Individuals saving for retirement must choose a composition for their portfolio. Conventional wisdom suggests that the younger the individual, the more risky should be the portfolio. We investigate this issue, comparing two risk averse, expected-utility maximizing investors who are identical except that the first investor will live longer than the second.
The first model explored has two assets every period, one has a riskless zero return, the other offering independent risks each period. In fact, the young investor should purchase a greater proportion of the risky asset if the utility function exhibits the condition of convex absolute risk tolerance. Most of the utility functions commonly used in economics and finance have linear absolute risk tolerance. Accepting such utility functions, there will be some conditions under which older investors should have riskier portfolios than younger ones. (In addition, with a positive risk-free rate, risk aversion at zero must be infinite).
We show that rational investors will only be myopic, i.e., select their portfolio without worrying about future investment opportunities, when they have constant relative risk aversion. Constant relative risk aversion is where one will take the same proportional gambles on one’s portfolio whatever one’s wealth.
This paper focuses on the effects of age on risk taking, but its results should have application in other arenas. For example, it should help us better understand the role of liquidity constraints in dynamic models of finance.
