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

Transcription

1 Life-cycle Asset Allocation ith Annuity Markets: Is Longevity Insurance a Good Deal? Wolfram J. Horneff Raimond Maurer Michael Z. Stamos Johan Wolfgang Goethe University of Frankfort for the 9th Annual Joint Conference of the Retirement Research Consortium Challenges and Solutions for Retirement Security August 9-1, 27 Washington, D.C. The research reported herein as pursuant to a grant from the U.S. Social Security Administration (SSA) funded as part of the Retirement Research Consortium (RRC). The findings and conclusions expressed are solely those of the author[s] and do not represent the vies of SSA, any ncy of the Federal Government, the RRC or the Michigan Retirement Research Center. Additional support as provided by the German Research Foundation (DFG) and the Fritz-Thyssen Foundation.

2 Abstract We derive the optimal portfolio choice over the life-cycle for households facing labor income, capital market, and mortality risk. In addition to stocks and bonds, households also have access to incomplete annuity markets offering a hedge against mortality risk. We sho that a considerable fraction of ealth should be annuitized to skim the return enhancing mortality credit. The remaining liquid ealth (stocks and bonds) is used to hedge labor income risk during ork life, to earn the equity premium, and to ensure estate for the heirs. Furthermore, e assess the importance of common explanations for limited participation in annuity markets. See the full paper at.mrrc.isr.umich.edu/publications/papers/pdf/p146.pdf - 1 -

3 Figure 1 Annuitization policy: pr(w,l=,t) pr Stocks policy: s(w,l=,t) s Bonds policy: m(w,l=,t) m Figure 1: Optimal Asset Allocation: Stylized Case. For this case, e assume a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS = 1/5, and a zero-bequest motive (k = ). The figure depicts the optimal holdings of annuities pr(, l, t) (upper graph), stocks s(, l, t) (middle graph), and bonds m(, l, t) (loer graph) depending on the andealthonhand. The state variable level of annuity payouts is set to l =. 35

4 Figure 2 With Costs With Costs + Bequest Annuitization policy: pr(w,l=,t) Annuitization policy: pr(w,l=,t) pr pr Stocks policy: s(w,l=,t) Stocks policy: s(w,l=,t) s s Bonds policy: m(w,l=,t) Bonds policy: m(w,l=,t) m m Figure 2: Optimal Asset Allocation ith Costs (Left Column) and Optimal Asset Allocation ith Costs and a Bequest Motive (Right Column). The figure depicts the optimal holdings of annuities pr(, l, t) (upper panel), stocks s(, l, t) (middle panel), and bonds m(, l, t)(loer panel) depending on the and ealth on hand. Left column: for this case, e assume administration costs for annuities δ =.73, mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table), and a zero-bequest motive (k = ). Right column: for this case, e additionally assume a bequestmotiveof(k = 2). The state variable level of annuity payouts is set to l =. Asin the stylized case, this optimization assumes a female ith maximum life-span 2 -, no initial endoment, andrra = 5, EIS = 1/5. 36

5 Figure savings (S+M) labor income (Y) consumption (C) annuity purchase (PR) Figure 3: Life-Cycle Profiles: Stylized Case (Top), ith Costs (Middle), and ith Costs and Bequest (Bottom). All three graphs depict expected consumption, labor income, savings, and annuity purchases over the life-cycle. Stylized case: for this case, e assume a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA =5,EIS =1/5, and a zero-bequest motive (k = ). Case ith costs: here, e additionally consider administration costs δ =.73 for annuities and mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table). Case ith costs and bequest: for this case, e add a bequest motive of (k = 2) to the case ith costs. The expected values are computed by simulating, life-cycle paths based on the optimal policies derived by the numerical optimization. 37

6 Figure 4 1 Fraction Bonds Stocks Annuities Age 1 Fraction Bonds Stocks Annuities Age 1.9 Fraction Bonds Stocks Annuities Age Figure 4: Expected Asset Allocation: Stylized Case (Top), ith Costs (Middle), and ith Costs and Bequest (Bottom). All three graphs depict the expected stock, bond, and annuity holdings. Stylized case: for this case, e assume a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS = 1/5, and a zero-bequest motive (k = ). Case ith costs: here, e additionally consider administration costs δ =.73 for annuities and mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table). Case ith costs and bequest: for this case, e add a bequest motive of (k =2)to the case ith costs. The expected values are computed by simulating, life-cycle paths based on the optimal policies derived by the numerical optimization. 38

7 Figure 5 8 Consumption Quantiles (1%,5%,9%) Age Figure 5: Consumption Percentiles (1th,5th, and 9th) ith and ithout Annuities. The dashed (solid) lines reflect the case ith (ithout) annuities. The blue, green, and orange lines reflect the 9th, 5th, and 1th percentile respectively. The calculations are based on, Monte-Carlo simulations. We assume the case ith bequest and costs. 39

8 Table I Expected Optimal Annuitization Strategy Table I reports the expected optimal annuitization policy for three alternative cases. The first, stylized case assumes a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS =1/5, and a zero-bequest motive (k = ). The second case introduces administration costs for annuities δ =.73 and mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table). The third case additionally considers a bequest motive (k =2). PR/W is the fraction of financial ealth used to purchase ne annuities at a certain. L/Y reports the magnitude of annuity payouts L relative to the labor income Y. L/(C Y ) depicts ho much of the consumption C not taken from the labor income is backed by annuity payouts. We compute the expected values based on, Monte-Carlo simulations by using the optimal policy functions s(, l, t) (stocks), m(, l, t) (bonds), pr(, l, t) (annuities), and c(, l, t) (consumption). All figures are reported as percents. Expected Optimal Annuitization Stylized case With costs With costs and bequest Age PR/W L/Y L/(C Y ) PR/W L/Y L/(C Y ) PR/W L/Y L/(C Y )

9 Table II Expected Optimal Asset Allocation for Alternative Cases Table II reports the expected asset allocation of the individual s portfolio consisting of stocks, bonds, and annuities. The expected asset allocations are displayed for the 3, 45, 6, 75. The first, stylized case assumes a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS = 1/5, and a zero-bequest motive (k = ). The second case introduces administration costs for annuities δ =.73 and mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table). The third case additionally considers a bequest motive (k = 2). The remaining cases are variations of the third case ith costs and bequest. The value of all annuities the investor holds at a certain is calculated as the premium the investor ould have to pay in order to achieve the same payout stream as ith the previously purchased annuities. We compute the expected values based on, Monte-Carlo simulations by using the optimal policy functions s(, l, t) (stocks),m(, l, t) (bonds), pr(, l, t) (annuities), and c(, l, t) (consumption). All figures are reported as percents. Stock fraction (%) Bond fraction (%) Annuity fraction (%) Age Age Age Case Stylized case With costs With bequest Males Bad health Lo IES (ψ =.1) High IES (ψ =.3) Lo RRA (ρ = 2) Lo pension income (λ =.5) High pension income (λ = 1)

10 Table III Welfare Analysis: Equivalent Increase in Financial Wealth (Percent Points) of Having Access to Annuity Markets Table III reports elfare gains in the presence of annuity markets for all cases considered previously. The first, stylized case assumes a female ith maximum life-span 2 -, no initial endoment, no administration costs for annuities, no mortality asymmetries, RRA = 5, EIS = 1/5, and a zerobequest motive (k = ). The second case introduces administration costs for annuities δ =.73 and mortality asymmetries (2 Population Basic vs US Annuity 2 Basic mortality table). The third case additionally considers a bequest motive (k = 2). The remaining cases are variations of the third case ith costs and bequest. Welfare gains are computed as the equivalent percent increase in financial ealth an individual ithout access to annuity markets ould need in order to attain the same expected utility as in the case ith annuity markets. The computations are done for 6, 7, 8, and 9. Age Case Stylized case With costs With bequest Males Bad health Lo IES (ψ =.1) High IES (ψ =.3) Lo RRA (ρ = 2) Lo pension income (λ =.5) High pension income (λ = 1)