In my [W.B.] opinion, the valuations that the Black- Scholes formula now place on our long-term put options overstate our liability, though the overstatement will diminish as the contracts approach maturity.
The Black-Scholes formula has approached the status of holy writ in finance, and we use it when valuing our equity put options for financial statement purposes. Key inputs to the calculation include a contract’s maturity and strike price, as well as the analyst’s expectations for volatility, interest rates and dividends.
If the formula is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.
Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens.
Even so, we will continue to use Black-Scholes when we are estimating our financial-statement liability for long-term equity puts. The formula represents conventional wisdom and any substitute that I might offer would engender extreme skepticism. That would be perfectly understandable: CEOs who have concocted their own valuations for esoteric financial instruments have seldom erred on the side of conservatism. That club of optimists is one that Charlie and I have no desire to join.
The games Buffett can play are based on how he’s so big and has so much cash. Since he’s holding these things on his book to maturity the only thing he’s got to do is make sure that collateral he’s going to need to post is there. It’s as though the main point is that he’s got a lot of assets to post if things should go bad midway through – and as long as there’s discipline about not playing the game too hard he’ll be fine. The underlying assumption in part is that reinsurance losses from disasters and what-not aren’t going to be correlated with lousy stock returns.
I don’t know if the puts he’s written can be sold to a third party or if they’re indexed to inflation.
To “blame” B-S is so sophomoric, don’t you think?
I mean the ‘troubles’ he notes are well known to people who value options and for quite some time (like almost 20 years…).
I guess blaming “model risk” is complex enough to snow people with an explanation, other than that ‘we doubled-down that there wouldn’t be a downside this big and we were wrong’.
I agree with Warren, have you ever looked at LEAPS prices two years out? I think the puts he sold are pure market genius. He found a glitch in the Matrix and now he is going to exploit it.
Buffett’s derivatives trades are the right trades for Berkshire. Even though I took the opposite side of his type of derivatives trades when I could, my time horizon was very short. Buffett is generally not beholden to mark to market. Thus, over long term, his derivative positions should be profitable.
His logic is that of an insurer, using actuarial type probabilities rather than market indications. He is also correct in his criticism of Black Scholes for long tenor options. In fact, he mentions just a few of the problems among many.
Still, these options may be more valuable for some than Black Scholes value. For example, a quant should start valuing them not as plain vanilla options, rather path dependent, knock-in options. In the end, the correct value depends on the assumptions you make, just like everything.
You guys are nuts and Buffett is right. You have to use common sense in applying any mathematical model to the real world. Buffett walks through the example of a 100-year put in his annual letter.
Buffett knows his stuff. From his perspective, these puts are little different from other insurance policies he writes. He may not win them all, but the odds are tilted in his favor.
I am beginning to think that WB too is has been collecting quarters in front of a bulldozer.
I wonder if Taleb thinks those puts are ‘too expensive’.
He’s right and he’s wrong. The BS method assumes continuous returns – no jumps – and zero transaction costs. If you make those two ‘small’ assumptions you can hedge your sold options and make the BS formula come true. In the real world you are lucky if you can hedge 70% of the risk. So real world option prices do not match the BS model, especially for way of the money options.
The hedging fails of course just when you need it most – when there are big jumps in the market. Older readers may recall the 1987 crash which was in large part caused by failed attempts to hedge against market declines. In those days it was called portfolio insurance.
Of course one might suspect that WB is making excuses for his losses selling options. One thing he doesn’t seem to have acknowledged is that the “investment returns” he is expecting to make from the premiums are going to be highly correlated with what he insuring. If the market tanks long term – as other markets have eg Japan – and he has to pay up on the puts, his investment returns are also likely to be lousy. Correlated risk is bad. Also note that WB is not a young man so the returns will have to be achieved by his successor who may not be as good an investor.
If my memory serves me well, Sigma (volatility) and T (time to exercise) are two separate parameters in the BS equation. [T] is a very well defined number but the true [Sigma] is an unknown and thus requires an estimate from what we observed.
Hey…! I was thinking the very same thing….! Whenever I’m short index puts, and the market takes a dump, I feel like switching-off the screens and declaring “It’s all a bunch of nonsense!”
Just too bad none of the brokers, counter-parties or clearling-firms buy such an argument (even if any were possibly stupid enough to do so, their own CDS would blow-up, fatally-damaging their own financing arrangements: thus winning themselves the Darwin Award)…..
Well, if he *truly* believes that Black-Scholes “overstates” long-dated options values, then he should just go all-in: Sell an infinite number of puts on an infinite number of indices what’s the worst that could *possibly* happen…?
After all, AIG is getting yet another free $30bil from the US Gov’t for it’s negative-convexity-bet gone wild, so why not do the same and pick pick-up some free cash from a negative-gamma dice-throw….?
In all seroiusness, If someone can come along with a “better” formula that prints money and doesn’t blow you up, then, hey, I’ll take it; I just find it awfully convenient that he’s cryyyying a river now that his “free money” bet (short the options, collect the premia for 20 years, and like, there’s *no* penalty to pay until the very end) is beginning to do a Nick Leeson on him, and his CDS premia are exploding, counter-parties are easing-back and it’s all hitting the Bloomberg screen at an inopportune time…
I found the part about selling his derivatives portfolio to some unknown buyer — with recourse back to BH — most illuminating. Why would I not be surprised to find that GS was the buyer here and this was an “unmentioned” part of that particular deal.
With regard to BS, “absurd” values are generated in times of extreme risk as uncertainty grows. How else are traders supposed to manage risk? It’s not like there’s a crystal ball out there that says “this low and no lower.” Unless of course you believe, like Bill Gross, that the government will set a floor to values…
“His worst-case scenarios may be a little more probable than he thinks”
So, I suspect and the market too, berkshire is trading around book, highly unusual.
Just explaining his arb, I guess. He was less specific on his reasoning behind his protection sales on high-yield corporates. That trade doesn’t seem to be working out too well, either. Wonder what his total exposure is there?
Lots of good stuff elsewhere. The foreshadowing of carnage in the municipals due was instructive, the incentive of cities to blow out their insurers before taxpayers bear any hardship is a fun observation, kind of a reverse of the dynamic we see now between struggling homeowners and MBS investors/servicers.
The Clayton Homes piece is good, too. Amazing that the industry as a whole stands at only 20% of its peak 10 years after its securitization binge , even in an environment of plentiful credit and expensive traditional housing. I’d also think Clayton will be killed stone dead as those same traditional houses become rapidly more affordable and government bends sideways to put marginal people in them, but I guess we’ll see.
I didn’t know that Berkshire’s run started in 1965 right as the first baby boomers turned 20 (and started their first jobs), and is now realizing its worst year ever as they turn 62 (retirement age, at least militarily speaking). His worst-case scenarios may be a little more probable than he thinks.
I am not so certain, but I don’t think he expected the market to tank as much as it did and for his puts to be as much underwater as they are, but he has a point, BS doesn’t work at all for very long-term options. He can rationalize all he wants, it was a rotten trade.
Somehow I feel certain he wouldn’t say that if the results favored BH.