Determine stock beta coefficient


You are given the following 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

1) Use a spreadsheet (or calculator with a linear regression function) to determine stock X’s beta coefficient.

2) 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.

3) Assuming (1) that the situation during Years 1 to 7 is expected to hold true in the future (that is r(x) = r(x); r(m); and both o(x) and b(x) in the future will equal their past values), and (2) that Stock X is in equilibrium (that is, its plots on the Security Market Line), what is the risk-free rate?

4) Plot the Security Market Line.

5) 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 r(x) = r(y) = 10.6%. Which stock should you choose?

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Finance Basics: Determine stock beta coefficient
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