Sunday, August 26, 2007

Catastrophe Bonds

In today's New York Times magazine, Michael Lewis writes about catastrophe bonds, with a focus on hedge fund manager John Seo.

In the article, Mr. Lewis gives a simplified example that he attributes to Dr. Seo. In that example, there is a glaring problem that I couldn't get out of my head.

According to Mr. Lewis, Dr. Seo was asked to price an option that would pay out $10 million if there were earthquakes in both California and Japan in the same year (a client had one plant on a fault line in Japan and another on a fault line in California). The example goes on to state that it would cost $2 million to buy $10 million of insurance in either market.

Mr. Lewis states that Dr. Seo came to the realization that he only had to buy a policy for $2 million of insurance in California. This would cost only $400,000. If there was an earthquake in California, he could then apply the $2 million to purchase $10 million of insurance in Japan. Any amount over $400,000 for the option would then be pure profit.

This example is used to explain why insurance companies tend to charge 4x their expected loss (probability of event multiplied by the value of the policy) as insurance premiums.

The problem, of course, with this approach is that it assumes that an earthquake would FIRST hit California, BEFORE any earthquake in Japan. Dr. Seo's firm would be on the hook for $1.6 million if they purchased the second policy (and $8 million if they didn't hedge the additional risk in California).

I was both excited and concerned when I realized this. While I am an expert in some areas of finance, catastrophe insurance was definitely not one of those areas.

I played around with the numbers for a while and calculated that it would cost $666,666.68 for two policies, one for Japan and one for California. Each of these policies would cost $333,333.34 for $1,666,666.70 of coverage. The proceeds from the first event would then pay for the cost of insuring the total amount in case of the second event. There should be some additional compensation for the time value of the $1,666,666.70 paid on the second policy, between the date of the purchase of the coverage and the actual receipt of the payment from the first event. Any amount over this would then be pure profit.

I was concerned that I might be kidding myself, so I waited to post this. In the mean time, I did a search on Google and found another blogger who had already identified the same discrepancy.

Okay, I wasn't the first to point it out, but at least my quant skills are still pretty good!

The rest of the Mr. Lewis' article is very good, and I recommend it.

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