Status on 62,63 Ni(n, ) Claudia Lederer Goethe University Frankfurt Cristian Massimi INFN Bologna.
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Transcript of Goethe University Frankfurt
Life-Cycle Asset Allocation with Annuity Markets:Life-Cycle Asset Allocation with Annuity Markets:Is Longevity Insurance a Good Deal?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 returnsUncertain labor incomeUncertain 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?
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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
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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)
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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
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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 potentialLost flexibility
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at
tsf
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Mortality credit
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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
Pt: permanent component with innovation Nt
Ut: transitory income shock
Logarithms of Nt and Ut: multivariate normal distributed with means zero, with volatilities N, U and correlation zero.
Retirement: t>K
.
,exp
1 ttt
ttt
NPP
UPtfY
Kt PKfY exp
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The Model: Wealth Accumulation
The budget constraint is
Wt: wealth on hand
Mt: amount invested in riskless bonds
St: amount invested in risky stocks
PRt: amount invested in annuities
Ct: consumption.
The individual’s cash on hand in t + 1 is given by
Lt+1: sum of annuity payments
Yt+1: labor income
Rf: riskless growth rate of bonds
Rt+1: risky growth rate of stocks
ttttt CPRSMW
1111 ttttftt YLRSRMW
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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
ps: personal survival probabilities
Optimization problem:
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tstt
sttt
stt BkpVpECpV
0,,, 0
max VT
tttt PRSMC
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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)
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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
agew agew
agew
Stocks s(w,l=0,t) Annuities pr(w,l=0,t) Bonds m(w,l=0,t)
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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)
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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
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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
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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.
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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
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Thank You for Your Attention!
Life-Cycle Asset Allocation with Annuity Markets:Life-Cycle Asset Allocation with Annuity Markets:Is Longevity Insurance a Good Deal?Is Longevity Insurance a Good Deal?
Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. StamosDepartment of Finance, Goethe University (Frankfurt)
Goethe University Frankfurt
Appendix
Life-Cycle Asset Allocation with Annuity Markets:Life-Cycle Asset Allocation with Annuity Markets:Is Longevity Insurance a Good Deal?Is Longevity Insurance a Good Deal?
Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. StamosDepartment 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
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