Measuring Risk In Investment
It is desirable to measure risk for another reason. In judging the significance of any observed difference in the rates of return on two portfolios, it is desirable to be able to distinguish between differences which can reasonably be attributed to random fluctuations in returns on each portfolio and differences which could only be attributed reasonably to differences in the skill with which the portfolios have been managed. This is an ancient and ordinary problem in statistical infer ence and all of the usual principles apply in this context. The distinction between random differences and other differences can be made only if there is knowledge of the variability in each series. Any observed difference for any particular period between rates on two different portfolios can more confidently be attributed to differences in skill if rates on each portfolio have been rather constant than if rates have been extremely variable. Since estimates of risk are typically based on variability in rates of return, measurements of risk seem to be useful in distinguishing between random and other differences in rates as well as for the more primary purpose of evaluating rates in terms of risks which were assumed.
Some of the difficulties of measuring risk have been discussed earlier, and we will not repeat that discussion. The Bank Administration Institute recommends the use of the mean absolute deviation of the time-weighted rates of return as its measure of risk. The mean absolute deviation is preferred to the standard deviation because the former is more stable through time and therefore is a more reliable estimate of risk.
It can and has been argued that a more appropriate measure of risk is the beta coefficient—the measure of the sensitivity of the portfolio to market movements rather than a measure of total variability such as is provided by the mean absolute deviation. As has already been discussed, in his theoretical articles William Sharpe argued that risk premiums depend only on systematic risk (sensitivity to market movements) and that risk should therefore be measured by the beta coefficient of rate of return on market returns.* If all investors held perfectly diversified portfolios, Sharpe's argument is persuasive. If all portfolios are perfectly diversified, risk as measured by the beta coefficient is equivalent to risk as measured by the standard deviation or the mean absolute deviation.