Integrative: Expected return, standard deviation, and coefficient of variation. Three assetsF, G, and Hare currently under consideration by Perth Industries. The probability distributions of expected returns for these assets are shown in the following table. Asset F Asset G Asset H j Prj Return, rj Prj Return, rj Prj Return, rj 1 0.1 40% 0.4 35% 0.1 40% 2 0.2 10% 0.3 10% 0.2 20% 3 0.4 0 0.3 -20% 0.4 10% 4 0.2 -5% 0.2 0 5 0.1 -10% 0.1 -20% a. Calculate the average return, r, for each of the three assets. Which provides the largest average return? b. Calculate the standard deviation, r , for each assets returns. Which appears to have the greatest risk? c. Calculate the coefficient of variation, CV, for each assets returns. Which appears to have the greatest relative risk? Solution a. Calculate the average return, r, for each of the three assets. Which provides the largest average return? Asset F PrF rF PrF rF 1 0.10 40% 40% 2 0.20 10% 0% 3 4 5 Total 0.30 Avg. return, rF Asset G PrG rG PrG rG 1 2 3 Total 0.00 Avg. return, rG Asset H PrH rH PrH rH 1 2 3 4 5 Total 0.00 Avg. return, rH Asset G provides the largest average return. b. Calculate the standard deviation, r , for each assets returns. Which appears to have the greatest risk? Asset F PrF rF rF rF - rF (rF - rF )2 PrF (rF - rF )2 1 2 3 4 5 Total 0.00 Standard deviation, F Asset G PrG rG rG rG - rG (rG - rG )2 PrG (rG - rG )2 1 2 3 Total 0.00 Standard deviation, G Asset H PrH rH rH rH - rH (rH - rH )2 PrH (rH - rH )2 1 2 3 4 5 Total 0.00 Standard deviation, H Based on standard deviation, Asset G appears to have the greatest risk, but it must be measured against its expected return with the statistical measure coefficient of variation because the three assets have differing expected values. An incorrect conclusion about the risk of the assets could be drawn using only the standard deviation. c. Calculate the coefficient of variation, CV, for each assets returns. Which appears to have the greatest relative risk? Asset F: Standard deviation, F Avg. return, rF Coefficient of variation, CVF Asset G: Standard deviation, G Avg. return, rG Coefficient of variation, CVG Asset H: Standard deviation, H Avg. return, rH Coefficient of variation, CVH