Problem 1 You have the following information:
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Portfolio
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Expected Return
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Standard Deviation
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risk free rate
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2%
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0
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Portfolio A
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6%
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4%
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Portfolio B
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9%
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8%
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a. The CAPM is true in these data and one of the portfolios is the market portfolio. Which portfolio is the market portfolio? Briefly explain your answer.
b. For this part, you can assume that the CAPM is true in these data and that portfolio A is the market portfolio. What is Portfolio B's beta? What is portfolio A's beta?
Problem 2 Assume that security returns are generated by the following factor model with 2 factors: Ri,t = ai + bi,1F1,t + bi,2F2,t + εi, where Fi,t is factor its realization at time t, bi,1 is the factor loading of stock i against the first factor, and εi,t is the residual risk of stock i at time t. The 2 factors are uncorrelated with each other.
a. Factor 1 has variance of 0.0025 and Factor 2 has variance of 0.01. Stock 1 has a loading of 2 on the first factor, a loading of 1 on the second factor and residual variance of 0.004. What is the variance of the return on stock 1?
b. Stock 2 has a factor loading of 1 on the first factor and 1 on the second factor. What is the covariance between the returns on stocks 1 and 2?
Problem 3 2. Your current position is 100% invested in Microsoft. Microsoft has an expected return of 6% and a standard deviation of 3%. You are considering diversifying your position, and want to look at adding another stock to your position.
a. Both Dell and IBM have the same expected returns and the same standard deviations. Their expected returns are 5% and they have standard deviations less than Microsoft's standard deviation. Dell has a correlation of zero to Microsoft and IBM has a correlation of -1 to Microsoft. You cannot add both of Dell and IBM to your portfolio. What stock do you add to your portfolio invested 100% in Microsoft, and why? Explain your answer graphically.
b. Given the information in part (a), plot the risk free rate, Microsoft, Dell and IBM in a mean versus standard deviation plot.
Problem 4 Are each of the following statements true of the efficient market hypothesis? You should discuss the reasons behind your answer. (For each statement, please indicate whether it is true or false along with the reason for your answer.)
a. It implies perfect forecasting ability.
b. It implies that prices reflect all available information.
c. It results from keen competition between investors
d. It implies that the market is irrational.
e. It implies that prices do not fluctuate.
Problem 5 Suppose that after conducting an analysis of past stock prices, you came up with the following observations. What are the implications of each observation for the weak form of the efficient market hypothesis? In your answer, you should indicate whether the statement supports, contradicts, or is inconclusive about the weak form efficiency and your reasons for the conclusion.
a. The average return is significantly greater than zero.
b. One could have made consistently superior returns by buying stocks after a 10% rise in price and selling after a 10% fall.
Problem 6 Which of the following observations provide evidence against the strong form of the efficient market theory? Please provide reasons for your answer. (For each statement, please indicate whether it provides evidence for or against the strong form efficiency along with the reason for your answer.)
a. Mutual fund managers do not on average make superior returns.
b. By buying stocks before the announcement of an abnormal rise in earnings, one would generally make superior profits.
c. Managers who trade in their own stocks make superior returns.
d. You cannot make superior profits by buying (or selling) stocks after the announcement of an abnormal rise in earnings.