When investment takes place over many periods, the portfolio selection criteria that are valid in the earlier periods narrow to a very small set of (short-run) utility functions for a wide variety of long-run goals spanning a continuum of risk attitudes all the way from risk neutrality to infinite risk aversion. These criteria were applied to the construction and rebalancing of portfolios composed of U.S. stocks, corporate bonds, government bonds and a risk-free asset over the period 1936–78. Probability distributions estimated from past realized returns, and both annual and quarterly holding periods, were employed.

Geometric means and standard deviations of returns were tabulated for a wide range of risk-tolerance strategies. The results reveal that the gains from active diversification among the major asset categories were substantial, especially for the highly risk-averse strategies. Not only did one very conservative strategy achieve a return significantly greater than the return on the risk-free asset (4.5 vs. 2.9 per cent), but it also displayed less variability (2.4 vs. 2.5 per cent). Furthermore, the risk-averse strategies relied fairly heavily on the stock market; the portfolio corresponding to the most risk-averse strategy examined held stocks continuously from 1948 to 1973.