Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? by Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. Stamos Department of Finance, Goethe University (Frankfurt) (ARIA, Quebec City, 2007) Goethe University Frankfurt

2/16Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Motivation  Rising life expectancies, low birth rates -> worldwide shift to privately funded pension systems  Household risk management:  Uncertain capital market returns  Uncertain labor income  Uncertain time of death (mortality risk)  Questions:  What is the optimal dynamic portfolio choice with constant life annuities, stocks, and bonds?  What are the welfare effects of purchasing a life-annuity in a realistically calibrated life-cycle model? 08/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Outline 1.Motivation 2.Prior Literature 3.The Model 4.Key Results 5.Conclusion 3/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Prior Literature  Long Horizon Asset Allocation with Stochastic Investment Opportunity Set: Brandt (1999 JF), Brennan and Xia (2000 EurFR,2002 JF), Campbell and Viceira (1999 QJE,2001 AER), Campbell, Chan, and Viceira (2003 JFE), Wachter (2002 JFQA,2003 JET), …  Labor Income Implications on Portfolio Coice: Bodie, Merton, and Samuelson (1992 JEDC), Cocco, Gomes, and Maenhout (2005 RFS), Heaton and Lucas (1997 MD), Viceira (2001 JF).  Also literature on housing, entrepreneurial risk, and taxes…  Mortality Risk and Annuity Markets: Koijen, Nijman, and Werker (2006 WP), Cairns, Blake, and Dowd (2006, JEDC) 4/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Contributions  Implications of annuity markets on household portfolio choice  Optimization of the annuitization strategy over entire life- cycle: gradual annuitization possible  Consideration of labor income risk and bequest motives  Sensitivity analysis including common explanations for limited annuity participation 5/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? The Model: Life-Annuity Market  Immediate Constant Payout Life Annuity: like a fixed coupon corporate bond (default: time of death)  Pricing:  Mortality credit is compensation for:  Lack of bequest potential  Lost flexibility Mortality credit 6/1608/06/2007

7/16Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? The Model: Labor Income Process  The process of labor income follows during (see Cocco et al. (2005) )  Working life t≤K f(t): deterministic function of age P t : permanent component with innovation N t U t :transitory income shock Logarithms of N t and U t : multivariate normal distributed with means zero, with volatilities  N,  U and correlation zero.  Retirement: t>K 08/06/2007

8/16Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? The Model: Wealth Accumulation  The budget constraint is W t :wealth on hand M t : amount invested in riskless bonds S t : amount invested in risky stocks PR t : amount invested in annuities C t : consumption.  The individual’s cash on hand in t + 1 is given by L t+1 : sum of annuity payments Y t+1 : labor income R f : riskless growth rate of bonds R t+1 : risky growth rate of stocks 08/06/2007

9/16Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? The Model: Preferences  Preferences as in Epstein and Zin (1989) are described by  level of relative risk aversion  elasticity of intertemporal substitution  personal discount factor k: the strength of the bequest motive p s :personal survival probabilities  Optimization problem: 08/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Results: Optimal Asset Allocation with Annuities  Optimal policies: cash on hand w allocated in  Stocks s(w,l,t)  Bonds m(w,l,t)  New annuities pr(w,l,t)  Consumption c(w,l,t)  Policies depend on normalized cash on hand w, normalized annuity income l, and age t (Normalization with permanent income) 10/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Stylized Case without Loads and Bequest (Figure 1) Motives to hold liquid wealth: (1) stock demand, (2) buffer stock savings Age effect: (1) increasing mortality credit (mortality risk), (2) decreasing human capital, and (3) labor income uncertainty Wealth effect: the higher wealth on hand compared to bond-like human capital, the lower is the relative stock demand age w w w Stocks s(w,l=0,t) Annuities pr(w,l=0,t) Bonds m(w,l=0,t) 11/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?  Asset allocation:  Gradual shift from liquid savings to illiquid annuities  First crowding out of bonds then of stocks Expected Life-Cycle Profile (Figure 3-4) 12/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Cost effect: annuitization postponed to age 59 Bequest effect: additional liquid wealth motive, but still substantial annuity demand Expected Life-Cycle Profile (Figure 3-4) With loads With loads and bequest motives 13/1608/06/2007

Sensitivity of annuity demand regarding to factors deemed to explain the annuity puzzle: costs, bequest, bad health, high pension income Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Robustness Analysis of Annuity Demand: Table II 14/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Welfare Analysis: Table III Equivalent Increase in Financial Wealth: additional financial wealth needed to compensate for the utility loss if no annuities available. 15/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Conclusions: Longevity Insurance a Good Deal?  Endogenizing the annuitization strategy shows  Gradual purchase optimal  Timing of annuity purchase crucial (Age effect, Wealth effect)  Model predicts empirically found timing of annuity purchase  Mortality credit high enough to compensate for forfeit bequest potential, illiquidity and lack of equity premium  Welfare increase equivalent to 10-30% more cash on hand  Outlook:  Allow for variable payout annuities  Model could be used to add behavioral explanations: e.g. informational costs 16/1608/06/2007

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Thank You for Your Attention! Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. Stamos Department of Finance, Goethe University (Frankfurt) Goethe University Frankfurt

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Appendix Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. Stamos Department of Finance, Goethe University (Frankfurt) Goethe University Frankfurt

19/15Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal? Technical Appendix: Numerical Solution  Dynamic optimization problem in a three-dimensional state space  Continuous state variables:  Normalized wealth  Normalized annuity payouts  Discrete state variable:  Age  Calculations of expectations (multiple integral): quadrature integration  One period optimization: numerical constrained minimization  Policy functions derived by cubic-splines interpolation 12/13/2006