USC  MARSHALL SCHOOL OF BUSINESS
FBE 441 Investments – P. Matos – Spring 2010
Solutions to Homework Assignment #2
Q.1. Consider the following data:
Expected Return
Standard Deviation
Russell Fund
16%
12%
Windsor Fund
14%
10%
S&P Fund
12%
8%
The correlation between the returns on the Russell Fund and the S&P Fund is .7.
The rate on Tbills is 6%. Which of the following portfolios would you prefer to hold
in combination with Tbills and why?
(a) Russell Fund
(b) Windsor Fund
(c) S&P Fund
(d) A portfolio of 60% Russell Fund and 40% S&P Fund.
SOLUTION:
The answer is D. The reason is that the 6040 portfolio combination of the Russell
Fund and the S&P 500 has the highest Sharpe ratio. In other words, this portfolio
gives the best investment opportunity set together with the riskfree Treasury bill.
More specifically, when you calculate the Sharpe ratio, that is, the slope of the
capital allocation line, (E(R
M
)
−
R
f
)/
M
, for each of the three mutual funds as well
as the 6040 combination, you find that the 6040 combination has the highest slope.
Here are the calculations:
 Russell Fund:
(E(R
Russel
)
−
R
f
)/
Russel
= (.16
−
.06) / .12 = .8333
 Windsor Fund:
(E(R
Windsor
)
−
R
f
)/
Windsor
= (.14
−
.06) / .1 = .8
 S&P Fund: (E(R
SP500
)
−
R
f
)/
SP500
= (.12
−
.06) / .08 = .75
 Portfolio of .6 in Russell + .4 in S&P 500:
We have to calculate E(Rp) and
p of
this 60:40 portfolio. To do this, we use the formulas for the mean and standard
deviation for a twoasset portfolio. Say that asset 1 is the Russell fund and asset 2 is
the S&P. First, we calculate E(Rp):
E(Rp) = .6E(R
1
) + .4E(R
2
) = .6(.16) + .4(.12) = .144
And now we calculate
p:
p = w
2
1
2
1
+ w
2
2
2
2
+ 2 w
1
w
2
1
2
1,2
+
= (.6)
2
(.12)
2
+ (.4)
2
(.08)
2
+ 2(.6)(.4)(.7)(.12)(.08) = .0094336
therefore
p
= .097127
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So for the 6040 combination we have:
(E(R
P
)
−
R
f
)/
P
= (.144
−
.06) / .097127 = .8648
Since .8648 > .8333 > .8 > .5, the slope for the capital allocation line with the
6040 mutual fund combination is largest
Q.2. Consider the data from the lecture notes on the US, UK and Japanese stock market:
US
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 Fall '07
 Callahan
 Variance, Modern portfolio theory, sharpe ratio

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