The Risk-return Fallacy

We assume that in the world of business, higher risks are only taken when rewarded with higher expected returns. This supposition has been confirmed empirically using capital market data. However, accounting measures have yielded puzzling results: using the mean and variance of ROE as measures of return and risk, respectively, Bowman (1980) and other researchers find a negative relationship between the measures. There are many suggested explanations of this seemingly paradoxical result, some of which relate to model misspecifications. Surprisingly, one obvious source of an artificial risk-return “paradox” has been neglected. This is the skewness of each firm’s ROE distribution. Using data from German firms, my study finds a significantly negative skewness. This skewness alone, even if firms were otherwise identical, brings about a negative relationship between mean and variance that is comparable in size to that found in the data. Thus, it is not clear if the empirical result really stems from a negative relationship between risk and return. It could be an artifact resulting from the inadmissible ex post measurement of risk. Hence, the “paradox” is highly questionable.