Assume the risk free rate equals Rf = 4%, and the return on the market portfolio has expectation E [RM] = 12% and standard deviation σM = 15%. (a) What is the equilibrium risk premium (that is, the excess return on the market portfolio)? (b) If a certain stock has a realized return of 14%, what can we say about the beta of this stock? (c) If a certain stock has an expected return of 14%, what can we say about the beta of this stock?

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22-10-2021
Business

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Assume the risk free rate equals Rf = 4%, and the return on the market portfolio has expectation E [RM] = 12% and standard deviation σM = 15%. (a) What is the equilibrium risk premium (that is, the excess return on the market portfolio)? (b) If a certain stock has a realized return of 14%, what can we say about the beta of this stock? (c) If a certain stock has an expected return of 14%, what can we say about the beta of this stock?

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ewomazinoade ewomazinoade · Answer 1 · 2021-11-05T11:31:08+01:00

The equilibrium risk premium is 8%.
The stock has a beta of 1.25.
If the stock has a certain return of 14%, it means that the beta of the stock is higher than that of the market. It means that the stock is more risky than the market portfolio.

The equilibrium risk premium is the excess of the return of the market portfolio less the risk free rate.

Risk premium = Return of the market portfolio - risk free rate

12% - 4% = 8%.

According to the capital asset pricing model, the return of an asset can be determined using this formula:

Expected return = risk free asset + (beta x risk premium)

If the realized return is 14%, the value of beta can be determined from the above formula.

14% = 4% + (beta x 8%)

Beta = (14% - 4%) / 8% = 1.25.

Beta is a measure of the risk of an asset. The beta of the market is 1. Ig the beta of a stock is greater than 1, it means that the stock has a greater measure of risk compared to the market. If the beta of a stock is less than 1, it means that the stock is less risky when compared with the market.

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