WSJ on Berkshire Index Puts

The Wall Street Journal commented on the oft discussed Berkshire Hathaway index puts in its 'Ahead of the Tape' column today:

In recent years, the Omaha, Neb., holding company sold what were essentially insurance policies against a long-term decline in U.S. and foreign stocks in exchange for $4.5 billion. When the contracts expire in periods of either 15 or 20 years, Berkshire will have to fork over cash -- possibly billions -- if the indexes are below where they stood when the deals were struck.

The S&P 500 is down about 50% from its peak, and indexes around the world have cratered. Berkshire has to calculate its potential liabilities on the contracts every quarter.

In the third quarter of 2008, Berkshire said its mark-to-market liabilities on the options were $6.7 billion. Since then, stocks have fallen more, and volatility, a key element in valuing options, has soared. That means Berkshire could take a fourth-quarter hit on the options, as much as $12 billion, says Fox-Pitt Kelton analyst Gary Ransom.

I am going to use the WSJ figures and a little common sense to illustrate the economics of the options deal and the fact that the estimate of a quarterly hit of $12 billion is off by greater then a factor of 4. Before we move to simple arithmetic, I would like to point out that the appropriate volatility figure would an estimate of volatility in the future 12 years (plus) of the contracts. Therefore, the fact that we have had high volatility recently should not have much impact on an estimate of future volatility. In fact, I believe that Berkshire picked a relatively conservative (high) volatility estimate when they booked the initial estimates and will continue to use the same estimate until it seems likely that we have had a permanent change in volatility.

As a little background, The notional amount of the contracts is about $36 billion.  There are no collateral requirements and no cash will change hands until the first contracts expire in 12 years.  They are "European" options and can only be exercised at expiration.    

The Berkshire liability is calculated using Black-Scholes and the "delta" is in the low 20% range.  Delta is the change in the value divided by the change in the underlying index.  For example, if the index decreased 1/4 of its notional value in the 4th quarter or $9 billion, the liability (pretax) would only increase by about 23% of that figure.  Therefore the liability is going to increase by about $2 billion.  

However, if we want to think about a more rational way to book the options each quarter, I suggest that any change in value be "amortized" by 1/60 each quarter, based on their 15 year life.  In that case, the time premium for the option would decrease about $65 million each quarter and an additional 1/60 of the amount the option is in the money would be booked each quarter.  This is an estimate of the liability components over 15 years.     

Using the same "straight line" amortization, and assuming that the indices finish exactly where they are today, the losses would be booked at $225 million per quarter over 15 years.  However, the economics of the deal also include the cash plus the investment income.  Showing this and the total net loss (green line) below gives you the economics of the deal with the indices down 50%:

Here you can see that the loss in 15 years is a little over $10 billion.  This is based on an assumed return of 6% on the initial premium.  The idea of using a "straight line" approach to accounting for the losses is a bit extreme, and may appear unrealistically optimistic.  However, I am sure that Buffett would also prefer to book only 1/60 of the time premium if the contracts were out of the money.  

The point of this exercise is to look at the options as contracts that amortize smoothly over a 15 year period.  Even if the results are extremely unfavorable, like the assumption that indices decline 50% over a 15 year period, the quarterly economic impact isn't particularly significant.  In addition, the amount of loss would not be a problem for a company with over $100 billion in capital.