The Fallacy of Maximizing Risk-Adjusted Returns

Routinely, investors in managed funds or those they employ to assess managed funds, do so with certain parameters. Some of these parameters are not performance related (e.g., age of the fund, assets under management, type of fund) whereas there are almost always performance-related measures. Most of these performance measures pertain to perceptions of risk, often in the way of measures of variance with respect to return, worst-case performance depth as well as duration, consistency of returns, etc., collectively often falling under the moniker of “risk-adjusted returns.” Herein we demonstrate that, in the limit of continuing time, to maximize risk-adjusted returns is the same exercise as maximizing absolute returns, and hence, an investor in a program that doesn’t seek to maximize absolute returns is not getting what he should be getting in terms of the investment fees he pays