Longevity Risk and Natural Hedge Potential in Portfolios of Life Insurance Products: The Effect of Investment Risk

Abstract

Payments of life insurance products depend on the uncertain future evolution of survival probabilities. This uncertainty is referred to as longevity risk. Existing literature shows that the effect of longevity risk on single life annuities can be substantial, and that there exists a (natural) hedge potential from combining single life annuities with death benefits or from investing in survivor swaps. The effect of financial risk on these hedge effects is typically ignored. The aim of this paper is to quantify longevity risk in portfolios of mortality-linked assets and liabilities, taking into account the effect of financial risk. We find that investment risk significantly affects the impact of longevity risk in life insurance products. It also significantly affects the hedge potential that arises from combining life insurance products, or from investing in longevity-linked assets. For example, our results suggest that ignoring the effect of financial risk can lead to severe overestimation of the natural hedge potential from death benefits, and underestimation of the hedge effects of survivor swaps.

Longevity Risk

“…8 The graph shows a number of quantiles (ranging from the 0.10-to the 0.90-quantile). The figure shows that there is already substantial longevity risk in the earliest projections Stevens et al (2010b) corresponding to t = 2007. 9 The quantile intervals for the remaining lifetime of a 65-year old in t = 2050 are even much wider.…”

“…In Figure 6 we present the distributions of a (m) 65,t and a ( f ) 65,t , when the future death probabilities are random as described above (including process, parameter, and model risk). The distribution for females (around just below 13 Euro) is shifted to the right compared to the distribution of males 20 For a detailed description we refer to the appendix of Stevens et al (2010aStevens et al ( or 2010b Figure 6 -Distribution annuity portfolio. This figure presents the distribution of the annuity portfolio at time t = 0 (corresponding to the year 2006) due to longevity risk only (i.e., after pooling).…”

“…However, when the market value margin does not accurately reflect the risk premium that a third party would require in order to be willing to take over the liabilities, it remains unclear to what extent the funding ratio approach accurately quantifies longevity risk. In this subsection we discuss an alternative approach to quantify longevity risk, namely by determining its effect on the probability of ruin (see, for example, Olivieri andPitacco 2003, andStevens et al 2010b). We also discuss how this approach relates to, and differs from, the approaches described in the previous two subsections.…”

“…In this subsection, we discuss literature regarding the impact of longevity risk on solvency requirements (for example, Olivieri andPitacco 2003, Hári et al (2008b), Stevens et al 2010b). Olivieri and Pitacco 2003 discuss the effect of longevity risk on solvency requirements for life insurers and pension funds.…”

“…Second, we discuss results from Hári et al (2008b) regarding the effect of longevity risk on the volatility of the funding ratio of pension funds. Third, we discuss the approach in Stevens et al (2010b), who quantify longevity risk by determining its effect on the probability of ruin, i.e., the probability that, for a given (re)investment strategy, the current value of the assets will not be sufficient to meet all future liabilities. 2 Finally, in Section 5 we investigate possibilities for longevity risk management for life insurers and pension funds, following Cairns et al (2008a).…”