Question

Stock X has systematic risk of β = 1 and the analyst forecasts its return to be 12%. Stock Y has β = 1.5 and a forecast return of 13%. The market portfolio’s expected return is 11%, and rf = 5%. i. According to the CAPM, what are the required returns of the two stocks? ii. What is the alpha of each stock? Which stock is a better buy? iii. Draw the SML. Mark each stock’s CAPM required rate of return on the line and the forecast return. Mark their alphas on the graph.

Answer 1

The solution to part i)

Return of Stock X using CAPM will be:

= r_f + (r_m - r_f ) * Beta

= 5% + (11%-5%) * 1

= 11.00%

Return of Stock Y using CAPM will be:

= r_f + (r_m - r_f ) * Beta

= 5% + (11%-5%) * 1.5

= 14.00%

The solution to part ii)

The Alpha of Stock X will be:

= Forecasted Return of Stock X - SML Return of Stock X

= 12% - 11%

= 1%

The Alpha of Stock Y will be:

= Forecasted Return of Stock Y - SML Return of Stock Y

= 13% - 14%

= - 1%

The solution to part iii)

Stock X should be a better option to buy as its alpha is positive. Positive alpha signifies that the return of the stock has performed better than SML return and stock is underpriced whereas a negative alpha signifies that the stock is overpriced.

Hence, its better to buy Stock X