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9 August, 08:19

Crabby Shores stock is expected to return 15.7 percent in a booming economy, 9.8 percent in a normal economy, and 2.3 percent in a recession. The probabilities of an economic boom, normal state, or recession are 15 percent, 73 percent, and 12 percent, respectively. What is the expected rate of return on this stock?

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  1. 9 August, 11:25
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    The expected return on the stock is 9.785%

    Explanation:

    The expected rate of return on a stock is the return of the stock expected in different scenarios multiplied by the probability that those scenarios will occur. The expected return can be calculated as follows,

    r = rA * pA + rB * pB + ... + rN * pN

    Where, rA, rB to rN expects return under different scenarios pA, pB to pN represents the probabilities of each scenario

    Thus,

    r = 0.157 * 0.15 + 0.098 * 0.73 + 0.023 * 0.12

    r = 0.09785 or 9.785
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