Both assets A and B plot on the SML.Asset A has an expected return of 15% and a beta of 1.7.Asset B has an expected return of 12% and a beta of 1.1.What is the expected return on the market portfolio?
A)5.0%
B)6.5%
C)11.5%
D)It cannot be determined from this information.

Question

Quizplus · Accepted Answer

We can use the SML equation to solve for the expected return on the market portfolio:
Rm = Rf + (Rm-Rf)βm
We know that both assets A and B plot on the SML, so they must have expected returns that are equal to what we solve for using the SML equation. Let's use the information we have for asset A to solve for the expected return on the market portfolio:
15% = Rf + (Rm-Rf)(1.7)
Simplifying, we get:
15% - Rf = 1.7(Rm - Rf)
8.82% = Rm - Rf
Now, we can use the information we have for asset B to solve for the risk-free rate:
12% = Rf + (Rm-Rf)(1.1)
Simplifying, we get:
12% - Rf = 1.1(Rm - Rf)
10.91% = Rm - Rf
Substituting this into the equation we found for Rm - Rf, we get:
10.91% = 8.82% + Rf
Solving for Rf, we get:
Rf = 2.09%
Now, we can use this to solve for the expected return on the market portfolio:
Rm = Rf + (Rm-Rf)βm
Rm = 2.09% + (Rm-2.09%)βm
Substituting in the values we have for asset A and B:
15% = 2.09% + (Rm-2.09%)(1.7)
12% = 2.09% + (Rm-2.09%)(1.1)
By solving these two equations simultaneously, we get:
Rm = 11.5%
So the correct answer is C, 11.5%.

Both Assets a and B Plot on the SML