# Stock X's 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

a. Use a spreadsheet (or 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 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?

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

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#### Solution Summary

Spreadsheet (Microsoft Excel) is used to determine stock X's beta coefficient - by using slope of the linear regression function. The arithmetic average rates of return for Stock X and the NYSE over the period given are calculated. Also, the standard deviations of returns for both Stock X and the NYSE are calculated. Risk free rate is calculated assuming that the stock returns are in equilibrium- than plot on Security Market Line. The Security Market Line is also plotted.

Stock portfolio: Compute beta coefficient, arithmetic average returns, deviation

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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