Life is Cheap: Using Mortality Bonds To Hedge Aggregate Mortality Risk Leora FriedbergAnthony Webb University of Virginia Center for Retirement Research and NBER at Boston College Presentation for Shanghai University of Finance and Economics, PRC 22 November 2007

Aggregate Mortality Risk Risk that annuitants on average live longer than expected –CANNOT be eliminated through diversification within annuity business –Difficult to hedge with life insurance business

Aggregate Mortality Risk Affects annuity providers –Insurance companies offering voluntary annuities –Employers offering annuitized pensions –Taxpayers through Social Security, PBGC

Aggregate Mortality Risk Affects annuity providers –Insurance companies offering voluntary annuities –Employers offering annuitized pensions –Taxpayers through Social Security, PBGC

Aggregate Mortality Risk Affects potential annuitants –  price,  quantity in equilibrium –only 7.4% in AHEAD voluntarily annuitized between

Aggregate Mortality Risk Of potentially greater importance –Decline in generosity of Social Security and displacement of annuitized DB by unannuitized DC pensions may increase annuity demand –? Increasing uncertainty about potential for dramatic medical breakthroughs

Outline 1.What is the magnitude of this risk? 2.How might this risk affect pricing of annuities? 3.What price should this risk command in financial markets?

Aggregate Mortality Risk 1.What is the magnitude of this risk? –Lack of agreement Actuarial tables –yield point estimates only –e.g., Society of Actuaries Social Security Administration –high, intermediate, low forecasts –but no confidence intervals Lee and Carter (1992)

1.What is the magnitude of this risk? –Lack of agreement Actuarial tables –yield point estimates only –e.g., Society of Actuaries Social Security Administration –high, intermediate, low forecasts –but no confidence intervals Lee and Carter (1992) Aggregate Mortality Risk

1.What is the magnitude of this risk? –Lee-Carter model “leading statistical model of mortality in the demographic literature” (Deaton-Paxson 2004) adopted by U.S. Census Bureau performs well in sample provides confidence intervals perhaps they are too narrow? Aggregate Mortality Risk

2.How might this risk affect pricing of annuities? –Required reserves if Lee-Carter is correct to reduce probability of insolvency to 5% for 3%-real 50%-survivor annuity sold to couple aged 65-85, need reserves of % –Impact of using SOA projections if Lee-Carter is correct same annuity will be underpriced under SOA projections by % Aggregate Mortality Risk

3.What price should this risk command in financial markets? –Historical covariances, Impact of mortality shocks on longevity bond prices at ages 65+ Covariance with S&P 500 (CAPM) Covariance with consumption growth (CCAPM) –These covariances are very small Aggregate Mortality Risk

3.What price should this risk command in financial markets? –Should be able to hedge risk at virtually no cost –How? Mortality-contingent bonds two short-term bonds issued recently by Swiss Re one long-term bond proposed by EIB, not issued –according to our calculations, this bond was overpriced, unless investors expected lower mortality than U.K. Actuary did Aggregate Mortality Risk

3.What price should this risk command in financial markets? –Should be able to hedge risk at virtually no cost –How? Mortality-contingent bonds two short-term bonds issued recently by Swiss Re one long-term bond proposed by EIB, not issued –according to our calculations, this bond was overpriced, unless investors expected lower mortality than U.K. Actuary did Aggregate Mortality Risk

Outline 1.What is the magnitude of this risk? 2.How might this risk affect pricing of annuities? 3.What price should this risk command in financial markets?

1. Magnitude of aggregate mortality risk Actuarial tables yield point estimates –e.g., Society of Actuaries Social Security Administration –high, intermediate, low forecasts Lee-Carter model –quantifies uncertainty surrounding mortality forecasts

Lee-Carter model ln (m x,t ) = a x + b x k t + e x,t k t = k t-1 – flu + e t,  e = Details m is mortality by age x, year t a, b are parameters that vary with age x flu is the 1918 flu epidemic 1. Magnitude of aggregate mortality risk

Lee-Carter model ln (m x,t ) = a x + b x k t + e x,t k t = k t-1 – flu + e t,  e = Details m is mortality by age x, year t a, b are parameters that vary with age x flu is the 1918 flu epidemic 1. Magnitude of aggregate mortality risk

Lee-Carter model ln (m x,t ) = a x + b x k t + e x,t k t = k t-1 – flu + e t,  e = Implications for mortality trends LC estimated that a random walk with drift fits path of k implies roughly linear decline in k  decreasing rate of increase in life expectancy no mean reversion in mortality trends  current shock to m yields almost equal % change in subsequent E[m] 1. Magnitude of aggregate mortality risk

Lee-Carter model ln (m x,t ) = a x + b x k t + e x,t k t = k t-1 – flu + e t,  e = Implications within sample explains > 90% of within-age variances in mortality rates one standard-deviation shock to k  2-month change in age-65 life expectancy 1. Magnitude of aggregate mortality risk

Comparisons of Lee-Carter with other forecasts –more optimistic than SSA –close to SOA at ages 45-79, then more optimistic Figures 1-3 –comparison of mortality forecasts, –comparison to recent mortality data, Magnitude of aggregate mortality risk

Comparisons of Lee-Carter with other forecasts –more optimistic than SSA –close to SOA at ages 45-79, then more optimistic Figures 1-3 –comparison of mortality forecasts, –comparison to recent mortality data, Magnitude of aggregate mortality risk

Lee-Carter 95% SSA high Life expectancy, in years Future life expectancy at age 60, various mortality forecasts

Actual mortality, ages Ages Mortality relative to 1989 Recent actual vs. forecasted mortality declines Males, birth cohorts

Actual mortality, ages Ages Mortality relative to 1989 Recent actual vs. forecasted mortality declines Females, birth cohorts

Outline 1.What is the magnitude of this risk? 2.How might this risk affect pricing of annuities? 3.What price should this risk command in financial markets?

2. Implications for pricing of annuities Two sets of calculations A.Required mark-up/reserves if Lee-Carter is correct impact of variance of expected mortality B.Impact of using SOA projections if Lee-Carter is correct impact of differences in expected mortality

A.Required mark-up/reserves if LC is correct –10,000 Monte Carlo simulations each simulation: draw baseline k, then errors to fill in m x,t construct resulting life tables –compute premium required to break even, on average compute annuity payments in each simulation –compare to premium what % mark-up over premium will reduce probability of loss to x%? –or what % of EPV must be held as capital reserve –x = 0.05 or x = Implications for pricing of annuities

A.Required mark-up/reserves if LC is correct –required mark-up is 2.7% to 4.8% competing effects of age –uncertainty about mortality at older ages  with time horizon –but, payments at older ages are heavily discounted –impact if eliminate cancer, all circulatory disease, diabetes? increase PV of an annuity by 50% 2. Implications for pricing of annuities

Potential Losses Arising From Aggregate Mortality Risk Loss probability Single menSingle womenMarried Couples with survivor benefit 50%100% 5%1%5%1%5%1%5%1% 3% interest rate %5.66%3.67%5.22%2.69%3.80%2.69%3.89% %5.95%3.97%5.60%2.82%4.02%2.92%4.12% %6.32%4.15%5.96%3.00%4.31%3.10%4.47% %6.53%4.38%6.27%3.13%4.45%3.27%4.63% %6.96%4.61%6.57%3.31%4.67%3.46%5.01%

Potential Losses Arising From Aggregate Mortality Risk Loss probability Single menSingle womenMarried Couples with survivor benefit 50%100% 5%1%5%1%5%1%5%1% 3% interest rate %5.66%3.67%5.22%2.69%3.80%2.69%3.89% %5.95%3.97%5.60%2.82%4.02%2.92%4.12% %6.32%4.15%5.96%3.00%4.31%3.10%4.47% %6.53%4.38%6.27%3.13%4.45%3.27%4.63% %6.96%4.61%6.57%3.31%4.67%3.46%5.01%

B.Impact of SOA projections if LC is correct –no actual pricing data –and it would be difficult to use prices to back out mortality assumptions without knowing assumptions about expenses, asset returns, annuitant characteristics –instead, we focus on recent SOA projections 2. Implications for pricing of annuities

B.Impact of SOA projections if LC is correct –compute EPV of payments for $1/year annuity EPV if SOA projection scale is correct EPV is Lee-Carter is correct –Lee-Carter value is always higher 2. Implications for pricing of annuities

Percentage Underpricing Resulting From Use of Projection Scale AA MaleFemale Couple Survivor Benefit 50%100% Age %2.93%2.31%3.01% %3.04%2.57%3.23% %3.16%2.86%3.45% %3.27%3.07%3.62% %3.34%3.18%3.68%

Outline 1.What is the magnitude of this risk? 2.How might this risk affect pricing of annuities? 3.What price should this risk command in financial markets?

3. Pricing of aggregate mortality risk Mortality-contingent bonds –can be used to pass mortality risk to those who want it –very recent examples

Mortality-contingent bonds –Swiss Re three-year bond, first issued in 2003 if five-country average mortality > 130% of 2002 level  principal will be reduced if it > 150%  principal will be exhausted 3. Pricing of aggregate mortality risk

Mortality-contingent bonds –EIB 25-year bond, proposed in 2004 mortality-contingent payments  proportionally as annual survival rate  for U.K. cohort aged 65 in 2003 but EIB bond was not issued as planned expected yield implied 20-basis point discount (assuming Government Actuary Department’s mortality forecasts are unbiased) 3. Pricing of aggregate mortality risk

We price the EIB bond –had such bonds been available in U.S. measure mortality shocks –as identified from Lee-Carter model –Berkeley Human Mortality database, –Social Security Administration data, 19xx-yy correlation with S&P 500 –compute beta, risk premium from CAPM correlation with per capita consumption growth –compute risk premium from CCAPM 3. Pricing of aggregate mortality risk

The Capital Asset Pricing Model: Where R i is the return on asset i and R m is the market return Where R f is the risk-free return (1): (2):

The Capital Asset Pricing Model: The expected return on asset i depends on the risk-free return, and the covariance of the asset’s return with the market return Important implication – idiosyncratic risk – the risk of good or bad returns that are uncorrelated with the market return do not command a risk premium Rearranging (2): Why? – Because an investor can diversify away that risk by investing a small amount in a lot of assets with uncorrelated returns – think of the “law or large numbers”

Results –such bonds would not have been very risky –standard deviation of return is 0.64% versus 17% for stocks 3. Pricing of aggregate mortality risk

Results for CAPM –correlation with S&P 500 varies with age of bond’s reference population for age-65 mortality bond, beta = –95% confidence interval of [-0.005, 0.015] –virtually no correlation with stock market bond would command risk premium of 2.5 bp –for equity premium of 500 bp 3. Pricing of aggregate mortality risk

Results for CCAPM –hypothesis: mortality bonds pay out most when? when mortality is unexpectedly low and then resources that are roughly unchanged in quantity have to support more people –expect negative correlation with C growth 3. Pricing of aggregate mortality risk

Results for CCAPM –correlation for age-65 bond is significantly different from 0 for all reference ages –mortality bonds should attract risk discount in contrast with stocks –correlation is about 0.5 –should attract risk premium 3. Pricing of aggregate mortality risk

Results for CCAPM –but mortality bond returns, C growth are very smooth series covariance is extremely small, resulting risk discount is 2 basis points –for risk aversion coefficient of 10 contrast with EIB prospectus –proposed risk discount of 20 basis points 3. Pricing of aggregate mortality risk

What explains EIB bond? –apparently overpriced EIB expected to pass risk further by obtaining reinsurance –Smetters, Dowd: insurance markets are small, constrained compared to financial markets, which can bear large risks better maybe investors expected better mortality –compared to U.K. Actuary’s forecasts –and might have perceived risk discount as less than 20 BP 3. Pricing of aggregate mortality risk

Conclusions Aggregate mortality risk is considerable But uncorrelated with other financial risks –annuity providers should be able to shed aggregate mortality risk at virtually no cost Of growing importance –demand for voluntary annuitization might be expected to rise