Score one for Warren Buffett in his crusade against the financial world’s worship of mathematical mumbo jumbo.
One of Buffett's most controversial bets -- a bubble-era wager on the long-term value of stock market indexes, using tools he once scorned as "weapons of financial mass destruction" -- started to pay off in the fourth quarter.
Berkshire (brka) posted a $222 million gain after its trading counterparty asked to unwind eight derivatives contracts known as equity puts, according to Saturday’s annual letter to Berkshire shareholders.
The gain marks Berkshire's first realized, cash-in-the-pocket profit on the puts since Buffett started writing them seven years ago -- not counting the money Berkshire has made by holding the cash its trading partners anted up in the first place.
Buffett says Berkshire’s gain on the widely criticized trade shows the mathematical models used on Wall Street don’t work – a fact Berkshire intends to exploit in its derivatives dealings. The Black-Scholes standard for option pricing “produces wildly inappropriate values when applied to long-dated options,” Buffett writes in the letter.
Berkshire entered into the put contracts between 2004 and 2008. They came under fire from pundits after the post-Lehman Brothers financial collapse seemed to sharply raise the odds the contracts would prove costly to Berkshire.
The puts obliged Berkshire to pay its unnamed counterparty at the end of the contact period, in this case between 2021 and 2026, if certain equity indexes such as the S&P 500 declined over the course of the contract. In a worst case scenario, in which puts expired with the indexes at zero, Berkshire would have been obliged to pay its counterparties in this and similar contracts a total of $38 billion at expiration.
Of course, when Buffett wrote the puts the major stock indexes didn't look all that likely to be lower in a decade or two, let alone go to zero. But the odds were looking distinctly less favorable for Berkshire around two years ago, when the S&P, for instance, traded as low as 666 -- 58% below its 2007 peak.
But since then, U.S. stocks have posted their fastest double on record. With the economy growing again and every market commentator furiously beating the inflation drum, Berkshire's unnamed counterparty apparently decided to cut its losses. It unwound its bet on falling stocks for the long term just three years after making it.
It is clear that Buffett views the results as a point in his favor in a long-running debate over the financial industry’s embrace of abstruse mathematical models. He has insisted he would continue to write derivatives contracts when it suits him in spite of the name-calling the practice inspired.
Buffett has said he would do so as long as he could see a good chance to make money on a given deal -- and on the condition Berkshire gets paid upfront by its trading partner, eliminating any of the counterparty risk that nearly helped bring down the financial system in 2008.
"I believe each contract we own was mispriced at inception, sometimes dramatically so," Buffett explained in his 2008 letter to Berkshire shareholders.
No small part of that mispricing, Buffett says, is driven by what he views as the false precision provided by models like Black-Scholes. It combines data including prices, contract duration, expected volatility, dividend and interest rates.
Buffett says academics, regulators and some market practitioners prize the formula -- named after the economists Fischer Black and Myron Scholes, who popularized its use it in a 1973 paper -- for its capacity to estimate a precise value for an option over a long span. That, alas, is a quality Buffett scoffs at.
Buffett says he cannot reliably come up with a pinpoint value for any given long-dated option, but adds that he would "rather be approximately right than precisely wrong."
How wrong is Black-Scholes? So wrong that Buffett says he applies the formula in Berkshire’s financial filings only through gritted teeth. He notes that doing so is standard accounting and allows auditors to reconcile the company’s numbers with those of its trading partners.
But Buffett believes the Black-Scholes estimate of Berkshire’s liability on the equity put contracts, for instance, is vastly overstated. That number is $6.7 billion at Dec. 31 -- down from $7.3 billion last year, when more contracts were outstanding, and $10 billion at the end of 2008, when stock markets were far lower.
But Buffett says that were stocks to flatline between now and 2026, when the last of the contracts expire, Berkshire would actually owe just $3.8 billion.
This is a rather large discrepancy. But rather than idly criticizing the financial industry's options pricing methods, "we put our money where our mouth was by entering into our equity put contracts," Buffett writes. "By doing so, we implicitly asserted that the Black-Scholes calculations used by our counterparties or their customers were faulty."
In this case, Berkshire, which had received $647 million in premiums in writing the contracts, paid $425 million to unwind them, resulting in the latest-quarter gain. But Buffett notes he also got the free use of the premiums over the three years the contracts were in effect. Buffett views the use of such so-called float as one of the key benefits of the insurance business, because it allows him to invest policyholder funds for Berkshire's benefit.
Closing out the eight equity puts leaves Berkshire with 39 remaining put contracts, with a notional liability (if the indexes go to zero at expiration) of $34 billion.
Buffett is hardly the only financial bigwig to take aim at Black Scholes. But some other critics have in a sense taken the other side of this trade, contending that if anything the formula underestimates the potential liability of long-dated options by failing to adequately account for so-called tail risk -- the prospect that the markets will collapse under the weight of, say, a giant housing bubble.
Such a downturn would increase Berkshire's liabilities by increasing the amount it stands to pay out on the put contracts. So there is the risk, however slight, that Buffett’s view understates the risk Berkshire is shouldering in the event of another unforeseen market meltdown.
“Black-Scholes has plenty of problems,” says Espen Robak of valuation adviser Pluris. “But there's a powerful argument that the chance of extreme events is greater than people probably think, and now is sort of a strange time to be implicitly making the everything-will-be-OK argument."
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(A member of FORTUNE's staff, senior editor at large Carol Loomis, edits the chairman's letter in Berkshire's annual report.)