Much as bankers are in the business of putting cheap funding to work, bloggers are in the business of putting cheap irony to work, and one of the cheapest of ironies has long been that Warren Buffett (1) has called derivatives "financial weapons of mass destruction" and (2) has been known to dabble in the occasional high-proof derivatives trade himself. Selling long-dated S&P 500 puts is perhaps the best-known example, though he'll buy big chunks of bank warrants too if the situation calls for it.

And in that vein, this Wall Street Journal item is a delight: Buffett's Berkshire Hathaway Inc. is insuring a $1 billion prize that Quicken Loans has offered to pay to anyone who can pick a perfect NCAA basketball tournament bracket. Because oh, sure, derivatives are evil, but let's bet a billion dollars on an essentially random outcome!

The first thing to talk about here is pricing, because it's fun. If you were Berkshire, how much would you charge for this $1 billion policy? The answer to that starts -- though it does not end -- with the related question, "what is the fair price of this $1 billion policy?" The answer to that question is $1 billion times the probability that someone will actually win the contest.^{1}

My Bloomberg View colleague Kavitha Davidson says that the odds of picking a perfect bracket are about 1 in 9 quintillion. That's just the odds of a random bracket winning, though, and would only be the true odds if the NCAA tournament were decided by a series of unbiased coin flips, which would make for very boring television. (I would watch!) More reasonable guesses -- cutting out brackets that have 16 seeds winning or whatever -- range from 1 in 772 billion to 1 in 128 billion. Odds of 1 in 128 billion imply a fair price for Buffett's billion-dollar policy of just under a penny.

But you can improve on that a bit further. Here is a claim that "favorites historically win about 72% of the time, which would yield a probability of perfection of one in 970 million," which sounds like the odds of a perfect all-favorites bracket but whatever. Or consider that last year's winners of the ESPN Tournament Challenge had 9 and 12 errors. One quick way to put an upper bound on the price is to imagine a contest made up only of people who were that "good"' at predicting the tournament, and asking what their odds of being perfect are. The odds of a bracket with no more than 12 errors being perfect are about 1 in 4,000.^{2}
That implies a fair price of around $250,000.^{3}

So we get a fair price bounded by (nothing, $250,000). Which, compared to a billion dollars, is a pretty tiny range: Let's just call the fair price $250,000. On top of that fair price you need to add some profit, and that profit probably needs to be pretty hefty, for obvious reasons. Nobody likes to sell teenies: A trade with a tiny profit and a large but improbable potential loss will just look like a squicky situation, at its fair price, so you gotta charge more for it. This is mostly a matter of risk aversion: Losing a billion dollars is more than a thousand times as bad as making an extra million dollars is good, even if you're as big as Berkshire Hathaway. It raises uncomfortable questions on earnings calls and so forth.^{4}

Figure Berkshire should get paid a couple of million bucks on this, which squares with reports that it previously insured a billion-dollar contest run by Pepsi that had 1-in-1,000 odds (fair price of $1 million) for "a seven-figure premium."

Now let's ask this question: What would you say about a bank that did a derivatives trade where it took on $1 billion of risk in exchange for a payment of a few million dollars? What if that risk was binary risk generated by a random number generator? The NCAA Tournament is not strictly speaking a random number generator (though it's close!), but that billion-dollar Pepsi contest was literally for matching a random number. Drawn by a monkey. Really, a chimpanzee would pick the number. On television, apparently.

Imagine the outrage you could get with a story titled "Goldman Sachs Makes Millions Selling 500-to-1 Monkey-Linked Derivatives"!^{5}

Of course there are differences. For one thing, Berkshire is leveraged, but not nearly as leveraged as the big banks. (Though there is leverage built into this trade: I assume that Berkshire is not holding $1 billion in assets against its potential liability here.^{6}
) And its funding is considerably more stable than theirs; even if Berkshire loses a billion dollars on this trade, it's not going to suffer a crippling run on its funding. Also the "weapons of mass destruction" crack was in the context of highly popular, correlated trades that created systemic risks. The NCAA tournament doesn't correlate to much.^{7}

Still though. An increasingly important story in finance is the growth of "regulatory capital relief" trades, sometimes referred to as "capital arbitrage" trades. The "arbitrage" is that banks are required by very fiddly Basel rules to hold certain amounts of capital against certain types of risks. If they can sell off the risks that are inefficient under Basel rules, and get back other similar risks that are more capital-efficient, then they are happy. On the other hand, no bank would take the other side of that trade, because other banks are subject to the same fiddly rules. But non-banks might. Hedge funds and asset managers and pension funds that are subject to different rules might well feel frisky enough to offload some of your regulated risk. Insurance companies have long had a profitable line doing just that; reducing banks' capital requirements is pretty much what brought down AIG.^{8}

But you have to have a certain daredevil attitude to sit down opposite a global investment bank and say, "oh, sure, you can pay us to take on the risks your regulators think are too risky for you." If Berkshire is any indication, these days there's no lack of that daredevil attitude.

^{1}
Not true! The prize actually pays out in 40 annual installments of $25 million, so you have to discount that back to present value. (For reference, Quicken offers the option of taking a lump sum payment of $500 million, which I guess is around a 4 percent discount rate.) So the real answer is around half the answer in the text, but that's close enough.

^{2}
That is, just 2^12. The odds of a bracket with no more than 9 errors being perfect are 1 in 500. I owe this argument to Timothy McKenna on Twitter, though I am probably mangling it.

^{3}
Really $244,140, or $1 billion divided by 4,096. If you use the discounted value the fair price is $120,000, give or take. If you use the 1-in-500 odds then the fair price is around $2 million. Etc.

^{4}
Also, though, just like compensation for your time. You gotta go to a lot of committees to take on a billion dollars of risk, so you gotta get paid for all that work. On the other hand, you might knock a bit off the price for marketing purposes, since this trade is getting a lot of free publicity, and I guess the next company that wants to do a silly overpriced prop bet will call Berkshire first.

^{5}
Ooh, that gives me an idea. (The idea is the headline of this post obviously.)

^{6}
I casually assume it reserves in a straightforwardly actuarial way, that is, based on the fair price of the thing. Which is roughly zero.

^{7}
Though I'm sure that come March there'll be articles to the effect of "the stock market goes up 2 percent more on average when teams with blue uniforms win" or whatever, that seems to be a thing.

^{8}
That's a pretty amazing slide deck, by the way. It actually says "Regulatory Capital Corporate Transactions" in the headlines.