Comment on “aging population, retirement, and risk taking”

Levy [Levy H (2016) Aging population, retirement, and risk taking. Management Sci. 62(5):1415-1430] argues that the portfolio with the maximal geometric mean (MGM) asymptotically dominates any other portfolio; that is, as the investment horizon becomes very long, the MGM portfolio is preferred over any other portfolio for all preferences with marginal utility bounded from above, U' ≤ M. The important economic implication is that in the long run, an all-equity portfolio dominates bond (or mixed) portfolios, which have lower geometric means. This comment shows that Levy's result holds only if the marginal utility is also bounded from below. This seemingly technical correction has profound economic implications, because many commonly accepted preferences do not satisfy the lower bound condition. Indeed, for some standard preferences, the optimal stock-bond mix shifts toward bonds, not stocks, as the horizon increases, exactly opposite to Levy's conclusion.