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71
CHAPTER 7: CAPITAL ALLOCATION BETWEEN
THE RISKY ASSET
AND
THE RISKFREE ASSET
1.
Expected return = (0.7
±
18%) + (0.3
±
8%) = 15%
Standard deviation = 0.7
±
28% = 19.6%
2.
Investment proportions:
30.0% in Tbills
0.7
±
25% =
17.5% in Stock A
0.7
±
32% =
22.4% in Stock B
0.7
±
43% =
30.1% in Stock C
3.
Your rewardtovariability ratio:
3571
.
0
28
8
18
S
=
±
=
Client's rewardtovariability ratio:
3571
.
0
6
.
19
8
15
S
=
±
=
4.
Client
P
0
5
10
15
20
25
30
0
1
02
03
04
0
±
(%)
E(r)
%
CAL (Slope = 0.3571)
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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
²
8
.
0
10
8
16
y
=
±
=
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 Tbills
0.8
³
25% =
20.0% in Stock A
0.8
³
32% =
25.6% in Stock B
0.8
³
43% =
34.4% in Stock C
c.
´
C
= 0.8
³
´
P
= 0.8
³
28% = 22.4%
6.
a.
´
C
= y
³
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
b.
E(r
C
) = 8 + 10y = 8 + (0.6429
³
10) = 8 + 6.429
= 14.429%
7.
a.
3644
.
0
44
.
27
10
28
5
.
3
01
.
0
8
18
A
01
.
0
r
)
r
(
E
y
2
2
P
f
P
*
=
=
±
±
²
=
³
²
=
Therefore, the client’s optimal proportions are: 36.44% invested in the risky
portfolio and 63.56% invested in Tbills.
b.
E(r
C
) = 8 + 10y* = 8 + (0.3644
³
10) = 11.644%
´
C
= 0.3644
³
28 = 10.203%
8.
a.
Slope of the CML
20
.
0
25
8
13
=
±
=
The diagram follows.
b.
My fund allows an investor to achieve a higher mean for any given standard deviation than
would a passive strategy, i.e., a higher expected return for any given level of risk.
73
CML and CAL
0
2
4
6
8
10
12
14
16
18
01
0
2
0
3
0
Standard Deviation
Expected Retrun
CAL: Slope = 0.3571
CML: Slope = 0.20
9.
a.
With 70% of his money invested in my fund’s portfolio, the client’s expected
return is 15% per year and standard deviation is 19.6% per year.
If he shifts
that money to the passive portfolio (which has an expected return of 13% and
standard deviation of 25%), his overall expected return becomes:
E(r
C
) = r
f
+ 0.7[E(r
M
)
±
r
f
] = 8 + [0.7
²
(13 – 8)] = 11.5%
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This note was uploaded on 03/10/2011 for the course FMIS 3601 taught by Professor Vizanko during the Spring '08 term at University of Minnesota Duluth.
 Spring '08
 Vizanko

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