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21 September, 15:49

Bruno's stock should return 14 percent in a boom, 11 percent in a normal economy, and 4 percent in a recession. The probabilities of a boom, normal economy, and recession are 8 percent, 90 percent, and 2 percent, respectively. What is the variance of the returns on this stock?

a. 0.011387

b. 0.000169

c. 0.001506

d. 0.001538

e. 0.011561

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Answers (1)
  1. 21 September, 16:02
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    option (b) variance of the returns is 0.000169

    Explanation:

    Given data

    boom return = 14% = 0.14

    normal economy = 11% = 0.11

    recession = 4% = 0.04

    boom probability = 8% = 0.08

    normal economy probability = 90 % = 0.90

    recession probability = 2 % = 0.02

    to find out

    the variance of the returns on this stock

    solution

    we know variance of the returns is sum of standard deviation

    expected return = boom return * boom probability

    expected return boom = 0.14 * 0.08 = 0.0112

    expected return = economy * economy probability

    expected return economy = 0.11 * 0.9 = 0.099

    expected return = recession * recession probability

    expected return recession = 0.04 * 0.02 = 0.0008

    total expected return = 0.0112 + 0.099 + 0.0008 = 0.111

    for boom

    standard deviation = probability * (return - 0.111) ²

    standard deviation = 0.08 * (0.14 - 0.111) ² = 0.00006728 ... 1

    for normal economy

    standard deviation = probability * (economy - 0.111) ²

    standard deviation = 0.90 * (0.11 - 0.111) ² = 0.00000090 ... 2

    for recession

    standard deviation = probability * (recession - 0.111) ²

    standard deviation = 0.02 * (0.04 - 0.111) ² = 0.00010082 ... 3

    variance of the returns is sum of standard deviation

    variance of the returns = 0.00006728 + 0.00000090 + 0.00010082

    variance of the returns is 0.000169
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