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    Stock X's beta coefficient

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    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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    https://brainmass.com/business/capital-asset-pricing-model/28350

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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.

    $2.19

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