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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. Motivation.

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Life cycle asset allocation with annuity markets is

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

Goethe University Frankfurt


Motivation
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?

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Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?


Outline
Outline

Motivation

Prior Literature

The Model

Key Results

Conclusion

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Prior literature
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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Contributions
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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The model life annuity market
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

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The model labor income process
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 sN, sU and correlation zero.

Retirement: t>K

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The model wealth accumulation
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

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The model preferences
The Model: Preferences

Preferences as in Epstein and Zin (1989) are described by

r: level of relative risk aversion

y:elasticity of intertemporal substitution

b: personal discount factor

k: the strength of the bequest motive

ps: personal survival probabilities

Optimization problem:

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Results optimal asset allocation with annuities
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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Stylized case without loads and bequest figure 1
Stylized Case without Loads and Bequest (Figure 1)

Stocks s(w,l=0,t) Annuities pr(w,l=0,t) Bonds m(w,l=0,t)

w

w

w

age

age

age

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

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Expected life cycle profile figure 3 4

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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Expected life cycle profile figure 3 41

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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Robustness analysis of annuity demand table ii

Sensitivity of annuity demand regarding to factors deemed to explain the annuity puzzle: costs, bequest, bad health, high pension income

Robustness Analysis of Annuity Demand: Table II

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Welfare analysis table iii
Welfare Analysis: Table III explain the annuity puzzle: costs, bequest, bad health, high pension income

Equivalent Increase in Financial Wealth: additional financial wealth needed to compensate for the utility loss if no annuities available.

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Conclusions longevity insurance a good deal
Conclusions: Longevity Insurance a Good Deal? explain the annuity puzzle: costs, bequest, bad health, high pension income

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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Life cycle asset allocation with annuity markets is

Thank You for Your Attention! explain the annuity puzzle: costs, bequest, bad health, high pension incomeLife-Cycle Asset Allocation with Annuity Markets:Is Longevity Insurance a Good Deal?Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. StamosDepartment of Finance, Goethe University (Frankfurt)

Goethe University Frankfurt


Life cycle asset allocation with annuity markets is

Appendix explain the annuity puzzle: costs, bequest, bad health, high pension incomeLife-Cycle Asset Allocation with Annuity Markets:Is Longevity Insurance a Good Deal?Wolfram J. Horneff, Raimond H. Maurer, and Michael Z. StamosDepartment of Finance, Goethe University (Frankfurt)

Goethe University Frankfurt


Technical appendix numerical solution
Technical Appendix: Numerical Solution explain the annuity puzzle: costs, bequest, bad health, high pension income

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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Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?