You are given the following two equations: E(Ri) = Rf + (E(Rm) - Rf)ßi E(Rp) = R

Question

You are given the following two equations:

E(Ri) = Rf + (E(Rm) - Rf)ßi
E(Rp) = Rf + ( (E(Rm) - Rf)/sm ) sp

(Please note that all the i's, f's, m's, and p's in this question are subscripts)

You also have the following information: E(Rm) = .15, Rf = .06, sm = .15 Answer the following questions, assuming that the capital asset pricing model is correct.

a)Which equation would you use to determine the expected return on an individual security with a standard deviation of returns = .5 and a ß = 2? Given the parameters above, what is the expected return for that security?

b) Which equation would you use to determine the expected return on a portfolio knowing that it is an efficient portfolio (consisting of the market portfolio M combined with the risk-free rate)? If you were told that the standard deviation of returns on that portfolio is equal to sm and you were given the above parameters, what is the expected return on that portfolio?

c) Can you determine the ß of the portfolio in (b)?

d) Given your answers above, expand on what type of risky assets equation (1) can be used for, and what type of risky assets equation (2) can be used for.

Explanation / Answer

a) The equation to determine the expected return is E(R) = Rf + [E(Rm) - Rf] * beta = 0.06 + [ 0.15 -0.06] * 2.0 = 0.06 + 0.18 = 0.24 or 24% b) The equation used to determine the expected return on a efficient portfolio is E(Rp) = Rf + (Sm /S) [E(Rm) - Rf] = 0.06 + (0.15 / 0.5) [ 0.15-0.06] = 0.06 + 0.3 (0.09) = 0.06 + 0.027 = 0.087 or 8.7% c) The beta in the part (b) is calculated as: We know that the expected return on the portfolio is E(Rp) = WA * 0.24 + (1-WA) * 0.06 0.087 = 0.06 + 0.18 WA 0.027 = 0.18 WA WA = 0.15 or 15% Therefore, weight of risk free asset is 85% Portfolio beta = WA * Beta(A) + (1- WA) * Beta (Rf) = 0.15 * 2 + 0.85 * 0 = 0.3 Therefore, the portfolio beta is 0.3 d) The CAPM model takes into account the asset's sensitivity to non-diversifiable risk also known as Systematic risk or market risk, often represented by the quantity beta as well as the expected return on the market and the expected return of the risk free asset.

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