FOOTNOTES

^* Kevin P. Sheehan is a senior economist in the Single Family Model Development and Portfolio Management Division of Freddie Mac.

The comments and suggestions of James Marino and Lynn Shibut are gratefully acknowledged. Sarah Bohn, Melissa King, and Justin Combs provided excellent research assistance. The views expressed are those of the author and not necessarily those of the Federal Deposit Insurance Corporation or Freddie Mac.

¹ See Froot (1997).

² See Cummins, Doherty, and Lo (2002).

³ To see this, consider a risk-averse individual whose wealth, W, is subject to a random loss, L. Risk aversion can be represented by a concave utility function, U(). Given the concavity of U(), one can show that EU (W – L) <U (W – ), where E is an expectation operator and is the expected value of losses. This result lends itself to the interpretation that follows. First note that the expression EU (W – L) defines the expected utility of random wealth while the expression U (W – ) defines the utility for a specific amount of certain wealth. Certain wealth can be obtained by purchasing complete insurance, and the amount of this wealth equals the initial wealth less an insurance payment. Now, if a risk-averse individual acquires complete insurance by paying a premium equal to the expected value of losses, the utility from insured (i.e., certain) wealth, U (W – ), is greater than the expected utility from uninsured (i.e., random) wealth, EU (W – L). Such an individual is therefore better off purchasing insurance, and this would be true even if the premium were slightly larger than .

⁴ Even so, an insurance fund is necessary to cover unexpected losses. However, little capital is needed when insurance losses are relatively constant through time.

⁵ In theory this capital should be readily available. Modern portfolio theory tells us that a security should be priced in terms of its correlation with the market portfolio. The return on Treasury securities is not correlated with the returns on stocks and bonds. Given that catastrophe exposures are not correlated with the returns on a market portfolio, an insurance company could attract capital by promising to pay an expected return equal to the return on Treasury securities. To generate this required return, holders of these zero-beta assets would receive the interest earnings from the insurer’s portfolio of liquid securities as well as additional compensation for expected insurance losses. The insurance company would fund this risk premium by charging policyholders an amount equal to the expected value of the losses. However, since risk-averse individuals are willing to pay amounts greater than the expected value of losses, the insurer could fund an even larger premium and offer investors excess returns for the use of this risk-taking capital. Of course, capital constraints may exist, and possible sources of this market friction are identified below.

⁶ Geographical diversification is another important objective of reinsurance. See Cummins and Weiss (2000) for a general discussion of reinsurance.

⁷ This article argues that such limited coverage can be explained to some degree by the presence of moral-hazard and adverse-selection problems. Again, see Froot (1997) for additional explanations for the limited use of catastrophe reinsurance coverage.

⁸ Froot (1999), 12.

⁹ Ibid., 6.

¹⁰ Cummins and Weiss (2000), 181.

¹¹ Doherty (1997), 87.

¹² Ibid.

¹³ Catastrophe reinsurance contracts are typically issued with insurance limits that preclude coverage for the very highest layers of losses. A possible explanation for this lack of coverage is that ex post moral-hazard problems are most severe for the very highest layers of losses. According to this explanation, insurance limits are in place because the presence of such severe moral-hazard problems precludes the provision of reinsurance coverage.

¹⁴ Greenberg (2001) reports that just before the September 11, 2001, terrorist attacks, the U.S. commercial property/casualty insurance industry had between $100 billion and $125 billion in aggregate capital.

¹⁵ Cummins and Weiss (2000), 207.

¹⁶ On the CBOT, the level of industry-wide losses was converted to an index, and the catastrophe option contracts were written in terms of the index. Since an index point represented $10 million insurance losses, the long position described above, for example, was an option with a strike price of 3 index points.

¹⁷ A call option provides the holder with the right to buy an underlying asset at a fixed price, called the strike price. The holder exercises a call option only if the value of the underlying asset is greater than the strike price. A catastrophe option is a call option in which insurance losses determine the value of the underlying asset. In the example above, the holder exercises the option because the level of industry-wide insurance losses sets the value of the underlying asset to an amount that is greater than the strike price.

¹⁸ Doherty (1997), 87.

¹⁹ Niehaus (2002), 590.

²⁰ Harrington and Niehaus (1999), 50.

²¹ Doherty (1997), 87.

²² Cummins, Lalonde, and Phillips (2000), 2. However, a few studies have concluded that the basis risk associated with derivative contracts based on state-specific indices is not large. See, for example, Harrington and Niehaus (1999) and Cummins, Lalonde, and Phillips (2000).

²³ The bonds were actually sold by a special purpose reinsurer called Residential Re. For tax and regulatory purposes, this company had to be run independently of USAA. USAA paid Residential Re a monthly premium, and Residential Re used this payment plus the earnings on a portfolio of liquid securities to pay interest to bondholders. If USAA were to incur insurance losses greater than $1 billion, Residential Re would provide insurance coverage by liquidating its portfolio.

²⁴ Notice the similarity between catastrophe bonds and the historical marine insurance described by Jaffee and Russell (1997, p. 207): "[A] market for marine insurance operated among ancient Greeks and Phoenicians and flourished in London from as early as the seventeenth century. [The insurance took the form of a loan that offered the ship owner some degree of debt forgiveness.] In . . . the so-called contract of bottomry, a lender advanced the ship-owning merchant the full cost of the voyage as a loan. If the voyage was successful, the ship owner repaid the bank at an interest rate which included a premium to reflect the risk of loss. If the ship was lost, the loan was forgiven."

²⁵ See Froot et al. (1995) for a discussion of the lack of correlation between catastrophic risk and traditional asset classes.

²⁶ USAA paid a total premium of 576 basis points for this layer of coverage. The premium for essentially identical coverage fell to 412 basis points in 1998 and to 366 basis points in 1999. These bonds provided no principal protection and the reduction in costs can be attributed to lower estimates of expected losses.

²⁷ Borden and Sarkar (1996), 5.

²⁸ Even though potential insurance losses have increased, consolidation may be responsible for a decline in the likelihood of losses. That is, consolidated banks hold portfolios that are more diversified, so the probability of bank failure may be lower.

²⁹ See Marsh & McLennan Companies (2001), 5 and 21.

³⁰ Cummins, Lalonde, and Phillips (2000), 32.

³¹ The FDIC could issue catastrophe bonds on individual banks, but such securities would introduce problems of adverse selection. Adverse selection arises when one side of a transaction has more reliable information than the other side. Disclosure is a common solution to this problem, and in an insurance market for catastrophic bank losses, the disclosure of information would address any such problems. However, it is highly unlikely that the FDIC or other federal regulators would provide investors with proprietary information on large banks. Still, the FDIC could address this problem by issuing a security with payments linked to deposit insurance losses across all large banks. The risk of adverse selection would then be minimized inasmuch as such a security would prevent the FDIC from (adversely) selecting only high-risk banks for securitization.

³² Cummins and Weiss (2000), 165–66.

³³ Froot (1997), 13.