An analysis of Berkshire’s derivative position that caused a minor furore on the Yahoo message boards when they wrote down $1B.

From Financial Crookery;

Between 2005 and 1Q 2008 Berkshire Hathaway sold index put options totaling approximately $40bn notional amount, receiving almost $5bn in premium. These at-the-money options were written over the S&P500 and three international indices (most likely the FTSE100, EuroStoxx50 and Japan’s Nikkei or Topix - these are the most liquid indices for long dated options). The initial term of the options was either 15 or 20 years.

Before taking the other side of these trades, the investment bank counterparty would have formed a view on the following risks:

(1) What is the right price for long dated index volatility? Very long dated options have significant vega (sensitivity to implied volatility). One volatility point changes the model value of a 20 year S&P500 put by approximately 0.75% of the notional amount. By contrast, a 1% move in the index changes the model value by only 0.09% (9% delta).

There are takers for the other side of this volatility risk. Well, maybe not for 20 year duration, but at least out to 10 years or so. Constant buyers of long dated vega are retail investors, usually purchasing structured protected products - the simplest protected product is a zero coupon bond plus a long dated call option.

(2) Where is the 20 year forward for the S&P500? Buying puts from Buffet means the bank is short the S&P500 forward. Unfortunately, selling calls to retail investors also leaves them short the forward. The market’s demand for long dated forwards has always been so one-way that these forwards tend to trade rather high. Put another way, long dated options typically imply very low estimates of cash dividend growth. Presently, the 15 year S&P500 cash dividend growth implied from forward prices is negative 3%pa. Do we really think $30 of S&P500 dividends today (2.15% yield) will have dwindled to $16 in 2028? It’s the same for international indices too.

Berkshire and Buffet think completely differently to an investment bank in relation to these risks. Roughly summarised, their thought process is “markets ain’t gonna be down in 20 years, we could use the premium income wisely, we never have to post collateral so let’s just hit vega bids when they look attractive.” Note the market call here is perfectly in sync with Berkshire’s view that long term returns on equity markets will be in the mid single digit range. Selling puts for premium in the absence of collateral covenants is a useful source of risk-adjusted long term funds.

But it is the forward quirk which leads me to question Berkshire’s strategy. No, I don’t agree with Mish Shedlock that “anyone short S&P puts is asking to have their heads handed to them on a platter.” Berkshire’s approach is simply not the same as a “hidden” put selling strategy embedded in a so called lemon hedge fund.

No, the flaw in Berkshire’s put selling strategy is that it locks in negative dividend growth rates: they get less money for their puts than they deserve. If Berkshire do stand behind their long run market call, they ought to believe that cash dividends will grow, on average, over the same timeframe. Sure, financial stocks may cut dividends in the short run, but it seems inconceivable that the market grows 5%pa over 20 years and cash dividends fall 3%pa - the index dividend yield in 2028 would be less than 0.5%!

Berkshire could be paid up front for opposing this paradox. So, Warren, I would have overlaid a fixed for floating dividend swap to reverse your forward position. 1 year cash dividends on the S&P are around 2.15%, or say $1bn on $46bn notional. The “fixed” leg paid by Berkshire would be an annual payment of $1bn increased by a fixed 3%pa for 20 years. The floating leg received by Berkshire would be the actual dividends paid on a notional portfolio of $46bn invested in the S&P500.

This dividend swap should generate an up-front payment to Berkshire of some 13% of the notional amount, or $6bn. This is the same order of premium that Berkshire received for selling the puts in the first place. Two premia for the price of one view! Provided cash dividends grow by 3% or more on average, there is also the promise of further payments to come. If Berkshire like their put selling strategy, this one’s the proverbial no-brainer.