Problem 1)
Part 1
0.6
0.04
Part 2
0.2
= beta(Super)*SD(Mkt)/SD(Super) = 1.6*0.15/0.4 =
0.6
Part 3
of Supertech. Then you have:
This gives 0.4*1.6+0.6*0.6=1.0.
Part 4
A portfolio of Powergas and Supertech with an expected rate of return of 24% needs to have a beta such that:
Hence the beta of the portfolio has to be 2.0
Then we use the same approach as above:
portfolio value in Supertech and finance the extra 40% by shorting Powergas.
The variance of this portfolio is equal to:
0.25
Hence, the standard deviation of the portfolio return is equal to
49.52%
Part 5
The expected return on the portfolio is 24%. We have established in part 4 that this implies
a beta of 2.0. The least risky portfolio is the one that invests only in the market portfolio and
the risk free asset. The same steps as in part 4 give us that we invest 200% of the portfolio
value in the market, and finance the extra 100% by borrowing at the risk free rate of interest.
In other words, we are moving on the CML to the point were the expected return is equal to 24%.
The risk of this portfolio is:
0.09
Hence, the standard deviation of the portfolio return is equal to
30.00%
We can easily see that this portfolio reduces risk dramatically relative to the twoasset portfolio
in part 4.
Beta = Cov/SD(Market)
2
= 0.0135/0.15
2
=
Covariance = Beta*SD(Market)
2
=1.6*0.15
2
=
ρ
(Powergas,Mkt) = Cov/(SD(Mkt)*SD(Powergas)) = 0.0135/(0.15*0.45) =
ρ
(Supertech,Mkt) = Cov/(SD(Mkt)*SD(Super)) = Cov*SD(Market)/(SD(Mkt)
2
*SD(Super)) =
In order to get the expected return of the market, invest in a portfolio that has a beta of 1. x
S
=portfolio weight
beta(Portfolio)=x
S
*1.6+(1x
S
)*0.6=1.0
Then
x
S
=0.4
, hence invest
40%
in Supertech and
60%
in Powergas.
Er
Portfolio
= rf+beta
Portfolio
*(ER
market
rf) = 6%+beta
portfolio
*(15%6%) = 24%.
beta(Portfolio)=x
S
*1.6+(1x
S
)*0.6=2.0
This gives
140%
in Supertech and
40%
in Powergas. We have to invest 1.4 times our
Var(Portfolio)
= 1.4
2
*0.4
2
+ 0.4
2
*0.45
2
 2*1.4*0.4*0.5*0.4*0.45 =
Var(Portfolio)
= 2.0^2*0.15^2=
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Problem 2)
Data
Company
beta
MCap
Business
SmallCap
1.5
100
Food
LowCost
1.2
400
Software
riskfree
5%
premium
8%
Part 1
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 Fall '09
 Net Present Value, merged company

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