Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance

North American Actuarial Journal, Jul 2004 by Bensics, Frank

Hardy, Mary R. 2003, Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, John Wiley and Sons, Inc., Hoboken, New Jersey, xv 286 pages, $95.00 ISBN 0471392901

Actuarial students are first exposed to the stochastic modeling of insurance values through Actuarial Mathematics (Bowers et al. 1997). The text replaced Life Contingencies (1967) more familiarly known as Jordan on Society of Actuaries Examinations in the early 1980s, with the Casualty Actuarial Society adopting subsequently. Traditional (or non-stochastic) life contingencies under Jordan allowed for the calculation of expected present values, but gave no insight as to measurement of risk. The principal innovation of the new or stochastic approach was the notion that policy values were random variables, allowing for measurement of value uncertainty, at least to a limited extent.

Insurance, as with all financial instruments, is subject to multiple sources of value uncertainty including; payment likelihood, payment timing, payment amount and the present value factor given time of payment. The approach of Actuarial Mathematics (Bowers et al. 1997) is to explicitly model likelihood and/or timing uncertainty, through a survival model (or mortality table in a discrete context). Payment amounts, and the present value factors are presumably deterministic functions of time of payment. Values of interest such as premiums and reserves are calculated as expectations of the time conditional values. Distributions for values are occasionally found through transformations of the timing random variable, or for more basic analysis, quantiles or standard deviations determined.

While the approach is valuable from a conceptual point of view, it is of less practical value. Mortality, which is the usual contingent event, is generally only a significant source of risk in cases, which do not meet the independence assumption of Actuarial Mathematics (Bowers et al. 1997). More significantly, for most contemporary life insurance products with a savings component, changing asset values dominate as a source of risk, either through the asset accumulation supporting the policy or through the impact of changing asset values on benefits paid to policyholders.

While actuarial students are introduced to the notion of amount risk through the subjects of risk theory and loss distributions, the context is property casualty or health insurance based claims' payments and the underlying assumption is again one of independence of outcomes. Exposure to the notion of investment risk, and the standard paradigms upon which modern investment theory is based; portfolio theory, the GAPM, and the Black-Scholes model first comes in a corporate finance context on the current Course 2, while product design is introduced on Course 5. The integration of product and investment risk is generally not present until Course 8, and there only to a somewhat ad hoc extent, varying with exam specialty.

What has been lacking is a cohesive source that integrates contemporary modeling of investment risk in the context of modern insurance contracts. Financial Economics: With Applications to Investments, Insurance, and Pensions (Panjer et al. 1998) synthesized much of the underlying theory. However, despite mentioning practical applications in the title, the focus was clearly on a more theoretical presentation, providing little in the way of a bridge from the underlying theoretical models to actual application in either a pricing or risk management context.

Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance however, does provide such a bridge, specifically where the source of risk arises through changing equity prices. Stochastic interest rates, the second major source of investment risk, are dealt with only to the extent that they affect values of equity-based products. Much of the material is a consequence of studies undertaken by the Canadian Institute of Actuaries Task Force, here after referred to as the Task Force.

With investment based insurance products, the basic idea is to create upside potential with limited downside risk. Chapter 1 introduces the contractual variations of this concept within various countries, such as the United States (Variable and Equity Indexed Annuities), the United Kingdom (Unit-Linked Insurance), Germany (Equity-Linked Insurance) and Canada (segregated funds). While the title of the book refers to life insurance, it does not deal with the original version of the equity based concept, variable life insurance which appeared in Europe in the 1960s and the United States in 1970s, or the more recently introduced analog to equity indexed annuities known as Equity Indexed life. The omission is not serious as the techniques presented modeling investment-dominated contracts are adaptable to modeling the equity risk of the insurance dominated contracts.

Asymmetric loss structures invariably lead to option analogies. Brennan and Schwartz (1976) and Boyle and Schwartz (1977) are early examples of what the author refers to as the dynamic hedging approach to risk management in which an equity based insurance liability is treated as an option and hedged with a dynamically adjusted portfolio of marketable assets. The actuarial profession, at the time, paid little notice as equity risks were generally fully assumed by policyholders through separate account funds without guarantees. High interest rates in the 1980s, and an explosion of Single Premium Deferred Annuity (SPDA) business, created awareness of the investment risk of long-term guarantees through guaranteed deposit rates (call options) and book value surrender guarantees (put options). Unfortunately, not enough attention was paid in certain cases, as the author describes the case of the Equitable (U.K.) where overly generous promises made to policyholders have led to disastrous consequences. Similar cases in the United States could have easily been mentioned as well. The lack of formal analysis is referred to as the ad hoc approach, which is hopefully diminishing through either regulatory mandate, or voluntary choice.