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# PS4Answers - Problem 1 Part 1 Beta = Cov/SD(Market)2 =...

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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 two-asset 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+(1-x 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+(1-x 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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