Question

Compare the means and standard deviations of the final accumulations for the two strategies, Constant mix strategy and Age-phasing strategy, in order to determine whether one strategy dominates the other.

Consider a simplistic investment environment with only two securities and two periods. If $1 is invested in one of the securities at the beginning of a period, the pay-off at the end of the period is $2 with probability 0.5 and $0.50 with probability 0.5. The other security earns a zero rate of return with certainty. Consider the case of a life cycle investor who contributes (saves) $50 at the beginning of the first period, and another $50 at the beginning of the second period.

Under an ‘age-phasing’ strategy, the investor invests her entire contribution in period 1 in the risky asset, whilst in period 2 she invests her period 1 accumulation and period 2 $50 contribution 50:50 in the risky and safe securities.

Under a ‘constant mix’ strategy, by contrast, the available funds are at all times invested 60% and 40% in the risky and safe securities, respectively.

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