A substantial literature has developed models of optimal consumption and asset allocation based on the assumption that stocks and bonds have fixed returns, with normal independent, identically distributed disturbances. Households optimally rebalance from stocks to bonds as they age, reflecting the declining proportion of their wealth that is represented by low-risk human capital.
Using annual return data for large-capitalization stocks and corporate bonds covering the period 1926 through 2011, the paper calculates optimal consumption and asset allocation over the life cycle for a household with Social Security benefits and uncertain labor market earnings. It considers the alternative assumptions that stock and bond returns 1) are normally distributed, 2) follow a vector autoregressive path (VAR) with normally distributed disturbances, and 3) follow a VAR with disturbances drawn from a stable distribution. The assumptions have a significant effect on asset allocation. At age 65, the optimal stock allocation is 52 percent, 68 percent, and 55 percent, respectively, for the three alternatives. When returns follow a VAR with stable disturbances, a household with a constant relative risk aversion assuming a coefficient of risk aversion of 2 would require a 1 percent increase in lifetime consumption to compensate it for assuming that the disturbances to returns follow a normal distribution. Households with a coefficient of risk aversion of 5 would require less than 0.1 percent, reflecting their lower accumulation of wealth and smaller stock allocations.