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find the bonds attractive because they have very little systematic risk. (See Section 1.3 for a discussion of systematic risk.) The bond payments depend on how long people live and this is largely uncorrelated with returns from the market.

      3.5 PROPERTY-CASUALTY INSURANCE

      Property-casualty insurance can be subdivided into property insurance and casualty insurance. Property insurance provides protection against loss of or damage to property (from fire, theft, water damage, etc.). Casualty insurance provides protection against legal liability exposures (from, for example, injuries caused to third parties). Casualty insurance might more accurately be referred to as liability insurance. Sometimes both types of insurance are included in a single policy. For example, a home owner might buy insurance that provides protection against various types of loss such as property damage and theft as well as legal liabilities if others are injured while on the property. Similarly, car insurance typically provides protection against theft of, or damage to, one's own vehicle as well as protection against claims brought by others.

      Typically, property-casualty policies are renewed from year to year and the insurance company will change the premium if its assessment of the expected payout changes. (This is different from life insurance, where premiums tend to remain the same for the life of the policy.) Because property-casualty insurance companies get involved in many different types of insurance there is some natural risk diversification. Also, for some risks, the “law of large numbers” applies. For example, if an insurance company has written policies protecting 250,000 home owners against losses from theft and fire damage, the expected payout can be predicted reasonably accurately. This is because the policies provide protection against a large number of (almost) independent events. (Of course, there are liable to be trends through time in the number of losses and size of losses, and the insurance company should keep track of these trends in determining year-to-year changes in the premiums.)

      Property damage arising from natural disasters such as hurricanes give rise to payouts for an insurance company that are much less easy to predict. For example, Hurricane Katrina in the United States in the summer of 2005 and a heavy storm in northwest Europe in January 2007 that measured 12 on the Beaufort scale proved to be very expensive. These are termed catastrophic risks. The problem with them is that the claims made by different policyholders are not independent. Either a hurricane happens in a year and the insurance company has to deal with a large number of claims for hurricane-related damage or there is no hurricane in the year and therefore no claims are made. Most large insurers have models based on geographical, seismographical, and meteorological information to estimate the probabilities of catastrophes and the losses resulting therefrom. This provides a basis for setting premiums, but it does not alter the “all-or-nothing” nature of these risks for insurance companies.

      Liability insurance, like catastrophe insurance, gives rise to total payouts that vary from year to year and are difficult to predict. For example, claims arising from asbestos-related damages to workers’ health have proved very expensive for insurance companies in the United States. A feature of liability insurance is what is known as long-tail risk. This is the possibility of claims being made several years after the insured period is over. In the case of asbestos, for example, the health risks were not realized until some time after exposure. As a result, the claims, when they were made, were under policies that had been in force several years previously. This creates a complication for actuaries and accountants. They cannot close the books soon after the end of each year and calculate a profit or loss. They must allow for the cost of claims that have not yet been made, but may be made some time in the future.

      CAT Bonds

      The derivatives market has come up with a number of products for hedging catastrophic risk. The most popular is a catastrophe (CAT) bond. This is a bond issued by a subsidiary of an insurance company that pays a higher-than-normal interest rate. In exchange for the extra interest, the holder of the bond agrees to cover payouts on a particular type of catastrophic risk that are in a certain range. Depending on the terms of the CAT bond, the interest or principal (or both) can be used to meet claims.

      Suppose an insurance company has a $70 million exposure to California earthquake losses and wants protection for losses over $40 million. The insurance company could issue CAT bonds with a total principal of $30 million. In the event that the insurance company's California earthquake losses exceeded $40 million, bondholders would lose some or all of their principal. As an alternative, the insurance company could cover the same losses by making a much bigger bond issue where only the bondholders’ interest is at risk. Yet another alternative is to make three separate bond issues covering losses in the range $40 to $50 million, $50 to $60 million, and $60 to $70 million, respectively.

      CAT bonds typically give a high probability of an above-normal rate of interest and a low-probability of a high loss. Why would investors be interested in such instruments? The answer is that the return on CAT bonds, like the longevity bonds considered earlier, have no statistically significant correlations with market returns.5 CAT bonds are therefore an attractive addition to an investor's portfolio. Their total risk can be completely diversified away in a large portfolio. If a CAT bond's expected return is greater than the risk-free interest rate (and typically it is), it has the potential to improve risk-return trade-offs.

      Ratios Calculated by Property-Casualty Insurers

      Insurance companies calculate a loss ratio for different types of insurance. This is the ratio of payouts made to premiums earned in a year. Loss ratios are typically in the 60 % to 80 % range. Statistics published by A. M. Best show that loss ratios in the United States have tended to increase through time. The expense ratio for an insurance company is the ratio of expenses to premiums earned in a year. The two major sources of expenses are loss adjustment expenses and selling expenses. Loss adjustment expenses are those expenses related to determining the validity of a claim and how much the policyholder should be paid. Selling expenses include the commissions paid to brokers and other expenses concerned with the acquisition of business. Expense ratios in the United States are typically in the 25 % to 30 % range and have tended to decrease through time.

The combined ratio is the sum of the loss ratio and the expense ratio. Suppose that for a particular category of policies in a particular year the loss ratio is 75 % and the expense ratio is 30 %. The combined ratio is then 105 %. Sometimes a small dividend is paid to policyholders. Suppose that this is 1 % of premiums. When this is taken into account we obtain what is referred to as the combined ratio after dividends. This is 106 % in our example. This number suggests that the insurance company has lost 6 % before tax on the policies being considered. In fact, this may not be the case. Premiums are generally paid by policyholders at the beginning of a year and payouts on claims are made during the year, or after the end of the year. The insurance company is therefore able to earn interest on the premiums during the time that elapses between the receipt of premiums and payouts. Suppose that, in our example, investment income is 9 % of premiums received. When the investment income is taken into account, a ratio of 106 − 9 = 97 % is obtained. This is referred to as the operating ratio. Table 3.2 summarizes this example.

TABLE 3.2 Example Showing Calculation of Operating Ratio for a Property-Casualty Insurance Company

      3.6 HEALTH INSURANCE

      Health insurance has some of the attributes of property-casualty insurance and some of the attributes of life insurance. It is sometimes considered to be a totally separate category of insurance. The extent to which health care is provided by the government varies from country to country. In the United States publicly funded health care has traditionally been limited and health insurance has therefore been an important consideration for most people. Canada is at the other extreme: nearly all health care needs are provided by a publicly funded system. Doctors are not allowed to offer most services privately. The main role of health insurance in Canada is to cover prescription costs and dental care, which are not funded publicly. In most other countries, there is a mixture of public and private health care. The United Kingdom, for example, has a publicly funded health care system,

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