Abstract

Basis Risk of Index­Linked CAT Risk Securities

J. David Cummins, David Lalonde and Richard D. Phillips

University of Pennsylvania, Applied Insurance Research, Georgia State University

This paper provides an empirical analysis of the basis risk of index­linked catastrophic loss (CAT) derivative securities. The paper is motivated by the emergence of CAT derivative securities in 1992 and the subsequent growth and evolution of the market. CAT derivatives securitize losses from random catastrophic events, providing an innovative new approach to financing catastrophic risk. Interest in these securities has grown for a variety of reasons. Potential hedgers, such as insurers and industrial firms exposed to catastrophic risk, have become interested because of the increasing frequency and severity of property catastrophes due to hurricanes and earthquakes since the late 1980s and to the recognition that projected catastrophes in the $30 to $100 billion range are beyond the capacity of the international insurance and reinsurance markets. Although losses of this magnitude may be significant events in terms of insurance markets, they are small in relation to the value of traded securities and hence can easily be absorbed by securities markets. Moreover, catastrophic losses are "zero­beta" events, rendering CAT securities extremely valuable to investors from a portfolio diversification perspective. To date, the principal trading in CAT securities has been in two types of contracts: (1) Index­linked CAT call option spreads of the type traded on the Chicago Board of Trade; and (2) insurer­specific CAT bonds, where a specified catastrophic event triggers total or partial forgiveness of the repayment of principal. An important difference between these types of contracts is that index­linked call spreads typically pay off on an industry-wide loss index while the payoff on CAT bonds is based on insurer­specific loss experience. Thus, CAT bonds have very low basis risk but are subject to moral hazard, resulting from potential manipulation of reported losses by insures, while index­linked options have low moral hazard but are subject to an indeterminate amount of basis risk. Our study provides new information on the basis risk of index­linked CAT securities by providing extensive simulations of the hedging effectiveness of the contracts for 255 insurers writing 95 percent of the insured property values in Florida, one of the U.S. states most severely affected by exposure to hurricanes. The estimates are obtained by simulating catastrophic events using a sophisticated model developed by Applied Insurance Research (AIR), one of the leading modeling firms in the CAT risk field. The model combines actuarial data, historical climatological data, and meteorological models of the underlying physical processes that drive the severity and trajectory of hurricanes. Taking advantage of detailed county level data on the amount of insured property value exposed to loss reported to the Florida insurance regulator, we use the AIR model to obtain very accurate estimates of insurer losses over a simulation sample of 10,000 years of hurricane experience.
The principal finding of the study is that insurers of all sizes can hedge effectively using statewide loss indices. Hedging is more effective using sub­state indices, even for insurers that are relatively undiversified geographically in terms of exposure to loss. Contrary to the contention of some prior researchers, it is not necessary to for an insurer to be large in order to hedge effectively using index­linked contracts. The findings have important implications not only for insurer usage of index­linked CAT securities but also for underwriting exposure management. The results should also be of interest to insurance regulators and policymakers concerned about the increasing interest in index­linked securities by insurers. Finally, the results also provide a useful case study of the development of a new asset class, insurance­linked CAT securities, and thus provide guidance for the securitization of other unconventional financial exposures.