Assume the risk free rate equals Rf = 4% and the return on the market portfolio

Question

Assume the risk free rate equals Rf = 4% and the return on the market portfolio has expectation E [ Rm ] = 12% and standard deviation sm = 15%

(The m after the R and the m after the s are subscripts, as if the f after the R in the risk free rate)

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?

Explanation / Answer

a) The equillibrium risk premium is calculated as:

Equillibrium risk premium = E(Rm) - Rf
= 0.12 - 0.04
= 0.08 or 8%

The excess return on the market portfolio is 8%

b) Realized return is the return that is actually earned over a given time period.it is important to understand that nothing can change the realized return.

According to Capital asset pricing model,

E(Ri) = Rf + [E(Rm) - Rf] * Beta

0.14 = 0.04 + 0.08 * Beta

0.1 = 0.08 * Beta
Beta = 1.25

Therefore, the beta of the stock is 1.25

c) Calculating the beta of the stock when the expected return is 14%

E(Ri) = Rf + [E(Rm) - Rf] * beta
0.14 = 0.04 + (0.08 * Beta)
0.1 = 0.08 * Beta
Beta = 1.25

Expected return equals some risk free rate plus a risk premium multilpled by the assets beta.

It is important to understand that the realized return is no way connected to the expected return.

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