Risk-Seeking Behavior and Its Implications for the Optimal Decision Making of Annuity Insurers

Abstract

This study investigates risk-seeking and optimal decisions of annuity providers. On the basis of a sample of U.S. life and annuity (L/A) insurers between 1997 and 2016, the results show clear performance-dependent risk attitudes. Specifically, insurers with returns below aspiration levels take more risks, whereas those with returns above reference levels decrease their risk-seeking, which supports the basic propositions of the cumulative prospect theory (CPT). Given initial evidence of mixed risk preferences in the L/A insurance industry, we derive an annuity insurer’s optimal investment and business strategies in a CPT decision-making framework. We show that changing risk preferences considerably affect an annuity provider’s decisions. We further illustrate how risk management changes an annuity insurer’s optimal strategies. Our results suggest that risk management lowers downside risk and allows a loss-averse decision maker to assume more risk and achieve a higher level of utility.

ACKNOWLEDGMENTS

We are grateful to the Editor Patrick Brockett and the two anonymous referees for their constructive comments.

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Notes

1 Both buy-in and buy-out annuities are bulk annuities purchased by DB sponsors from annuity insurers to transfer investment and longevity risk for some or all of their pension liabilities.

2 According to A.M. Best, high-risk assets in the U.S. L/A insurance industry include stocks, mortgage loans, real estate, schedule BA assets, and other investment assets.

3 Tversky and Kahneman (1992) extended prospect theory and developed CPT by applying separate cumulative weighting functions to gains and losses. Different from the prospect theory by Kahneman and Tversky (1979), CPT satisfies first-order stochastic dominance.

4 To determine whether our results are simply driven by the skewness of returns, we calculate the negative risk–return association ratios ρ for the above-target group and the below-target group respectively based on a randomly sampled set of returns using different distributional assumptions and then compare them with the values in Table 2. The ρ values of the low-return and high-return groups with different distributional assumptions (including normal distribution, Student’s t-distribution, Gamma distribution, Weibull distribution, and Pareto-type II distribution) at different parameter values based on the simulations imply no changing risk preferences, different from our empirical results. This analysis suggests that simply the fact that returns are skewed will not lead to our results.

5 Our model can be readily extended to the one with dividend payment as a decision-making variable determined by the CPT optimization model.

6 As a robustness check, we use the medians of N simulated $X(t-1)$s and $S(t-1)$s as the realized total assets and the realized total surplus at time t – 1, respectively. Our inferences remain qualitatively unchanged.

7 The Human Mortality Database, published by the University of California, Berkeley, and the Max Planck Institute for Demographic Research, contains original calculations of death rates and life tables for national populations (countries or areas), as well as the input data used in constructing those tables. The input data consist of death counts from vital statistics, plus census counts, birth counts, and population estimates from various sources. www.mortality.org.

Additional information

Funding

Cuixia Chen gratefully acknowledges financial support from the Social Science Fund Project of Hebei Province (HB20YJ038) and Ming Zhou is grateful for financial support from the National Natural Science Foundation of China (11971506).