Academic journal article Journal of Risk and Insurance

To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies

Academic journal article Journal of Risk and Insurance

To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies

Article excerpt

ABSTRACT

Demographic risk, i.e., the risk that life tables change in a nondeterministic way, is a serious threat to the financial stability of an insurance company having underwritten life insurance and annuity business. The inverse influence of changes in mortality laws on the market value of life insurance and annuity liabilities creates natural hedging opportunities. Within a realistically calibrated shareholder value (SHV) maximization framework, we analyze the implications of demographic risk on the optimal risk management mix (equity capital, asset allocation, and product policy) for a limited liability insurance company operating in a market with insolvency-averse insurance buyers. Our results show that the utilization of natural hedging is optimal only if equity is scarce. Otherwise, hedging can even destroy SHV. A sensitivity analysis shows that a misspecification of demographic risk has severe consequences for both the insurer and the insured. This result highlights the importance of further research in the field of demographic risk.

INTRODUCTION

The financial performance of insurance companies writing life insurance and annuity policies is heavily dependent on possible deviations from the mortality assumptions made at the time the contracts were underwritten. Random deviations from mortality assumptions are therefore an important aspect of life insurance company risk management. Life tables used for pricing life insurance and annuity products typically incorporate an assumed future development (trend) of life expectancy improvement. Deviations from this development, on the one hand, can arise if the insurer's liability portfolio is too small to get the law of large numbers working fully. On the other hand--and this is the focus of our contribution--there is demographic risk, which we define as the risk that mortality laws and life tables themselves change in a non-deterministic way (see Olivieri, 2001). For example, imagine that a path-breaking technological or medical innovation leads to a sudden decrease in mortality at all ages. This would result in a severe deterioration of an annuity provider's solvency situation and a drop in its shareholder value (SHV), whereas a life insurance provider would benefit. Alternatively, an increase in the prevalence of obesity, which increases mortality at all ages (Swiss Re, 2004), would be beneficial for an annuity provider, but would result in a severe decline of SHV for a life insurance provider. (1) In either case, the inverse performance of annuity and term life insurance liabilities creates natural hedging opportunities (see Blake and Burrows, 2001; Cowley and Cummins, 2005).

That such issues of demographic risk are highly relevant is shown by the ongoing controversial scientific discussion on the future development of human life expectancy and the maximum possible lifespan. (2) Random deviations from presently assumed life tables are considered significantly probable. (3) However, despite its obvious importance, the risk management implications of demographic risk for a life insurer have received little attention in the scientific literature. (4) In our contribution, we analyze these policy implications in a SHV maximization framework. We derive the optimal risk management mix, i.e., the amount of equity to be inserted by shareholders, asset allocation (risky/risk-free), and product policy (term life insurance/life annuities) for a publicly held life insurance company with limited liability and access to a perfect capital market. Potential insurance buyers are assumed to be risk averse and not able to trade or diversify their risks perfectly. This implies that they are willing to pay insurance premiums beyond the expected value of insurance benefits. Thus, our model allows for premium loadings, which we assume to be given exogenously. (5) Empirical evidence on the dependence of insurance demand on an insurer's solvency situation (Cummins and Sommer, 1996; Sommer, 1996; Cummins and Danzon, 1997; Phillips, Cummins, and Allen, 1998) and the experimental evidence on insolvency aversion (Wakker, Thaler, and Tversky, 1997) are incorporated into our model via a demand-reaction function for insurance contracts that decreases for a given insurance premium as the insurer's solvency situation worsens. …

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