ActSc 372 WINTER 2010
Assignment 4
Due Date: Wednesday, March 10, 2010 (Beginning of Class)
1. Assume that the returns of individual securities are generated by the following two
factor model:
R
i
=
E
(
R
i
) +
β
i
F
1
+
β
i
F
2
,
where
R
i
is the return for security
i
and
F
1
and
F
2
are market factors with zero
expectation and zero covariance.
In addition, assume that there is a capital market for four securities, and the capital
market for these four assets is perfect in the sense that there are no transaction costs
and short sales are permitted. The characteristics of the four securities follow:
Security
β
1
β
2
E
(
R
)
1
1.0
1.5
20%
2
0.5
2.0
20%
3
1.0
0.5
10%
4
1.5
0.75
10%
(a) Construct a portfolio containing (long or short) securities 1 and 2, with a return
that does not depend on the market factor
F
1
in any way. Compare the expected
return and
β
2
coeﬃcient for this portfolio.
(b) Following the procedure in (a), construct a portfolio containing securities 3 and
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 Spring '10
 Tan,KenS
 Variance, Financial Markets, Probability theory, Ri

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