Longevity risk in portfolios of pension annuities

Longevity Risk

“…Assuming that such numbers apply more generally, the economic implications of longevity become obvious. This is confirmed by results from Hári et al (2008b), who illustrate the effect of longevity trends on the expected present value of annuity payments. Specifically, they consider a (deferred) annuity that pays off one Euro (in arrears) every year that the annuitant survives, and is older than 65.…”

“…Thus, to calculate (5), we need future projections of the oneyear death probabilities q (g) x,t , for t ≥ t. Not using such projected one-year death probabilities might result in a serious underestimation of the expected number of years an individual will survive and of the expected discounted value of the annuity. Indeed, Hári et al (2008b) show that the expected remaining lifetime changes substantially when future changes in mortality rates are taken into account. 4 For the age x = 65, they report an increase in the expected remaining lifetime for males from 11.2 years in 1900 to 15.4 years in 2000, and projected to be 16.1 years in 2025, while for females of the same age these numbers are 11.8 years for 1900, 19.4 for 2000, and the projected value for 2025 is 20.6.…”

“…Table 1, taken from Hári et al (2008b), shows a (g) x,t as a function of age, for ages varying from 25 to 85 based on so-called period tables (first column), i.e., assuming that q (g) x,t = q (g) x,t , for t ≥ t = 2004, and based on forecasted one-year probabilities (second column), 5 for groups of men and women. Comparison of the first and the second columns reveals that the present value of annuity payments based on period life tables underestimates 6 the value based on forecasted death probabilities by 7.7% for a 25-year-old man and 8.8% for a 25-year-old woman.…”

“…Instead, it would seem more realistic to deal with this uncertainty, by assuming that the one-year death probabilities q (g) x,t are stochastic at time t, for t > t. If so, we are confronted with longevity risk: the probability at year t that an individual of age x and belonging to group g survives at least τ other years (see (4)) is not known deterministically, but is random. The literature therefore distinguishes two sources of mortality risk: 7 5 In Hári et al (2008b) longevity risk is already taken into account at this stage, but for pedagogical reasons only we proceed as if the forecasts are deterministic. Hári et al (2008b) employ a term structure of interest rates calibrated on the interest rates in 2004.…”

“…First, we extend Olivieri (2001) to demonstrate the relative importance of individual mortality risk and longevity risk, and the effect of portfolio size. 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.…”