Complete all five problems below. The homework will be graded mostly based on completeness (refer to the syllabus for details). You may work with other students, but you must submit your own work. Please do not copy somebody's homework as we will be checking for that.
Problem 1:
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Price, 03/2012
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Price 03/2013
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Beta
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Standard Deviation
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S&P 500 Index
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1400
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1560
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1.0
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14.01%
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Heinz (HNZ)
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53
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73
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0.53
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15.7%
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Las Vegas Sands (LVS)
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52
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54
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3.65
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35.5%
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Colgate (CL)
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96
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114
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0.45
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18.2%
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(a) Explain why the beta estimates make sense intuitively. Hint! Why would LVS have a high beta? etc.
(b) Assume the CAPM is correct. How should you invest? Do you need more information to answer this question?
(c) Which stock has the highest expected return according to the CAPM? Why? Plot all the stocks and the S&P on the SML. The risk free rate is 2% and the expected return on the market is 10%.
(d) Consider a portfolio that allocates 25%, 40% and 35% to HNZ, LVS and CL respectively. What is the beta of this portfolio? What is the expected return (use the CAPM)? What is the standard deviation?
(e) What is the expected return on the portfolio in (d) using historical information instead of the CAPM?
(f) CL has a higher standard deviation than HNZ. Is this consistent with the CAPM? Why or why not?
Problem 2:
Assume the risk free rate is 6% and the market risk premium is 7.5%. Ragnarok Unlimited Corp. (RUC) has a beta of 4, and it offers a return of 27% at the moment. Is RUC fairly priced according to the CAPM? Why or why not? If the price is not fair, what does the CAPM say will happen to the price of RUC stock?
Problem 3:
If the CAPM assumptions are true, then it follows that all investors hold the same portfolio.
Is this statement true or false? Explain why your answer makes sense.
Yes. CAPM assumes that everyone holds the market-portfolio, because the optimal investment is a combined portfolio that consists of the Market portfolio and the risk-free rate. Thus, all investors will choose to hold the Market Portfolio as their risky portfolio.
Problem 4:
(a) Suppose that there are many stocks in the security market and that the characteristics of Stocks A and B are given as follows
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Stock
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Expected Return
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Standard Deviation
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A
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10%
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5%
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B
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15%
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10%
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Correlation = -1
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Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? Explain.
HINT!!! The stocks are perfectly negatively correlated.
(b) Calculate the expected return and standard deviation of an equally weighted portfolio of Stock A, Stock B and the risk-free asset
Problem 5:
A share of stock sells for $100 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 0.8. What do investors expect the stock to sell for at the end of the year? The risk-free rate of interest is 4% and the expected rate of return on the market is 12%