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UNIVERSITY OF TORONTO
Joseph L. Rotman School of Management
RSM332
Tutorial #9 Problem Set
Nov.16/Nov.17 2011
1. In your research of two mutual funds, Thrifty Fund and Ponzi Fund, you estimate
their respective expected returns over the next year as 3 percent for Thrifty and 21.4
percent for Ponzi. Thrifty Fund invests only in shortterm Tbills and is riskfree. Its
return for the following year is known in advance. Ponzi invests in risky securities.
The estimated standard deviation of its returns is 64 percent. To better gauge Ponzi’s
risk you ran the usual CAPM regression in Excel,
R
Ponzi

R
f
=
α
+
β
(
R
m

R
f
) +
±.
The regression generated the following output (Δ is an unknown you will need to
compute below):
Regression Statistics
R Square
0.262
Observations
120
Coeﬃcients
t Stat.
Intercept
Δ
0.875
R
m

R
f
2.050
4.235
The market expected return is 11% and market standard deviation is 16 percent.
(a) You would like to create the minimumvariance portfolio using Thrifty and Ponzi.
Compute the weights of the two funds in the MVP. (5 points)
(b) Given the estimated coeﬃcients, what is the correlation between returns on Ponzi
and returns on the market? (5 points)
(c) Given the estimated coeﬃcients, does Ponzi fund lie above, on, or below the Security
Market Line? Estimate how much more or less return Ponzi fund earns relative to the
expected return the CAPM predicts for a portfolio of Ponzi’s risk? (5 points)
(d) Does your answer to (c) imply that the CAPM holds or that is it violated? How
conﬁdent are you making this statement? (Please, maximum three sentences here.
Anything longer than three sentences will not be graded.) (5 points)
Solution:
(a) Thrifty fund is riskfree, so the variance of its returns is 0. No other portfolio
can have a lower variance, so the Minimum Variance Portfolio will assign the weight
of 100% to Thrifty and 0% to Ponzi. (You could get the same answer by using the
1
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View Full Document formula derived in class. In that case you will also need to notice that the covariance
between Thrifty and Ponzi is zero.)
(b)
β
Ponzi
=
cov
(
R
Ponzi
,R
market
)
σ
2
market
⇒
cov
(
R
Ponzi
,R
market
) = 2
.
05
×
0
.
16
2
= 0
.
05248
,
corr
(
R
Ponzi
,R
market
) =
cov
(
R
Ponzi
,R
market
)
σ
market
σ
Ponzi
= 0
.
5125
.
(c)Ponzi fund’s alpha is
α
Ponzi
=
E
[
R
Ponzi
]

R
f

β
Ponzi
(
E
[
R
market
]

R
f
) = 0
.
02
The alpha is positive and indicates that Ponzi earns 2% more per year than what
the CAPM predicts for a portfolio of its risk. Thus, Ponzi fund lies above the SML,
which may mean that its manager, Mr. Charles Ponzi, is able to identify underpriced
companies.
(d) As we showed in (c), Ponzi fund lies above the SML, which seems to contradict the
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This note was uploaded on 12/20/2011 for the course RSM 332 taught by Professor Raymondkan during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 RAYMONDKAN

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