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INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL – Effects of Heterogeneity on Portfolio Choice

INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL - Effects of Heterogeneity on Portfolio ChoiceIn this section we illustrate the effects of investor heterogeneity on optimal consumption and portfolio choice. First, we consider heterogeneity of preferences, calculating optimal behavior for highly risk-averse investors with 7 = 10 and impatient investors with B = 0.8. Second, we consider differences in labor income risk of the sort illustrated in section 4.1. To highlight these differences, we simulate the behavior of households whose income is particularly risky and highly correlated with asset returns: self-employed college graduates.
Table 6 shows average consumption and liquid wealth (in thousands of dollars) and the share of liquid wealth invested in stocks for different age groups. This is a more compact way for us to summarize the information presented graphically in Figures 2 through 4. The first three columns of Table 6 use the baseline parameters and consider retirement systems with aR = 0; aR = 0.5 and the same 10% tax rate as with aR = 0; and aR = 0.5 and a lower 6% tax rate that maintains the same average replacement ratio as with aR = 0.
The next two columns of Table 6 present results for a higher risk aversion coefficient of 10 rather than 5. Since the tax rates do not depend on 7, they are the same as in the baseline case. To understand the results for higher 7 it is important to remember that with isoelastic preferences this parameter measures both risk aversion and prudence (Kimball 1990). Greater prudence increases precautionary savings and explains why highly risk-averse investors consume less, and save more, until age 65. After this age the precautionary savings motive is reduced since there is no labor income risk and retirement wealth is converted into a riskless annuity. Thus highly risk-averse investors consume more after retirement.
Table 6 also shows that, as one would expect, highly risk-averse investors have a lower portfolio share in stocks. One interesting pattern that is not visible in the table is that very early in life, these investors’ equity portfolio share is increasing with age. This pattern does not show up for investors with 7 = 5 because in early life these investors are constrained by their inability to borrow to finance equity investments. The reason for this increasing pattern is explained in CGM. In the presence of an increasing labor income profile the annuity value of future labor income, equivalent to implicit holdings of the riskless asset, increases with age at first as peak earnings years move closer in time. Investors respond to this increase by shifting liquid wealth towards risky financial assets. Later on the annuity value of future labor income starts to decrease as peak earnings are realized and retirement approaches; investors respond by shifting out of stocks in middle age.

Table 6: Life Cycle Profiles.

Consumption
Baseline Case 7 = 10 B = 0.8 Self Employed
Age 0/100 50/50 50/50 0/100 50/50 0/100 50/50 0/100 50/50
20-35 20.22 20.26 21.07 20.13 20.88 20.53 20.61 25.09 26.10
36-50 25.48 26.11 26.15 25.12 24.86 26.50 26.47 38.39 38.28
51-65 24.61 26.06 25.46 24.23 24.54 23.94 23.78 35.23 35.35
66-80 22.43 26.64 24.19 22.65 24.46 15.95 15.73 32.67 34.02
81-100 16.98 25.61 18.27 19.04 20.60 14.27 14.27 27.26 28.70
Wealth
Baseline Case 7 = 10 B = 0.8 Self Employed
Age 0/100 50/50 50/50 0/100 50/50 0/100 50/50 0/100 50/50
20-35 5.94 5.77 6.39 8.20 7.92 3.39 2.73 12.84 13.75
36-50 29.34 23.17 35.87 39.28 50.57 7.25 5.64 65.75 81.99
51-65 75.77 40.34 96.26 100.16 126.78 10.23 7.83 173.70 195.02
66-80 77.28 26.06 92.81 105.50 128.71 5.71 4.71 159.76 169.73
81-100 13.60 4.15 18.40 30.85 39.94 0.11 0.11 46.75 52.00
Liquid Portfolio Share in Stocks
Baseline Case 7 = 10 B = 0.8 Self Employed
Age 0/100 50/50 50/50 0/100 50/50 0/100 50/50 0/100 50/50
20-35 1.00 0.93 1.00 0.97 0.97 0.99 0.99 0.57 0.53
36-50 0.99 1.00 0.98 0.95 0.72 1.00 1.00 0.91 0.68
51-65 0.88 0.81 0.61 0.61 0.08 1.00 0.90 0.57 0.14
66-80 0.90 0.96 0.85 0.57 0.49 1.00 1.00 0.54 0.51
81-100 0.92 0.58 0.90 0.68 0.57 1.00 1.00 0.61 0.53
Tax Rates
10.00% 10.00% 6.00% 10.00% 6.00% 10.00% 6.00% 10.50% 6.75%