Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
6-1
CHAPTER 6: RISK AVERSION AND
CAPITAL ALLOCATION TO RISKY ASSETS
PROBLEM SETS
1.
(e)
2.
(b) A higher borrowing is a consequence of the risk of the borrowers’ default. In perfect
markets with no additional cost of default, this increment would equal the value of the
borrower’s option to default, and the Sharpe measure, with appropriate treatment of the
default option, would be the same. However, in reality there are costs to default so that
this part of the increment lowers the Sharpe ratio. Also, notice that answer (c) is not
correct because doubling the expected return with a fixed risk-free rate will more than
double the risk premium and the Sharpe ratio.
3.
Assuming no change in risk tolerance, that is, an unchanged risk aversion coefficient
(A), then higher perceived volatility increases the denominator of the equation for the
optimal investment in the risky portfolio (Equation 6.12). The proportion invested in the
risky portfolio will therefore decrease.
4.
a.
The expected cash flow is: (0.5
×
$70,000) + (0.5
×
200,000) = $135,000
With a risk premium of 8% over the risk-free rate of 6%, the required rate of
return is 14%. Therefore, the present value of the portfolio is:
$135,000/1.14 = $118,421
b.
If the portfolio is purchased for $118,421, and provides an expected cash inflow of
$135,000, then the expected rate of return [E(r)] is derived as follows:
$118,421
×
[1 + E(r)] = $135,000
Therefore, E(r) =
14%. The portfolio price is set to equate the expected rate or
return with the required rate of return.
c.
If the risk premium over T-bills is now 12%, then the required return is:
6% + 12% = 18%
The present value of the portfolio is now:
$135,000/1.18 = $114,407