Chapter 6 – Answer Key:
Problem Sets: 3, 4, 5, 10, 11, 13, 14, 15, 17, 18, & 20
CFA Problems: 1, 2, 3, 4, 5, 6, & 7
Problem Sets:
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
d.
For a given expected cash flow, portfolios that command greater risk
premia must sell at lower prices. The extra discount from expected value
is a penalty for risk.
5.