Unformatted text preview: ween 3 standard deviations from the expected value. 35 The Normal Probability DistributionExample Asset A Asset B Probability of Sd1.41% Sd5.66 Distribution Mean15% Mean15% (13, 15 ,17) (7, 15, 23) 13.5916.41 9.3420.66 68% 12.1817.82 3.6826.32 95% 10.1119.23 1.9831.98 99%
36 The Normal Probability DistributionExample If we assume that the probability distribution of returns for the Norman Company is normal, 68% of the possible outcomes would have a return ranging between 13.59 and 16.41% for asset A and between 9.34 and 20.66% for asset B; 95% of the possible return outcomes would range between 12.18 and 17.82% for asset A and between 3.68 and 26.32% for asset B; and 99% of the possible return outcomes would range between 10.77 and 19.23% for asset A and between 1.98 and 31.98% for asset B. The greater risk of asset B is clearly reflected in its much wider range of possible returns for each level of confidence (68%, 95%, etc.).
37 Coefficient of VariationCV The above table presents the standarddeviations for Norman Company’s assets A and B, based on the earlier data. The standard deviation for asset A is 1.41%, and the standard deviation for asset B is 5.66%. The higher risk of asset B is clearly reflected in its higher standard deviation.
Coefficient of VariationCV, is a measure of relative dispersion that is useful in comparing the risks of assets with differing expected returns. The Following Equation gives the expression for the coefficient of variation: The higher the coefficient of variation, the greater 38 Coefficient of VariationCV When the standard deviations (from Table ) and the expected returns (from Table) for assets A and B are substituted into the above Equation , the coefficients of variation for A and B are 0.094 (1.41%/15%) and 0.377 (5.66%/15%), respectively. Asset B has the higher coefficient of variation and is therefore more risky than asset A—which we already know from the standard deviation.
(Because both assets have the same expected return, the coefficient of variation has not pr...
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- Winter '12
- The Return, Norman Company