Expected Market Risk Premium Calculation
What is the expected market risk premium?
If the capital asset pricing model holds and stock A's beta is greater than stock B's beta by 0.84, what is the expected market risk premium?
Expected Market Risk Premium Calculation
The expected market risk premium can be calculated using the Capital Asset Pricing Model (CAPM). According to CAPM, the expected return on the market (E(Rm)) is given by the formula: E(Rm) = Rf + beta x (E(Rm) - Rf), where Rf is the risk-free rate of return, beta is the systematic risk or market risk of the security, and E(Rm) - Rf is the market risk premium.
To find the expected market risk premium, we first need to calculate the expected return on the market using the CAPM formula:
E(Rm) = Rf + beta x (E(Rm) - Rf)
We are given the probability, rate of return, and beta for stock A and stock B in different states of the economy. By using these values, we can calculate the expected return for each stock:
E(Ra) = 0.21 x 0.189 + 0.74 x 0.158 + 0.05 x (-0.246) = 0.131
E(Rb) = 0.21 x 0.097 + 0.74 x 0.076 + 0.05 x 0.042 = 0.078
Next, we can use the difference in betas between stock A and stock B to find the expected market risk premium:
0.131 - Rf = 0.84 x (0.078 - Rf)
Solving for Rf, we get: Rf = 0.6244
Therefore, the expected market risk premium is calculated as:
E(Rm) - Rf = 0.131 - 0.6244 = -0.4934 or -49.34%
The negative value for the market risk premium indicates that the market is expected to underperform the risk-free rate.