Question

Suppose the risk-free rate is 4.10% and the market portfolio has an expected return of 11.25%. A portfolio is invested equally in three securities with betas of 0.38, 1.13, and 1.18 respectively. What is the expected return on this portfolio?

Question 16 options:

	10.48%
	10.74%
	11.00%
	11.26%
	11.52%

Answer 1

Option (a) is correct

Expected return of the portfolio is given by:

Expected return = Risk free rate + Beta * (Market return - Risk free rate)

The beta that will be used in the above equation will be the weighted average beta of the portfolio. So, first we will calculate the weighted average beta of the portfolio as below:

Since it is equally invested portfolio, so the weights of each stocks in the portfolio are 1/3 , 1/3 and 1/3.

In the next step we will multiply the weights as above with the betas of the stocks to find the weighted betas of the stocks:

Stock A: 0.38 * 1./3 = 0.126666

Stock B: 1.13 * 1/3 = 0.376666

Stock C: 1.18 * 1/3 = 0.393333

Now, we will calculate the weighted average beta by adding the weighted betas of the stocks calculated above:

Weighted average beta = 0.126666 + 0.3766666 + 0.3933333 = 0.896666

Now, we will calculate the expected return of the portfolio by the following formula:

Expected return = Risk free rate + Beta * (Market return - Risk free rate)

Putting the values in the above formula, we get,

Expected return = 4.1% + 0.89666 * (11.25% - 4.1%)

Expected return = 4.1% + (0.896666 * 7.15%)

Expected return = 4.1% + 6.4111%

Expected return = 10.51% approx