Assume that the financial markets are in equilibrium.Information on three particular stocks is provided in the table below.Find the risk free rate and the expected return on the market portfolio.

A) 5%, 14%
B) 5%, 18%
C) 6%, 14%
D) 6%, 18%
E) 7%, 16%

Question

Assume that the financial markets are in equilibrium.Information on three particular stocks is provided in the table below.Find the risk free rate and the expected return on the market portfolio.

A) 5%, 14% 
B) 5%, 18% 
C) 6%, 14% 
D) 6%, 18% 
E) 7%, 16%

Quizplus · Accepted Answer

Use the Treynor Index. Recall that capital market equilibrium occurs when all securities lie on the SML - when the Treynor Indexes of all assets are equal. This means that all three assets will have the same Treynor Index, which is the slope of the SML. First use the Treynor Index to find the risk-free rate: Treynor Index = 11ea7fdb_fc0d_a756_a768_1f117f5b73cb_TB2902_11 Treynor Index for A = 11ea7fdb_fc0d_a757_a768_5911c235e3c4_TB2902_11 Treynor Index for B = 11ea7fdb_fc0d_a758_a768_9d513540b6f0_TB2902_11 We know that these two Treynor Indexes are equal, so we can set them equal to each other and solve for k_F: (0.076 - k_F) / 0.2 = (0.124 - k_F) / 0.8 0.8 (0.076 - k_F) = 0.2 (0.124 - k_F) 0.0608 - 0.8k_F = 0.0248 - 0.2k_F 0.0608 = 0.0248 + 0.6k_F 0.036 = 0.6k_F k_F = 0.6 or 6% Now solve for the market return using the CAPM Equation and stock A: E(k_i) = k_F + β_i[E(k_M) - k_F] 0.076 = 0.06 + 0.2[E(k_M) - 0.06] 0.016 = 0.2[E(k_M) - 0.06] 0.08 = E(k_M) - 0.06 E(k_M) = 0.14 or 14%

Assume That the Financial Markets Are in Equilibrium