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8 September, 10:21

The rate of return on the common stock of Flowers by Flo is expected to be 14% in a boom economy, 8% in a normal economy, and only 2% in a recessionary economy. The probabilities of these economic states are 20% for a boom, 60% for a normal economy, and 20% for a recession. What is the variance of the returns on the common stock of Flowers by Flo?

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  1. 8 September, 10:34
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    variance of the returns is 0.00144

    Explanation:

    Given data

    boom economy = 14% = 0.14

    normal economy = 8% = 0.08

    recessionary economy = 2% = 0.02

    boom probabilities = 20% = 0.20

    normal probabilities = 60% = 0.60

    recessionary probabilities = 20% = 0.20

    to find out

    the variance of the returns

    solution

    we know variance of the returns is sum of standard deviation

    expected return = boom return * boom probability

    expected return boom = 0.14 * 0.20 = 0.028

    expected return = economy * economy probability

    expected return economy = 0.08 * 0.60 = 0.048

    expected return = recession * recession probability

    expected return recession = 0.02 * 0.20 = 0.004

    total expected return = 0.028 + 0.048 + 0.004 = 0.08

    for boom economy

    standard deviation = probability * (return - 0.08) ²

    standard deviation = 0.20 * (0.14 - 0.08) ² = 0.00072 ... 1

    for normal economy

    standard deviation = probability * (economy - 0.08) ²

    standard deviation = 0.60 * (0.08 - 0.08) ² = 0 ... 2

    for recession economy

    standard deviation = probability * (recession - 0.08) ²

    standard deviation = 0.20 * (0.02 - 0.08) ² = 0.00072 ... 3

    variance of the returns is sum of standard deviation

    variance of the returns = 0.00072 + 0 + 0.00072

    variance of the returns is 0.00144
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