Sample%20Midterm%20Problems_sol

Sample%20Midterm%20Problems_sol - Sample Midterm Problems:...

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Sample Midterm Problems: Solutions 1. Assume that the whole US market is a 60-40 combination of stocks and bonds: that is, 60% of the US market portfolio is represented by stocks and 40% is represented by bonds (note: bonds can be risky). The standard deviations of the returns on stocks and bonds are 0.20 and 0.10, respectively. The correlation between the returns on stocks and bonds is 0.25. a) What is the covariance between the returns on stocks and bonds? Cov(Rs, Rb) = Corr(Rs,Rb)*SD(Rs)*SD(Rb) = 0.25*0.20*0.10 = 0.005 b) What is the variance of the market portfolio? Var(Rm) = (0.6 2 )*(0.2 2 ) + (0.4 2 )*(0.1 2 ) + 2*0.6*0.4*0.005 = 0.0184 2. The current price of a given stock is $32. We know that the price of the stock at some future date can take on the values {$30, $37, $43} with probabilities {0.3, 0.5, 0.2}, respectively. We also know that the stock is about to pay a $4 dividend. What is the expected return on the stock? There are three scenarios, and the returns in each scenario are: {(30 - 32 + 4)/32, (37 - 32 + 4)/32, (43 – 32 + 4)/32} or {6.250%, 28.125%, 46.875%}. Since these scenarios have probabilities {0.3, 0.5, 0.2}, the expected return is the weighted average of the returns: 0.3*6.25% + 0.5*28.125% + 0.2*46.875% = 25.31% 3. Suppose there is an economy with two risky assets, one risk-free asset, and two investors. Investor 1 can only invest in risky asset 1 in addition to the risk-free asset. Investor 2 can only invest in risky asset 2 in addition to the risk-free asset. Both investors
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Sample%20Midterm%20Problems_sol - Sample Midterm Problems:...

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