You recently purchased a stock that is expected to earn 12.6 percent in a booming economy, 8.9 percent in a normal economy and lose 5.2 percent in a recessionary economy. Each economic state is equally likely to occur. What is your expected rate of return on this stock?

r(e) = 0.05433 or 5.433% rounded off to 5.43%

Explanation:

To calculate the expected rate of return of a stock, we take the rate of return under each scenario and multiply it with the probability of that scenario and sum up the answers for each scenario. The formula for expected rate of return can be written as follows,

r(e) = pA * rA  + pB * rB  +  ...  +  pN * rN

Where,

As we have 3 scenarios with equal probability for each scenario, we can say the probability of each scenario is 1/3.

r(e) =  1/3 * 0.126  +  1/3 * 0.089  +  1/3 * -0.052

r(e) = 0.05433 or 5.433% rounded off to 5.43%

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