Question

Karen Kay, a portfolio manager at Collins Asset Management, is using the capital asset pricing model for making recommendations to her clients. Her research department has developed the information shown in the following exhibit.

a. Calculate expected return and alpha for each stock.

b. Identify and justify which stock would be more appropriate for an investor who wants to:

i. Add this stock to a well-diversified equity portfolio.

ii. Hold this stock as a single-stock portfolio.

Short answer

The Correct answer is:

a. E(r_X) = 12.2%,σ_X = 1.8% and E(r_Y) = 18.5% andσ_Y= –1.5%

b. (i) Stock X is recommended

(ii) Stock Y is recommended

Step-by-step solution

Calculation of expected return and alpha

E(r_X) = ( r_F ) +β[E(r_M – r_F ) = 5% + 0.8(14% – 5%) = 12.2%

σ_X = 14% – 12.2% = 1.8%

E(r_Y) = ( r_F ) +β[E(r_M – r_F ) = 5% + 1.5(14% – 5%) = 18.5%

σ_Y = 17% – 18.5% = –1.5%

Identifying and justifying the appropriateness of a stock

(i) For adding to a well-diversified equity portfolio, Kay should recommend Stock X because:

(a) Stock X has positive alpha while Stock Y has negative alpha and

(b) Stock X has a lower beta that may have a beneficial impact on overall policies

(ii) For adding to a single stock portfolio, Key should recommend Stock Y because:

(a) Stock Y has a higher forecasted return and

(b) Lower standard deviation