Figure 3 plots liquid wealth and liquid holdings of equities and bills over the life cycle. In each retirement system the borrowing constraint binds for young households; they would like to take more equity risk but are unable to do so. For approximately the first 20 years of life, they hold 100% of their portfolios in the form of equity. Households in midlife hold bills, but these holdings decrease again after retirement.
Figure 4 plots the portfolio share of stocks in liquid wealth. The crucial variables for portfolio composition are liquid wealth, retirement wealth and future labor income. In the model future labor income, although risky, can be thought of as implicit holdings of a riskless asset. Innovations to labor income are positively correlated with innovations to stock returns, but this correlation is not sufficiently large for future labor income to resemble more closely stocks than bills. Since early in life the implicit holdings of the riskless asset in the form of future labor income are large, the investor wishes to invest what little liquid wealth he has fully into stocks.
From age 40 onwards liquid wealth increases relative to future labor income and retirement wealth, so that implicit holdings of the riskless asset become less important. This induces a shift in the composition of liquid wealth towards bills. After retirement liquid wealth is run down more rapidly than the implicit annuitized holdings of the riskless asset. As this happens the implicit holdings of the riskless asset become relatively more important, inducing a shift in portfolio composition back towards stocks.
These considerations explain the life-cycle patterns in both Figure 4a and Figure 4b. There are however important differences in magnitudes between the two figures. In Figure 4b the midlife decrease in the share invested in stocks is much more dramatic. Since the investor already holds risky assets in the retirement account, he wishes to hold a safer liquid portfolio.
Another way to understand these results is to compare the patterns of current utility of consumption over the life cycle. Figure 5a shows the ratio of average current utility for households in the 50/50 system to the average current utility of households in the 100/0 system. We see that most of the gain from investing retirement wealth in stocks occurs early in life. The source of this gain is the higher levels of consumption that a lower social security contribution allows. Return risk in the retirement account allows some households to end up poorer so that after age 55 current utility is on average higher in the 100/0 system.
Figure 3a – Wealth, Stocks and T-Bills (Retirement Wealth Fully Invested in the Safe Asset)
Figure 3b – Wealth, Stocks and T-Bills (Retirement Wealth Invested 50/50 in Risky/Safe Asset)
Figure 4a – Liquid Portfolio Share invested in Stocks (Retirement Wealth Fully Invested in the Safe Asset)
Figure 4b – Liquid Portfolio Share invested in Stocks (Retirement Wealth Invested 50/50 in Risky/Safe Asset)
Fig 5a – Utility Gain