Decision Making and the Investment Horizon

11.8 Summary

The assumed investment horizon plays a key role in portfolio analysis. This is obvious in the case where distributions are not stationary and are dependent over time. However, we show in this Chapter that M-V efficiency analysis, M-V portfolio diversification, Sharpe’s reward-to-variability ratio, beta, and correlations are all dependent on the assumed horizon even if distributions are independent and identical over time (i.i.d.), let alone if the i.i.d. assumption does not hold.

Stochastic dominance efficiency analyses are also dependent on the assumed horizon. The size of the M-V efficient set does not decrease (and may increase) with increase in the investment horizon: The opposite is true with SD efficient set. This apparent contradiction between M-V and SSD is resolved once we recall that if the one-period distributions are assumed to be normal, the multiperiod distributions cannot be normal. Thus, M-V and SSD coincide for n=1 (if the one-period distribution is assumed to be normal) but for n > 1, the two efficient sets may diverge. SD analysis is distribution-free and, therefore, it is correct and consistent with expected utility paradigm, but M-V is not consistent with this paradigm. Given that the one-period distributions are normal, the M-V multi-period efficient set is incorrect because the distributions are no longer normal and, therefore, it will include portfolios that are SSD inefficient.