's a liability to Berkshire) by $15 billion or so since the end of the second quarter. Now this is a noncash loss, and Berkshire doesn't need to post any collateral or otherwise lose liquidity as a result of any such losses. But when Whitney Tilson says that "there could be an additional $1-2 billion in mark-to-market, noncash losses so far this quarter", he could be underestimating greatly.

On the other hand, he might be right: Berkshire might end up taking only a relatively small markdown of one or two billion or two dollars on those equity put contracts. But if it does so, questions will continue to be asked about why Berkshire's volatility numbers stubbornly refuse to rise even as every other volatility number in the world is going through the roof.

Essentially, the shorts' argument is that Berkshire is short volatility, thanks to these puts, and that being short volatility has been a very, very bad trade over the past few months. Berkshire is in the happy position of not needing to take any cash losses on its short-vol positions, and it's entirely reasonable for long-term shareholders (and most of Berkshire's shareholders are long-term shareholders) to just want to ride out the present craziness. All the same, on a mark-to-market basis -- and it's entirely reasonable for the stock market to be marking Berkshire's assets to market -- it makes sense that Berkshire's share price should be falling to reflect the mark-to-market losses on its equity puts, not to mention similar mark-to-market losses on its CDS, bond-insurance, and deposit insurance portfolios.

Now Berkshire's lost a lot of market capitalization of late: about $77 billion, in fact, since September 30. So it's entirely possible that mark-to-market losses on its equity puts and other derivatives contracts have been more than priced into its shares. But it'll certainly be interesting to see how Berkshire values those puts in its next quarterly report. If the volatility number rises to something a bit more reasonable, Berkshire could end up reporting a quarterly loss -- and that might spook quite a few investors.

Update: Many thanks to Andrew Clavell, who send me some long-term volatility numbers. They seem to be around 38%, which is a big spike up from the 22% which Berkshire used in its last 10-Q. Combine that with the drop in the S&P, and you could see a big noncash hit to earnings in Berkshire's next quarterly report.

It's worth noting, however, that long-term volatility at 38% implies a random walk in the index of near 2.5% every trading day for the next 20 years. If and when that number comes down, Berkshire's noncash losses today will simply be cancelled out by noncash profits tomorrow.