I’ve been trying to think about the financial structures around processes that exhibit highly skewed distributions. The insurance industry is a great place to find the examples. We buy insurance to hedge against the small but awful. Most of our houses don’t burn down, but it does happen. The chance of a fire is scale free, the insurance company protects it’s clients at the scale they care about, but who protects the insurance company against the rare event the burns down the entire town. There are three ways the insurance industry handles that scenario: they don’t cover it (excluding acts of god for example), they reinsure into a yet larger pool, or they avoid it by not insursing in certain venues. Over here at Bronte Capital is a posting arguing that Warren Buffet, who moved into the insurance industry in a big way over the last few years, has been working this third angle.
When process with a highly skewed distribution delivers it’s rare but powerful shock into the system, it’s black swans, everything designed to work with the median shocks is blows up. I’d be interested to know how the insurance industry handled the New England hurricane of 1938. I’d be interested to know how the insurance industry in Thailand handled the AID’s epidemic.
Another place I’ve been musing about exceptional, but inevitable, events is where you situate your career planning. I’ve a friend who likes to say that almost all the people he knows who made a fortune in their life “fell off a log into a pile of money” thru no special merit of their own except in some cases they consciously picked a good log to sit on. On the other hand a lot of people just fall off a log sooner or latter. It would be nice if, as you plan your career, you had a better sense of what the chances are in the trade you pick, in the economy at large. The fetish people have for presuming that career path probablities are entirely a matter of personal merit seem wreckless. I was quite impressed when an acquantance of mine with a degree in biology explained he was moving into lawyering because, well he didn’t put it this way, the climate was more predictable.
Recently I’ve been trying to explain how wily US cell phone pricing is. They sell monthly plans with N minutes and then when the exceptional crisis comes down the pike, you fall in love example, they charge you huge over charges. The typical plan delivers minutes at about five cents each and forty cents a minute. Better, at least for them, is that as little crissis come and go your start changing your plan to buy more minutes, which in the absense of a crissis you don’t use. That in turn raises the real cost of even you noncrisis minutes. It’s a very impressive pricing scam isn’t it! I recomend prepaid (t-mobile for gsm, pageplus for cdma on verizon).
If we ignore prepaid cell phone service, the cell phone contracts with a bundle of minutes every month are a bit like lousy insurance policies. You buy the option to use five hundred minutes, not because you need them, but because your insuring against the risk that you’ll run over and get stuck with the over charges. That’s great, and I mean that sarcasticly, they are selling you insurance against a risk they created.
It amuses me to wonder what would happen if everybody in the country could be coordinated into using all those free minutes one month. I very much doubt the phone companies can fufill that promise.
The options contracts implicit in those monthly cell phone contracts are analogous to the insurance pools. If we could coordinate the month of the phone it would be the analogous to a hurricane or a plague, at least from the point of view of the phone company.
That scenario has been playing out with the internet service providers, at least for the incompetent ones. For example Comcast sells me a package with certain assurances about what bandwidth I get into the Internet. Unsurprisingly the consumption patterns of their customers is highly skewed, and I’m one of the higher users since this site runs over that connection. Inspite of 20 plus years of history showing that Internet consumption grows extremely fast and quickly grows to fill the pipe provided Comcast was suprised when more users actually exercised the option they had bought. It is not relevant what these users are doing with the bandwidth (P2P, video, voice over IP, spam) because if it hadn’t been one of those it would have been something else.
This last example, the ISP’s problems, is not actually an example of pricing design in the face of a highly skewed distribution. It just looks like one at first blush. The real problem the ISPs face is the rapidly rising tide of usage. They thought they had a slower growing usage situation, something more like what is seen with the cell phones, but they were wrong. When they discovered some of the users were consuming all the bandwidth they thought they had purchased the ISPs presumed those users were little trouble makers rather than early movers. But that’s a mistake, soon everybody will consume all the bandwidth they can get.