Stephen P. D'Arcy and Richard W. Gorvett examine the sensitivity of the liabilities of property/casualty insurers to interest rates.

The property/casualty insurance industry is beginning to adopt some of the asset-liability management strategies that have been developed by, and applied to, other financial institutions. This development reflects an increase in the financial sophistication of many property/casualty insurers. However, our industry is different enough from other financial services that the standard tools developed for those other industries are not directly applicable to property/casualty insurers. This article will examine one aspect of asset-liability management - the sensitivity of liabilities to interest rates - to illustrate this difference and explain how the existing tools need to be altered.

In the 1970s, interest rates in the United States became much more volatile than they had been previously (see Figure 1). This occurred in part because the United States Federal Reserve began to focus on controlling inflation, rather than interest rates. The resulting interest rate volatility caused significant problems for banks, savings and loans, life insurers, and other financial institutions with significant exposure to interest rate risk. In order to cope with the greater volatility, a number of financial innovations and new products have been introduced that could, if properly used, help these institutions manage their exposure to interest rate risk. As part of the process of managing interest rate risk, tools to measure this exposure have also been developed.

Assets and liabilities are both exposed to interest rate risk - ie, their values can change when interest rates change - but sometimes they are exposed in very different ways. The savings and loan industry in the United States discovered, to its dismay, that having assets that consisted primarily of long-term fixed interest rate mortgages, and liabilities that consisted mainly of short-term demand deposits, could prove disastrous when interest rates increased. Similarly life insurers throughout the world experienced similar problems in the 1980s when interest rates rose above the contractual loan rate on cash value policies, prompting a bout of disintermediation that impaired the viability of many life insurers and led to a restructuring of policy loan provisions.

Because changes in interest rates can affect the values of assets and liabilities, they also can affect the net worth of a company. Asset-liability management provides tools to help financial institutions manage their exposure to interest rate risk. One relatively simple method, termed duration matching, involves setting the interest rate sensitivity of assets and liabilities equal to each other, so that any change in interest rates has an offsetting effect: eg, asset values are affected, but liability values are also impacted, and from a net worth perspective, the two changes offset. Duration is a calculated value that is an approximation of the sensitivity of a financial instrument, either an asset, a liability, or a portfolio, to interest rate changes. The economic value of a financial instrument changes as interest rates change, since future cash flows are discounted at the new interest rate.

For example, Figure 2 illustrates the present value of a $1 million dollar ten-year 8% annual coupon bond given various current interest rates. (Such a bond is an asset for its owner and a liability for its issuer.) The cash flows do not change as the interest rate changes. Each year the bond provides an $80,000 coupon payment, and the bond matures for $1 million at the end of ten years. However, each annual payment has a different present value as interest rates change, since the payment is discounted at the new interest rate.

Duration is, essentially, the slope of the tangency line to the present value curve at the current interest rate. This indicates the approximate percentage change in the present value of the bond for a one percentage point change in interest rates. On Figure 2, the tangency line has a slope of -6.71 at an interest rate of 8%. Thus, for every one percentage point increase in interest rates, the present value of the bond will decline by approximately 6.71%.

Actually, as interest rates change, the true bond value will move along the present value curve, not the tangency line. If interest rates were to increase by one percentage point, from 8% to 9%, the bond value would actually decline by 6.42%, not 6.71%. Duration is just an approximation of the interest rate sensitivity. For small changes in interest rates, this approximation may be close enough. If not, then an additional adjustment can be incorporated (termed convexity) to obtain an even more accurate estimate.

The duration calculation is based on several critical assumptions. First, it is assumed that there is a single interest rate that applies to all time periods. Thus, the one-year interest rate and the ten-year interest rate are both at the same level. Second, it is assumed that any change in interest rates affects all time periods the same. If interest rates increase by one percentage point, then both the one-year and the ten-year rate increase by one percentage point (eg, from 8% to 9%). Finally, it is assumed that the cash flows are not affected by the level of interest rates. In the bond example given, no matter what interest rate applies, each year a payment of $80,000 will be made and the bond will mature in ten years.

The flat rate and parallel shift interest rate assumptions are recognized as being overly simplistic, and significant research has addressed these issues. In addition, the cash flows on many financial instruments vary with interest rates. For example, callable bonds, collateralized mortgage obligations (CMOs), and floating-rate bonds all have cash flows that depend on the level of the interest rate. As interest rates decline, for example, homeowners refinance their fixed-rate mortgages, so that the payments on a CMO are made more quickly. Measuring the sensitivity of an interest-sensitive cash flow is more complicated than for a fixed cash flow. A measure termed effective duration is used to describe how assets and liabilities are affected when their cash flows change as interest rates change.

The assets of property/casualty insurers are fairly similar to the assets held by other financial institutions, although the distribution of assets varies. Thus, the techniques used by other financial institutions to measure the interest rate sensitivity of bonds, stocks, and mortgage-backed securities can also be applied to the assets of property/casualty insurers. However, the liabilities of property/casualty insurers are significantly different from those of banks and life insurers. The three major categories of liabilities for property/casualty insurers are loss reserves, loss adjustment expense reserves, and the unearned premium reserve. Each of these categories is sensitive to future inflation. Since interest rates and inflation are related, these liabilities are, in effect, interest-rate sensitive.The loss reserve is established to cover all losses that have occurred to date that have not yet been paid. This includes losses that have been reported, investigated, negotiated and in the process of being settled; claims reported so recently that no information is available to establish a loss value or likely settlement amount; and losses that have not yet even been reported (IBNR). Although claims that await only the issuance of a check are not going to be affected by a sudden increase in the inflation rate, other claims are likely to be affected. For a bodily injury claim, future medical treatment will be more expensive if inflation increases than it otherwise would be. This increase in medical costs could also increase the judgment for pain and suffering and other intangible bodily injury costs.

The loss adjustment expense reserve contemplates the unpaid expenses associated with settling claims, both by company personnel (unallocated LAE) and outside adjusters, lawyers and expert witnesses (allocated LAE). These expenses are subject to future inflation. Thus, an increase in interest rates, accompanied by an increase in inflation, would cause these future payments to increase.

The unearned premium reserve is a statutory requirement based on a pro-rata portion of the written premium reflecting the unexpired portion of the contract term. This value is widely recognized as being conservative. The objective of this reserve is to assure that an insurer maintains an adequate amount of the premium to pay for losses that have not yet occurred but will occur during the remaining term of policies that have already been written. The insurer is obligated to pay these future claims. Since the claims have not yet occurred, any increase in the rate of inflation will increase the future cash flow emanating from the unearned premium reserve. Thus, this cash flow is interest rate sensitive.

Measuring exactly how the cash flows from the loss reserve, loss adjustment expense reserve, and unearned premium reserve will change as interest rates change is difficult. Unfortunately, most applications of asset-liability management to property/casualty insurance simply assume that these cash flows are not related to interest rates. This is an incorrect assumption, and will lead to erroneous conclusions when used to match assets and liabilities.

The correct relationship depends on the correlation between interest rates and the inflation rate, which can vary by line of business. It also depends on how quickly the cost of a claim is fixed in value, even though the claim remains unpaid. For example, if an insurer is negotiating with a claimant over the value of property that was damaged due to the negligence of an insured, then the cost of the repairs, which may already have been completed, will not change with future inflation. On the other hand, if a bodily injury claimant is still receiving medical treatment, then future increases in medical costs will increase the cost of future treatments, although treatments that have already been received will not be affected. One very difficult question to answer is whether inflation after a loss occurs but prior to the settlement of the claim affects the value a jury assigns to pain and suffering and other intangible bodily injury claims.

By including the interest rate sensitivity of the liability cash flows, the effective duration of liabilities is significantly less than the standard duration measure. This means that an insurer that is matching the duration of assets and liabilities in an attempt to minimize the company's interest rate risk actually remains exposed to this risk. Thus, asset-liability management for property/casualty insurers is even more complicated than for other financial institutions. However, rather than being dissuaded from attempting to manage this risk, property/casualty insurers simply need to be aware that their liabilities are interest rate sensitive and incorporate an adjustment to reflect this relationship.

Stephen P. D'Arcy and Richard W. Gorvett teach at the University of Illinois at Urbana-Champaign; Mr D'Arcy in the Finance Department and Mr Gorvett in the Actuarial Science Program in the Mathematics Department. Both are Ph.D's in finance and FCAS's (Fellow of the Casualty Actuarial Society).