Longevity Risk in Reinsurance and Equity Markets
Authors:   , Laursen Nicolai Søgaard 
Published: June 2023

This PhD dissertation centers on systematic longevity risk, which refers to the uncertainty of future survival rates for a group of individuals. Each chapter provides independent contributions to the challenge of how to alternatively redistribute longevity risk. The first chapter, Longevity hedge effectiveness using socioeconomic indices coauthored with Malene Kallestrup-Lamb, uses Danish mortality data stratified into socioeconomic groups to eval-uate basis risk in longevity hedging. The study addresses the question of how annuity providers, exposed to different socioeconomic mortality rates, can hedge the variability of a life annuity most efficiently. We assume that the annuity provider can engage in a mortality-linked security via two alternative hedging strategies, with and without basis risk, and evaluate the costs and benefits. The cost is represented by the notional amount of hedging contracts optimally bought times the actuarial risk premium, whereas the benefit is denoted as the risk reduction in the variability of a life annuity. We find that eliminating basis risk is more cost-effective for the annuity provider, as it allows a higher degree of hedge effectiveness at a cost equivalent to a hedge with basis risk. Lastly, the yearly expenses of hedging longevity risk require, at most, an extra added rate of return of no more than 0.2%. The current assumption in the actuarial literature is that the evolution of mortality rates is independent of financial risks. The second chapter, Unsystematic mortality and time-varying re-turns, however, shows that an increase in unsystematic mortality raises one-year ahead real returns heterogeneously for portfolios sorted by industry and dividend-price ratios in the U.S stock mar-ket. For half of the industry portfolios, the magnitude is equivalent to a comparable increase in the dividend-price ratio, whereas the remaining industry portfolios are not influenced. In addi-tion, standardized mortality shocks account for 80% of the average real return gap between value and growth portfolios. I assume that higher unsystematic mortality rates pose temporary adverse demand shocks. Therefore, I analyze unsystematic mortality shocks in a two-good consumption-based asset pricing model and infer economic point estimates of the loss in consumption of various goods for unsystematic mortality’s adjacent ages. This validates the heterogeneous impact on real returns across industry returns; however, the equivalent impact on the dividend-price sorted port-folios cannot be attributed to industry composition alone. The value premium has previously been suggested as capturing an omitted risk variable (Ball, 1978; Fama and French, 1992), which conforms with longevity risk as the underlying uncertainty, mortality rates, are published with a two-year lag. In the third chapter, Longevity risk and the value premium, I introduce stochastic survival rates in the intertemporal budget constraint for a repre-sentative agent with standard recursive preferences. Thus, higher longevity (mortality) changes increase (decrease) the representative agent’s intertemporal budget constraint. The assumption of a representative agent is justified as changes in conditional survival rates are perfectly positively correlated across ages. Longevity risk also evolves as a random walk, which suggests that any impact on asset prices would be unrelated to hedging demands and, instead, could influence re-turns comparably to market cash-flow risk. The model suggests that the risk premium linked to longevity risk is slightly higher than the equivalent related to news regarding the market portfo-lio’s cash flows. I find empirical support for the model and show that the monthly Sharpe ratio associated with longevity risk is around 10%.