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You are given the following set of data:
Historical Rates of Return
Year
NYSE
Stock X
1
-26.5%
-14.0%
2
37.2
23.0
3
23.8
17.5
4
-7.2
2.0
5
6.6
8.1
6
20.5
19.4
7
30.6
18.2
a. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X"s beta coefficient.
b. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE.
c. Assume that the situation during Years 1 to 7 is expected to prevail in the future (i.e., ^r x ¼ ¯rx; ^rM ¼ ¯rM, and both sX and bX in the future will equal their past values). Also assume that Stock X is in equilibrium-that is, it plots on the Security Market Line. What is the risk-free rate?
d. Plot the Security Market Line.
e. Suppose you hold a large, well-diversified portfolio and are considering adding to that portfolio either Stock X or another stock, Stock Y, which has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns: ^r x ¼ ^ry ¼ 10:6%. Which stock should you choose?
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