Our Take on Berkshire's Equity Put Option Positions

 Berkshire Hathaway's (BRK.B) stock has been under pressure in the past year, and a few observers have taken to the airwaves to criticize the firm for its recent investment performance. Some of the largest holdings in the firm's equity portfolio have declined significantly, particularly its common equity investments in financial services firms such as  Wells Fargo (WFC),  American Express (AXP), and  U.S. Bancorp (USB). The firm's soon-to-be-released annual results for 2008 are likely to include some significant losses in its equity portfolio, particularly in the fourth quarter. In turn, Berkshire's reported 2008 results will also include investment-related losses on equity derivatives contracts.

Berkshire has written long-dated put options on a number of stock indexes in recent years. In exchange for more than $4 billion in cash, Berkshire has provided protection for counterparties against long-term stock market deterioration. They are "European-style" options, meaning that they require payment from Berkshire only if the underlying index on the exercise date--the earliest of which is 2019--is below where it was when the option was written. The amount Berkshire pays, if it does have to pay, depends on how far the index is below where it was when the contract was struck; the bigger the decline (if any), the larger the payout from Berkshire.

How Does Berkshire Value These Positions?
For financial reporting purposes, Berkshire has estimated its liability under these positions using the Black-Scholes model, a model widely used to value options. The main inputs and assumptions in this formula include the risk-free rate of interest, the time to expiration for the option, the current price of the underlying instrument, the exercise price, and an estimate of the volatility of the underlying instrument. For example, the greater the volatility, the more likely the option will be valuable to the buyer, and the greater the estimated liability of an option seller. For Berkshire's position as a seller of an equity index put option, the lower the current index relative to the price at inception date, the higher the estimated liability. Quantifying the theoretically "right" price is no mean feat, however, and arguments over Black-Scholes and other option models can involve a lot of Greek letters and complex equations.

Here's what Charlie Munger, Berkshire's vice chairman, has said about the Black-Scholes model:

"Black-Scholes is what I would call a know-nothing value system. If you don't know anything at all about value compared to price ... then Black-Scholes, on a very short-term basis, is a pretty good guess over, say, a 90-day option. The minute you get into longer-term options, then it's crazy to use Black-Scholes."

We agree, but the question arises--why, then, does Berkshire use Black-Scholes to value these positions?

Berkshire uses Black-Scholes to value these positions for financial reporting purposes, which are the product of regulatory requirements. Berkshire uses a few other things to think about these positions' value, including experienced judgment, and we are going to learn more about that judgment in the upcoming annual report to shareholders for 2008. For fourth-quarter reported results, these positions will likely couple with significant price declines in some of Berkshire's largest holdings in its equity portfolio to produce significant losses. Volatile short-term reported results are not a new thing at Berkshire Hathaway, however. The firm's ability to absorb short-term swings in its reinsurance as well as investment portfolio is a major factor underpinning its superior long-term record.

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