7-3
CML and CAL
0
2
4
6
8
10
12
14
16
18
0102030
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 (13 – 8)] = 11.5%
The standard deviation of the complete portfolio using the passive portfolio
would be:
C
= 0.7
M
= 0.7 25% = 17.5%
Therefore, the shift entails a decrease in mean from 14% to 11.5% and a
decrease in standard deviation from 19.6% to 17.5%. Since both mean return
and standard deviation decrease, it is not yet clear whether the move is beneficial.
The disadvantage of the shift is that, if the client is willing to accept a mean
return on his total portfolio of 11.5%, he can achieve it with a lower standard
deviation using my fund rather than the passive portfolio.
To achieve a target mean of 11.5%, we first write the mean of the complete
portfolio as a function of the proportion invested in my fund (y):
E(r
C
) = 8 + y(18 8) = 8 + 10y
Our target is: E(r
C
) = 11.5%. Therefore, the proportion that must be invested in
my fund is determined as follows:
11.5 = 8 + 10y
35.0
10
85.11
y =
=
