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12 January, 02:25

A stock is expected to earn 15 percent in a boom economy and 7 percent in a normal economy. There is a 35 percent chance the economy will boom and a 65.0 percent chance the economy will be normal. What is the standard deviation of these returns?

A. 3.82 PercentB. 4.85 PercentC. 4.97 PercentD. 5.63 Percent.

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  1. 12 January, 02:40
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    A. 3.82

    Explanation:

    First, find the expected return of the stock;

    E (r) = SUM (prob * return)

    E (r) = (0.35 * 0.15) + (0.65 * 0.07)

    = 0.0525 + 0.0455

    =0.098 or 9.8%

    Next, use the variance formula to find the stock's standard deviation;

    σ² = 0.35 (0.15 - 0.098) ² + 0.65 (0.07 - 0.098) ²

    σ² = 0.0009464 + 0.0005096

    σ² = 0.001456

    As a percentage, it becomes; 0.001456 * 100 = 0.1456%

    The variance is therefore 0.1456%

    Find standard deviation;

    Standard deviation = SQRT (0.001456)

    STDEV = 0.03816 or 3.82%
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