1.
The expected dollar return on the investment in equities is $18,000 compared to the $5,000
expected return for T-bills. Therefore, the expected risk premium is $13,000.
5.
E(r) = (0.9 × 20%) + (0.1 × 10%) =19%
6.
The probability that the economy will be neutral is 0.50, or 50%.
Given
a neutral
economy, the stock will experience poor performance 30% of the time. The
probability of both poor stock performance and a neutral economy is therefore:
0.30
×
0.50 = 0.15 = 15%
Chapter 6, Study Problem Solutions
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.
When we specify utility by U =
E(r) – 0.5A
σ
2
, the utility level for T-bills is: 0.07
The utility level for the risky portfolio is: U = 0.12 – 0.5A(0.18)
2
= 0.12 – 0.0162A
In order for the risky portfolio to be preferred to bills, the following inequality
must hold:
0.12 – 0.0162A > 0.07
⇒
A < 0.05/0.0162 = 3.09
A must be less than 3.09 for the risky portfolio to be preferred to bills.
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