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?

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

Thus,

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

r = 0.09785 or 9.785

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