Question: 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
| 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 | |||||||||
| 2 | |||||||||
| 3 | |||||||||
| 4 | |||||||||
| 5 | |||||||||
| Total | 0.00 | 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 | |||||||||
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