An issue with a marked-loss vs an expiration payoff on Buffett's standard 1514 short European put. First with respect to Buffett's comments at the bottom of page 18:
The SPX EOY value was 903. 903/1514 -1 results in a 40% loss on the index value taken from the put-strike. Short the 10y 15% vol 1514-strike European put at 2% LIBOR and SPX=1514 is valued at $4,900,000,000. The 1514-strike put at SPX 903, 6-months later, 30% vol and 2% LIBOR is valued at 19,874,125,720. The LIBOR at 2% at EOY 2008 is grossly overstated and would result in an additional $3.4B ($23,300,699,120 value) loss on the option, due to a reduction on the implied forward (synthetic strike increase), if had I used 1% LIBOR which was indicative at the end of 2008. IOW, the risk-free rate drop hurts the position as it's massively-sensitive to rho.
The BS-model loss on the 10-year 1514 European put at 2.00 LIBOR is $14,974,125.720. The BS-model shows a 4-fold increase on the option under those constraints, yet Buffett is modeling a double. The loss declines as you add duration; roughly $300MM per year. A 15-year model would produce a loss of roughly $13.5B. We can't mark a duration, but simply taking the average of the dates listed puts it in the 15-year range.
An aggressive valuation, favorable to the seller (LIBOR at 2%, vol under market), results in a marked-loss of $13,500,000,000 at a blended 15Y expiration. A vol at inception of 15%, and a vol at MTM of 30%. Buffett's MTM loss of $5.1B ($10B liability less $4.9 premium)
assumes that his European puts are averaging a 10% vol with the SPX at 903.
If Buffett can keep the premium and loss-reserves then more power to him, but his calculation on MTM loss under GAAP is not remotely realistic. Of the other three indices, only the FTSE outperformed in 2008, so using the foreign-indices adjusted for vol (incept to MTM) would result in a larger loss. The true impact is the risk-free rate. An indicative LIBOR increases the loss tremendously.
Feel free to run the numbers yourselves:
BS for European options
10-year term
1514 strike on standard European put
Vol at inception: 15% at SPX 1514
Vol at MTM: 30% at SPX 903
LIBOR at inception: 2%
LIBOR at MTM: 2%
I am in agreement that it's not much of a concern if the GAAP reserve-pool is not netted like a swap at some fixed-interval. It's amazing to me that no money is changing hands on the variance on haircut. Buffet is marking vol to 10% under GAAP on the MTM, but 15% on the inception of the contracts. The only advantage to Buffett's position was the up&out -skew, but the more than doubling of vol in the interim is an order of mag more important.
Even at a MTM vol of 20%, the loss, net of premium, would be >$10B.
So, either Buffett is playing fast and loose with the marks, or this thing is a non-standard put; handicap, floating-strike, or something with another embedded feature. Another solution is that the options were considerably otm; an increase in synthetic vol through a reduction in initial delta. Obviously that is unlikely as the SPX never traded above 1573.
The only other alternative is that there is a massive hedge that is somehow been neglected in the annual letter.
