Fin 5633: Investment Theory and Problems: Chapter#7 Solutions
Chapter 7 Online Quiz
1 2 3 4 5 6 7 8 9 10
A C A D C B D E A A
1.
Expected return = (0.7 × 18%) + (0.3 × 8%) = 15%
Standard deviation = 0.7 × 28% = 19.6%
2.
Investment proportions: 30.0% in T-bills
0.7
×
25% = 17.5% in Stock A
0.7
×
32% = 22.4% in Stock B
0.7
×
43% = 30.1% in Stock C
S
=
18
−
8
28
=
0 .
3571
Client's reward-to-variability ratio: S
=
15
−
8
19 .
6
=
0 .
3571
4.
30
25
20
E(r)
%
15
10
5
0
0
Client
P
10
Fin 5633 Chapter #7 Solutions
20
σ (%)
30
CAL (Slope = 0.3571)
40
Page1

5. a. E(r
C
) = r f
+ y[E(r
P
) – r f
] = 8 + y(18
−
8)
If the expected return for the portfolio is 16%, then:
16 = 8 + 10 y
⇒ y
=
16
−
10
8
=
0 .
8
Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills. b.
Client’s investment proportions: 20.0% in T-bills
0.8
×
25% = 20.0% in Stock A
σ
C
0.8
×
32% = 25.6% in Stock B
0.8
×
43% = 34.4% in Stock C
= 0.8 × σ
P
= 0.8 × 28% = 22.4%
6. a.
σ
C
= y × 28%
If your client prefers a standard deviation of at most 18%, then: y = 18/28 = 0.6429 = 64.29% invested in the risky portfolio
E(r
C
) = 8 + 10y = 8 + (0.6429 × 10) = 8 + 6.429 = 14.429%
7.
a. y
* =
E
0 .
( r
P
)
−
01 A
σ r f
2
P
=
18
−
8
0 .
01
×
3 .
5
×
28
2
=
10
27 .
44
=
0 .
3644
Therefore, the client’s optimal proportions are: 36.44% invested in the risky portfolio and 63.56% invested in T-bills. b.
E(r
C
) = 8 + 10y* = 8 + (0.3644 × 10) = 11.644%
σ
C
= 0.3644 × 28 = 10.203%
11. a. If the period 1926 - 2002 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r
M
)
−
r f
= 8.22%,
σ
M
= 20.81% (we use the standard deviation of the risk premium from Table 7.4). Then y
*
is given by: y *
=
E ( r
M
)
−
0 .
01 A
σ 2 r
M f
=
0 .
01
×
8
4
.
22
×
20 .
81
2
=
0 .
4745
That is, 47.45% of the portfolio should be allocated to equity and 52.55% should be allocated to T-bills.
Fin 5633 Chapter #7 Solutions Page2

b.
If the period 1983 - 2002 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r
M
)
−
r f
= 8.38%,
σ
M
= 16.26% and y* is given by: y *
=
E ( r
M
)
−
0 .
01 A
σ 2 r
M f
=
0 .
01
×
8
4
.
38
×
16 .
26
2
=
0 .
7924
Therefore, 79.24% of the complete portfolio should be allocated to equity and 20.76% should be allocated to T-bills. c. In part (b), the market risk premium is expected to be higher than in part (a) and market risk is lower. Therefore, the reward-to-variability ratio is expected to be higher in part
(b), which explains the greater proportion invested in equity.
18. b
19. a
20.
a
(0.6
×
(
−
$30,000)]
−
$5,000 = $13,000
21. b
22. c
Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16%
Expected return of client’s overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12%
Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4%
23. a
10
Reward to variability ratio =
14
=
0 .
71
Fin 5633 Chapter #7 Solutions Page3