Monday, January 27, 2014

Oooh, Oooh: A Deep Dive Into The Berkshire Hathaway Derivatives (BRK.b)

It was Boston University's Zvi Bodie who, overcoming his MIT PhD, asked the most profoundly simple question I've heard regarding long term options: "If the risk of a portfolio declines the longer you hold it, why are long dated equity index puts more expensive than their shorter-term cousins?"
Here are some of the factors involved, from FT Alphaville:

Dig into the mysterious Buffett derivatives
The Sage of Omaha is folksy, down to earth and on the whole entirely open about his philosophy and his approach. But he has also managed a trick almost unheard of in the modern corporate era: he discusses the business he has run for half a century entirely on his own terms.

If you are a investor in Berkshire Hathaway you can read the annual letter to shareholders, you can trek to Omaha to try to ask a question at the annual meeting, and that is it. When Berkshire publishes quarterly results it does so on Friday evenings without commentary beyond the dry notes to the financial statements. Just the numbers and in the name of fairness, the Sage either speaks to all shareholders, or none.

But that does leave some mysteries and Pablo Triana, a Professor at ESADE business School, has followed up his look at how Berkshire’s very large legacy derivatives positions contribute cheap financing, with an examination of what can be inferred about the derivatives contracts themselves.

He is concerned with the series of very large and very long dated put options that Berkshire sold against stock indices in the US, UK, Europe and Japan between 2004 and 2008 . Due to the company’s size and financial strength, Buffett was able to negotiate the contracts without collateral requirements, meaning that Berkshire only bears the risk of mark-to-market swings in valuation that hit reported earnings, and the risk of large cash payments at the various settlement dates between 2019 and 2028.

Buffett took on the contracts because he was confident that use of the large premium paid upfront – almost $5bn, or 10 per cent of the notional exposure – would more than offset any losses that might arise. Losses that the professor estimates at settlement could total as much as $14bn to $20bn if low market levels from the recent past happened to recur at the wrong time in the future.

These tend to be cast as simple bets on index levels, the old Buffett optimism about stocks for the long run, but as Prof Triana explains, there is far more to it than that.
The main point is not that those unfavorable things will unfailingly happen, and we certainly don’t even try to assign any specific probability to their occurrence. The point, rather, is to illustrate the myriad of exposures Berkshire got itself entangled with by deciding to sell the puts and how the firm could hurt badly both accounting-wise and cash-wise just if some things that have already happened (and not that long ago, actually) were to happen again.
For those not expert in option pricing, there is a helpful refresher on the factors that effect the value of an option and how they apply to the sort of very long-term put contracts Buffett has sold. Bear with us, because the conclusion is that there is something odd in the way that the mark-to-market losses for Berkshire have not been larger (experts can skip down).
So, to value an option you use the Black Scholes model, which relies on the so-called greeks for inputs:

Delta, change in the value of the underlying. Important for short dated contracts, but pretty negligible for very long dated put contracts, as there is so much time left for the price to change again.

Gamma, also known as jump risk, the sensitivity of delta to changes in the value of the underlying. Option buyers like this, sellers not so much, but again it is negligible over very long time horizons....