Question

A stock is expected to earn 21 percent in a boom economy, 12.50 percent in a normal economy, and lose 25 percent in a recessionary economy. There is a 16 percent chance the economy will boom and a 62 percent chance the economy will be normal. What is the expected risk premium for this stock if the risk-free rate is expected to be 3.90 percent?

a. 1.71 percent
b. 75 percent
c. .31 percent
d. 1.42 percent

Answer 1

The expected risk premium for the stock is calculated using the probabilities of different economic conditions and the stock’s return in each condition. Subtracting the risk-free rate from the expected rate of return gives a risk premium of 1.71%, which corresponds to option (a).

Step-by-step explanation:

To calculate the expected risk premium for the stock, we use the probabilities of the various economic conditions and the returns associated with those conditions. The risk premium is the difference between the expected rate of return of the stock and the risk-free rate. The expected rate of return is computed as follows:

• Boom economy (21% return) × 16% probability = 3.36%
• Normal economy (12.50% return) × 62% probability = 7.75%
• Recessionary economy (-25% return) × (100% - 16% - 62%) probability = -5.50%

The sum of these products gives the expected rate of return: 3.36% + 7.75% - 5.50% = 5.61%

The risk premium is the expected rate of return minus the risk-free rate: 5.61% - 3.90% = 1.71%

Therefore, the expected risk premium for this stock is 1.71%, which corresponds to option (a).