6. Use the following data: State of the Economy Probability Stock A Stock B Stoc
ID: 2665701 • Letter: 6
Question
6. Use the following data:
State of the Economy Probability Stock A Stock B Stock C
Boom 0.2 4% 20% 60%
Normal 0.6 8% 10% 20%
Poor 0.2 12% -13% -40%
(a) If a portfolio os formed by investing 30% of the funds each in B and C, and 40% in A; What would be the expected return on the portfolio?
(b) What would be the standard deviation of the above portfolio?
8. A firm's stock has a beta of 1.2; the expected return on the market is 14%; and the risk-free rate is 4%. What is the expected rate of return on this stock?
9. The expected return on the market is 14%; and the risk-free rate is 5%. What is the market risk premium?
10. A firm's stock has a beta of 1.4; the risk-free rate is 5%; and the market risk premium is 10%. What is the expected rate of return on this stock?
Explanation / Answer
a) Calculating the expected returns for the individual stocks: E(Ra) = 0.2 * 0.04 + 0.6 * 0.08 + 0.2 * 0.12 = 0.08 or 8% E(Rb) = 0.2 * 0.20 + 0.6 * 0.10 + 0.2 * (-0.13) = 0.074 or 7.4% E(Rc) = 0.2*0.6 + 0.6 * 0.2 + 0.2 * (-0.4) = 0.16 or 16% Calculating the expected return on portfolio: E(Rp) = Wa * E(Ra) + Wb * E(Rb) + Wc * E(Rc) = 0.4 * 0.08 + 0.3 * 0.074 + 0.3 * 0.16 = 0.1022 or 10.22% Calculating the expected return when the economy booms: E(Rp) = 0.4 * 0.04 + 0.3 * .2 + 0.3 * 0.6 = 0.256 or 25.6% Calculating the expected return when the economy normal: E(Rp) = 0.4 * 0.08 + 0.3 * 0.10 + 0.3 * 0.2 = 0.122 or 12.2% Calculating the expected return when the economy Poor: E(Rp) = 0.4 * 0.12 + 0.3 * (-0.13) + 0.3 * -(0.4) = 0-.111 or -11.1% Variance = 0.2 (0.256 - 0.1022)^2 + 0.6 * (0.122 - 0.1022)^2 + 0.2 (-0.111 - 0.1022)^2 = 0.00472 + 0.00024 + 0.009 = 0.01396 STandard deviation = Sqrt (0.1396) = 11.8% 8) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.04 + 1.2 [0.14 - 0.04] = 0.04 + 0.12 = 0.16 or 16% 9) Market risk premium is E(Rm) - Rf = 0.14 - 0.05 = 0.09 or 9% 10) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.05 + 1.4[0.10] = 0.05 + 0.14 = 0.19 or 19% Calculating the expected return when the economy normal: E(Rp) = 0.4 * 0.08 + 0.3 * 0.10 + 0.3 * 0.2 = 0.122 or 12.2% Calculating the expected return when the economy Poor: E(Rp) = 0.4 * 0.12 + 0.3 * (-0.13) + 0.3 * -(0.4) = 0-.111 or -11.1% Variance = 0.2 (0.256 - 0.1022)^2 + 0.6 * (0.122 - 0.1022)^2 + 0.2 (-0.111 - 0.1022)^2 = 0.00472 + 0.00024 + 0.009 = 0.01396 STandard deviation = Sqrt (0.1396) = 11.8% 8) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.04 + 1.2 [0.14 - 0.04] = 0.04 + 0.12 = 0.16 or 16% 9) Market risk premium is E(Rm) - Rf = 0.14 - 0.05 = 0.09 or 9% 10) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.05 + 1.4[0.10] = 0.05 + 0.14 = 0.19 or 19% Calculating the expected return when the economy Poor: E(Rp) = 0.4 * 0.12 + 0.3 * (-0.13) + 0.3 * -(0.4) = 0-.111 or -11.1% Variance = 0.2 (0.256 - 0.1022)^2 + 0.6 * (0.122 - 0.1022)^2 + 0.2 (-0.111 - 0.1022)^2 = 0.00472 + 0.00024 + 0.009 = 0.01396 STandard deviation = Sqrt (0.1396) = 11.8% 8) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.04 + 1.2 [0.14 - 0.04] = 0.04 + 0.12 = 0.16 or 16% 9) Market risk premium is E(Rm) - Rf = 0.14 - 0.05 = 0.09 or 9% 10) Calculating the expected return on stock: Re = Rf + Beta [E(Rm) - Rf] = 0.05 + 1.4[0.10] = 0.05 + 0.14 = 0.19 or 19% Re = Rf + Beta [E(Rm) - Rf] = 0.05 + 1.4[0.10] = 0.05 + 0.14 = 0.19 or 19%Related Questions
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