“In the financial markets, you have to care what other people think, even if what they think is screwed up. Crowd dynamics build on each other. But these things — hurricanes, earthquakes — don’t exhibit crowd behavior. There’s a real underlying risk you have to understand. You have to be a value investor.” John Seo
The New York Times has a great article on the catastrophe insurance, emphasizing that freaky behavior occurs in the long tail of probability distributions. It’s a Sunday Magazine feature article (meaning that it’s a hefty ten web-pages long but it has some really cool stuff on statistics, finance, and the life of a mathematician named Seo who has made it big in finance. After taking a temp job because the insurance at his new post-doc didn’t cover his wife’s pregnancy, he ended up with a $250000 salary and $40000 signing bonus after six weeks of work.
Apparently he’s a genius at pricing unusual events. Rather than being counter-intuitive, the article suggests that he has a knack for coming up with prices that actually seem fair. For instance, a company that had only two factories, one in Japan and one in California wanted to know the price for $10 million of insurance against separate earthquakes wiping out both factories in one year. The odds were set at 10% for an earthquake wiping out a single factory in one year and the typical margin is double, so it costs $2 million for $10 million insurance on one. What Seo realized is that to pay for $10 million on two, he only needed to have enough insurance money on one to buy a $10 million policy on the other — $400000 or roughly 4 times the expected value of 10% times 10% times $10 million. (Of course that assumes that he has time to buy the second policy, but my cousin worked for a while supporting banking computers assuring that they could replace a given computer completely in 5 minutes, so I imagine they could do the same for this.)
The article also has some gloomy info on how the insurance industry still isn’t really ready to adsorb a large disaster, but at least it’s moving in the right direction. In the past the approach has been not so much to assure against disaster, as to pretend to and then bill retroactively for whatever insurance companies failed to take into account. The way the article presents it, the answer is in financial markets. Their point is that insurance companies can’t handle a $100 billion disaster, but that financial markets handle $59 trillion a year and frequently cope well with 1% losses — $590 billion. Finding a way to use that stability to provide insurance against unusual events is what is now being done.
The cool thing is that apparently financial markets have been pricing financial catastrophes for quite some time and the going rate (for no known, conscious reason) has been four times the expectation value. So Seo’s factor of 4 may be a coincidence or it may reasoning behind what the market already knew through its random oscillations. At any rate, all of this reminds me of one of my favorite functions — loglog, or more accurately, log(log(x)). It’s frickin’ sweet because it grows incredibly slowly — loglog(5) = 0.48, loglog(100) = 1.53, and loglog(100000) = 2.44. It would seem to me that if you were looking at tails, loglog might actually come up and that factor of 4 might handle events with a probability as low as 1 in 10^25 since loglog(10^25) = 4.05. But that’s just numerology on my part.
The only problem with the article is that they seem to assume everything is normally distributed…