Michael Lewis: In Nature's Casino (How Wall Street is trying to quantify the risk of catastrophic weather)
nytimes.com
nytimes.com
"An industrial company had called Lehman with a problem. It operated factories in Japan and California, both near fault lines. It could handle one of the two being shut down by an earthquake, but not both at the same time. Could Lehman Brothers quote a price for an option that would pay the company $10 million if both Japan and California suffered earthquakes in the same year? Lehman turned to its employee with a reputation for being able to price anything. And Seo thought it over. The earthquakes that the industrial company was worried about were not all that improbable: roughly once-a-decade events. A sloppy solution would be simply to call an insurance company and buy $10 million in coverage for the Japanese quake and then another $10 million in coverage for the California quake; the going rate was $2 million for each policy. "If I had been lazy, I could have just quoted $4 million for the premium," he says. "It would have been obnoxious to do so, but traders have been known to do it." If either quake happened, but not both, he would have a windfall gain of $10 million. (One of his policies would pay him $10 million, but he would not be required to pay anything to the quake-fearing corporation, since it would get paid only if both earthquakes occurred.)"
"But there was a better solution. He needed to buy the California quake insurance for $2 million, its market price, but only if the Japanese quake happened in the same year. All Seo had to do, then, was buy enough Japanese quake insurance so that if the Japanese quake occurred, he could afford to pay the insurance company for his $10 million California insurance policy: $2 million. In other words, he didn't need $10 million of Japanese quake insurance; he needed only $2 million. The cost of that was a mere $400,000. For that sum, he could insure the manufacturing company against its strange risk at little risk to himself. Anything he charged above $400,000 was pure profit for Lehman Brothers."
My question:
Shouldn't the text instead read "Anything he charged above $2,400,000..."? Suppose the CA earthquake occurs _before_ the JP earthquake. After the JP earthquake the insurer receives $2M but it's too late to buy CA insurance on a past event.
To use one policy to pay for another, the insurer must buy both policies at the same time. Otherwise the risk of an uncovered event would occur.
It would be cheaper to merely buy $10M worth of either CA or JP insurance alone (but not both), since, certeris paribus, either would cost only $2M.
Am I missing something?
Another surprising thing in that example is that the guy says he could get away with quoting $4M? If insuring either factory for $10M (or insuring both for $5M) costs about $2M, I'd suppose that's the upper bound for a cost evaluation, even if you're lazy.
Here's where the conclusion is unclear : it says "The cost ... was a mere $400,000." However, according to the article's math, that's the cost -per factory-. The policy for the entire company would cost $800,000.
However, that's not quite right either. In order to return $10M total, you'd only have to buy about $334,000 of insurance on each factory (I'm rounding the numbers for convenience). Since the example operates under the assumption that you can always use the proceeds from one policy to pay for the other -- ie, there's never a perfectly simultaneous event at both locations -- I'll take that as a given.
Let's say that Factory A gets hit first (California or Japan, it doesn't matter). We collect our insurance payment of $1,670,000 ($334,000 5) and spend the total amount on additional insurance for Factory B. When Factory B gets hit, we receive $8,350,000 ($1,670,000 5) from that supplementary purchase. So where does the missing $1,650,000 come from? Remember that we couldn't know which factory would be hit first, so we initially bought $334,000 policies on -both- factories ... and that policy is still in effect on Factory B. It returns $1,670,000, which brings our total to just over the $10M target (remember, I'm rounding for clarity). So the total that we need to spend on insurance is ($334,000 * 2 =) $668,000 per year.
IOW all purchases of insurance must be done beforehand at the same time. Purchases of insurance cannot be contingent, although the gains may be. So you can't wait and see if one incident occurs to decide whether to buy more insurance.
Dr. John (he of the bag lunch and the actuarial degree) says "well, the reporter says that Seo actually planned on using the proceeds from one policy to purchase additional insurance on the other factory. So this must be the scenario, and we should take that as a given." Well, as I wrote above, even with that assumption, the article's math is still wrong.
Fat Tony (of the Brooklyn accent and custom suits) says "This Seo guy isn't covered nearly as much as he thinks he is. If the two earthquakes happen on the same day, he's screwed. Heck, they'd better not happen less than a month apart ... have you seen how long it takes an insurance company to get a policy written up? If he thinks he's gonna have that second policy the next day after the first earthquake, he's dreaming." And he's right. The reporter has misrepresented the solution in some fundamental way -- either it didn't play out like this, or it's purely a hypothetical deal.
So which error is more egregious? I dunno; both aspects of this article bothered me when I read it. Not only does the reporter almost certainly misrepresent the terms of the deal, but he doesn't even get the math right on the terms he presented.
She faxed the numbers to insurers, then walked to Au Bon Pain. Everything was suddenly more vivid and memorable. She ordered a smoked-turkey and Boursin cheese sandwich on French bread, with lettuce and tomato, and a large Diet Coke.
Is the NYT so hard-up for revenues they're asking their authors to slip these in?
I can't imagine Lewis wrote that on his own.
Of course he did. Ever since Ian Fleming, writers have been inserting brand names to add a sort of edgy verisimilitude.