The risk premium for exposure to aluminum commodity prices is 4% and the firm has a beta relative to aluminum commodity prices of 0.6.The risk premium for exposure to GDP changes is 6% and the firm has a beta relative to GDP of 1.2.If the risk free rate is 4.0%,what is the expected return on this stock?

Question

Quizplus · Accepted Answer

First, we need to calculate the required return for each source of risk exposure:
Required return for aluminum commodity exposure = risk-free rate + risk premium for aluminum * beta relative to aluminum
= 4% + 4% * 0.6
= 6.4%
Required return for GDP exposure = risk-free rate + risk premium for GDP * beta relative to GDP
= 4% + 6% * 1.2
= 11.2%
Next, we need to weight these required returns by the proportion of risk faced by the firm from each source:
Weighted required return = (% of risk from aluminum exposure) * (required return for aluminum exposure) + (% of risk from GDP exposure) * (required return for GDP exposure)
= (0.5) * (6.4%) + (0.5) * (11.2%)
= 8.8%
Finally, we add the weighted required return to the risk-free rate to get the expected return on the stock:
Expected return on stock = risk-free rate + weighted required return
= 4% + 8.8%
= 13.6%

The Risk Premium for Exposure to Aluminum Commodity Prices Is