A company's common stock shares are expected to bring a 13 % return to their investors in case of "recession" state of the economy, 6 % return in case of "normal" state of the economy, and result in a 4 % loss in case of "boom" state of the economy. The probability of "boom" is 5 % and the probability of "recession" is 45 %. Calculate the expected rate of return on this company's common stock.

The expected rate of return is 8.65%

Explanation:

The expected return on a stock can be calculated by multiplying the return in each scenario by the probability of that scenario. This will provide the expected value of the return based on all these scenarios. Thus, the rate of return is,

Rate of return = rA * pA + rB * pB + rC * pC

Where,

r represents the return in each scenario p represents the probability of each scenario

The probability of normal state is = 1 - 0.45 - 0.05 = 0.5

Rate of return = 0.13 * 0.45 + 0.06 * 0.5 + (-0.04) * 0.05

Rate of return = 0.0865 or 8.65%