Suppose you are an investor with a choice between three securities that are identical in every way except in terms of their rates of return and risk.
Investment A:Total return = 10 percent with probability 50 percent Total return = 20 percent with probability 50 percent Investment B:Total return = 12 percent with probability 40 percent Total return = 18 percent with probability 60 percent Investment C:Total return = 5 percent with probability 60 percent Total return = 25 percent with probability 40 percent?
a.Which investment provides the highest expected return? Show your work by calculating the expected return of all three investments. b.Calculate the standard deviation of all three investments. c.What type of investor might prefer investment A? Who might prefer investment B?
What will be an ideal response?
| a. | A: (0.5 × 10%) + (0.5 × 20%) = 15.0% |
| B: (0.4 × 12%) + (0.6 × 18%) = 15.6% | |
| C: (0.6 × 5%) + (0.4 × 25%) = 13.0% | |
| Investment B has the highest expected return. | |
| b. | A: {[0.5 × (0.1 ? 0.15)2] + [0.5 × (0.2 ? 0.15)2]}1/2 = 5.0% |
| B: {[0.4 × (0.12 ? 0.156)2] + [0.6 × (0.18 ? 0.156)2]}1/2 = 2.9% | |
| C: {[0.6 × (0.05 ? 0.13)2] + [0.4 × (0.25 ? 0.13)2]}1/2 = 9.8% | |
| c. | No risk-averse investor would ever prefer investment A because it has a lower expected return and higher risk than investment B. Similarly, no risk-averse investor would ever prefer investment C. Given these choices, all risk-averse investors would choose investment B. |
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