Suppose a discount bond costs $5,000 today and pays off some amount b in one year. Suppose that b is uncertain according to the following table of probabilities:
b:$5,000
$5,500
$6,000
$6,500
$7,000
Probability:0.1
0.2
0.3
0.2
0.2
?
a.Calculate the return (in percent) for each value of b. (Note: you may just calculate the total return and not worry about how this is split up between current yield and capital-gains yield.) b.Calculate the expected return. c.Suppose an investor has a choice between buying this security or purchasing a different security that also costs $5,000 today, but pays off $5,500 with certainty in one year. How is an investor's choice of which security to purchase related to her degree of risk aversion?
What will be an ideal response?
| a. | The returns are found by: return = [(b? $5000)/$5000] × 100% | ||
| b | return | ||
| $5000 | 0% | ||
| $5500 | 10% | ||
| $6000 | 20% | ||
| $6500 | 30% | ||
| $7000 | 40% | ||
| b. | E | = (0.1 × 0%) + (0.2 × 10%) + (0.3 × 20%) + (0.2 × 30%) + (0.2 × 40%) | |
| = 22% | |||
| c. | The trade-off is between a certain return of 10 percent versus a risky return of 22 percent. Which one the investor would choose depends on her degree of risk aversion; the more risk averse she is, the more likely she is to pick the safe asset instead of the risky one. As the degree of risk aversion declines, she is more likely to pick the risky asset. | ||
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