Catastrophe bonds and the investor's choice problem

Consider the following proposition. You put up an amount of capital X for one year. There is a small probability p (e.g., p = .01) that you will lose the entire amount. With probability (1-p) you get the entire amount back. What interest rate (fee) should you charge to participate?

What I've just described is a catastrophe bond. A catastrophe bond allows an insurer to transfer the tail risk from a natural disaster (hurricane, earthquake, fire, etc.) to an investor who is paid appropriately. How can we decide the appropriate fee for taking on this risk? It's an example of the fundamental investor's choice problem. That is, what is the value of a gamble specified by a given probability distribution over a set of payoffs? (Which of two distributions do you prefer?) One would think that the answer depends on individual risk preferences or utility functions.

Our colloquium speaker last week was John Seo of Fermat Capital, a hedge fund that trades catastrophe bonds. Actually, John pioneered the business at Lehman Brothers before starting Fermat. He's yet another deep thinking physicist who ended up in finance. Indeed, he claims to have made some fundamental progress on the investor's choice problem. His approach involves a kind of discounting in probability space, as opposed to the now familiar discounting of cash flows in time. I won't discuss the details further, since they are slightly proprietary.

I can discuss aspects of the cat bond market. Apparently the global insurance industry cannot self-insure against 1 in 100 year risks. That is, disasters which have occurred historically with that frequency are capable of taking down the whole industry (e.g., huge earthquakes in Japan or California). Therefore, it is sensible for insurers to sell some of that risk. Who wants to buy a cat bond? Well, pension funds, which manage the largest pools of capital on the planet, are always on the lookout for sources of return whose risks are uncorrelated with those of stocks, bonds and other existing financial instruments. Portfolio theory suggests that a pension fund should put a few percent of its capital into cat bonds, and that's how John has raised the $2 billion he currently has under management. The market answer to the question I posed in the first paragraph is roughly LIBOR plus (4-6) times the expected loss. For a once in a century disaster, this return is LIBOR plus (4-6) percent or so. Sounds like a good trade for the pension fund as long as the event risk is realistically evaluated.

Note there is no leverage or counterparty risk in these transactions. An independent vehicle is created which holds the capital X, invested in AAA securities (no CDOs, please :-). If the conditions of the contract are triggered, this entity turns the capital over to the insurance company. Otherwise, the assets are returned at the end of the term.

In the colloquium, John reviewed the origins of present value analysis, going back to Fibonacci, Fermat and Pascal. See Mark Thoma, who also attended, for more discussion.