Optimal Portfolio Choice Over the Life Cycle with Social Security

Abstract

This paper examines how households should optimally allocate their portfolio choices between risky stocks and risk-free bonds over their lifetime. Traditional lifecycle models in previous work suggest that the allocation toward stocks should start high (near 100%) early in life and decline over a person’s age as human capital depreciates. These models also suggest that, with homothetic utility, the allocation should be roughly independent of a household’s permanent income. The actual empirical evidence, however, indicates more of a “hump” shape allocation over the lifecycle; the lifetime poor also hold a smaller percentage of their portfolio in stocks relative to higher income groups. Households, therefore, appear to be making considerable “mistakes” in their portfolio allocation. Target date funds, which have grown enormously during the past five years, aim to simplify the investment process in a manner consistent with the predictions of this traditional model. We reconsider the portfolio choice allocation in a computationally-demanding lifecycle model in which households face uninsurable wage shocks, uncertain lifetime as well as a progressive and wage-indexed social security system. Social security benefits, therefore, are correlated with stock returns at a low frequency that is more relevant for lifecycle retirement planning. We show that this model is able to more closely replicate the key stylized facts of portfolio choice. In fact, when calibrated to the age-based income-wealth ratios found in the Survey of Consumer Finances, we demonstrate that the portfolio allocation “mistakes” being made by the vast majority of households actually lead to larger levels of welfare relative to the traditional advice incorporated in target date funds.

Keywords: Portfolio, Social Security, Income, Model, Retirement, Households, Wages, Lifecycle, Wealth, Allocation, Stocks, Correlation, Model