Suppose stock returns can be explained by the following three-factor model: R i

Question

Suppose stock returns can be explained by the following three-factor model:

Ri = RF + 1F1 + 2F2 3F3

Assume there is no firm-specific risk. The information for each stock is presented here:

The risk premiums for the factors are 7 percent, 6.2 percent, and 6.6 percent, respectively. You create a portfolio with 20 percent invested in Stock A, 20 percent invested in Stock B, and the remainder in Stock C.

What is the expression for the return on your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

If the risk-free rate is 4.1 percent, what is the expected return on your portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected Return:     %

Explanation / Answer

Factor betas of the portfolio will be the weighted average of the individual stocks.

Thus,
Factor 1 = 0.20 * 1.70 + 0.20 * .84 + 0.6 * 0.82 = 1
Factor 2 = 0.20 * 0.70 + 0.20 * 1.30 + 0.6 * -0.31 = 0.214
Factor 3 = 0.20 * 0.45 + 0.20 * -.65 + 0.6 * 1.42 = 0.09 - 0.13 + 0.852 = 0.812

Portfolio return = Rf + 1*F1 + 0.214*F2 + 0.812*F3

if Rf = 4.1%, F1 = 7%, F2 = 6.2% and F3 = 6.6%

Portfolio return = 4.1% + 7% + 0.214*6.2% + 0.812*6.6% =17.786%

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