Measuring Risk In Investment
Measuring Risk In Investment
Measuring Risk In Investment
Measuring Risk In Investment
It is desirable to measure risk for another reason. In judging thesignificance of any observed difference in the rates of return on two portfolios, it is desirable to be able to distinguish between differenceswhich can reasonably be attributed to random fluctuations in returnson each portfolio and differences which could only be attributed reasonably to differences in the skill with which the portfolios have beenmanaged. This is an ancient and ordinary problem in statistical infer ence and all of the usual principles apply in this context.
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The distinction between random differences and other differences can be madeonly if there is knowledge of the variability in each series. Any observeddifference for any particular period between rates on two differentportfolios can more confidently be attributed to differences in skillif rates on each portfolio have been rather constant than if rates havebeen extremely variable. Since estimates of risk are typically basedon variability in rates of return, measurements of risk seem to be usefulin distinguishing between random and other differences in rates aswell as for the more primary purpose of evaluating rates in termsof 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 deviationof the time-weighted rates of return as its measure of risk. The meanabsolute deviation is preferred to the standard deviation because theformer is more stable through time and therefore is a more reliableestimate of risk.
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It can and has been argued that a more appropriate measure ofrisk is the beta coefficientthe measure of the sensitivity of the portfolio to market movements rather than a measure of total variabilitysuch as is provided by the mean absolute deviation. As has alreadybeen discussed, in his theoretical articles William Sharpe argued thatrisk premiums depend only on systematic risk (sensitivity to marketmovements) and that risk should therefore be measured by the beta coefficient of rate of return on market returns.* If all investors heldperfectly 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 orthe mean absolute deviation.
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