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. Vega, or volatility. The more volatility there is, the more owning an option is worth, so increases in volatility are bad for option sellers, and the longer the option the more that is worth. Prof Trian gives the example: The 15-year, 100-strike, 20-percent-volatility, 3-per- cent-interest rate, 100-spot put would have a Black-Scholes vega of 0.967 (0.770 if spot is at 50), while the one-year equivalents would be 0.387 (0.001). Theta, or time risk. Your option value decays as time passes, but if settlement is 15 year away, the days are so small as not to matter. Rho, or interest rate risk. This is the one that can be easily forgotten, but is one of the most important for Berkshire's puts. The model assumes stock prices grow at the risk free rate (i.e. Treasury yields), so higher rates mean expected higher prices, and lower rates lower prices. For long dated puts then, this can be far bigger an impact than volatility. Rho is about the future (growth rate of the underlying), and long maturities have more future in them. A 15-year, 100- strike, 20-percent-volatility, 3-percent- interest rate, 100-spot put would have a Black-Scholes rho of -4.048 (-7.254 if spot is at 50), while the one-year equivalents would be -0.466 (-0.970). The 15-year option is worth 10.338 when spot is at 100 - thus, the option would experience a whopping 39 percent gain in value if interest rates go down by 1 per- cent. That would be a whopping 39 per- cent increase in liabilities for the option seller. One wonders if the huge interest rate bet implied by long-dated options would deter traders from selling such contracts (which are in fact illiquid). So Berkshire has actually taken bets which put it very long the dollar (versus the euro, sterling and the yen), and long interest rates. Selling these just before the crisis explains big mark to market losses - volatility (vega) jumped, and interest rates (rho) plunged. As we have written before, these were huge and Buffett professes not to care about them. Still, Prof Triana also notes a mystery. Experts, rejoin us. With our emphasis: It seems odd that put liabilities would be just $10 billion in Q4 2008 and Q1 2009. Contracts that had cost $4.9 billion during 2004-Q1 2008 (very calm period generally, low volatility, ever-rising stock prices, ever-increas- ing interest rates, the "great modera- tion") were now worth just a bit over twice that amidst incredible, historically unprecedented volatility and dramati- cally tanking markets (well below strike prices) - causing much lower interest rates. It is true that the dollar was in those quarters stronger against the pound, especially, and the euro than it had been in 2004-Q1 2008 (while being weaker against the yen), but it still seems puzzling that the put portfolio's liquidation value would be only two times the premium originally collected. During late 2008 and early 2009, the put portfolio faced the triple threat of a market meltdown that would lead to explosively enhanced volatility and urgently lower rates (as officials tried to fight the panic). This should have spelled total accounting massacre for short put option positions, and yet it looks like Berkshire may have suffered a lesser pain. There is also plenty of good stuff in the paper about Berkshire's currency exposures, which the professor has done original work to estimate, and he has a good stab at the worst case for the puts come settlement ($14bn to $15bn on lower index levels, and another few billion potentially from dollar weakness). He also points out that the option buyers did extremely well - they could have sold on their exposure during the crisis or its aftermath for a significant profit, as they don't need to wait until expiry to capitalise. But the accounting mystery remains. Perhaps someone could ask Mr Buffett about it when they get to Omaha? Related Links: The ghost of the leveraged super senior - FT Alphaville Derivatives reform: now what? - FT Alphaville Dodd-Frank, destruction and Buffett's derivatives - FT Alphaville Investors line up for Buffett clues - FT