Consider three alternative bonds that you might invest in, each of which matures in one year. The following table shows the probability that you will receive each possible return. For example, if you buy bond A, the probability is 90 percent that your return will be 20 percent and the probability is 10 percent that your return will be ?100 percent (in other words, you lose the entire amount invested).
BondProbability
Return
Bond A90%
20%
10%
?100%
Bond B75%
40%
25%
?40%
Bond C60%
10%
40%
?10%
?
a.Calculate the expected return for all three bonds in percentage terms. b.The standard deviations of the returns on these bonds are: Bond A, 36.0 percent; Bond B, 34.6 percent; Bond C, 9.8 percent. If you are extremely risk averse, which of the three bonds would you buy? Why? c.Would a risk-averse investor ever buy Bond A instead of one of the other bonds? Why or why not? Explain and show all your work. In your calculations, you may round after three significant digits.
What will be an ideal response?
| a. | E(A) = (0.9 × 0.2) + [0.1 × (?1.0)] = 0.08 = 8% |
| E(B) = (0.75 × 0.4) + [0.25 × (?0.4)] = 0.2 = 20% | |
| E(C) = (0.6 × 0.1) + [0.4 × (?0.1)] = 0.02 = 2% | |
| b. | You would buy bond C, which has the lowest risk, even though the expected return is very low. |
| c. | You would never buy bond A because it is dominated by bond B; B has a higher expected return and a lower standard deviation. |
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