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Beta coefficient, arithmetic average returns, deviation

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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. Assuming (1) that the situation during Years 1 to 7 is expected to hold true in the future (that is, rx = rx; rm = rm; and both sx and bx in the future will equal their past values), and (2) 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 the portfolio either Stock X or another stock, Stock Y, that has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns; that is, rx = ry = 10.6%. Which stock should you choose?

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The solution explains how to calculate the beta coefficient, arithmetic average returns and standard deviation

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