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.

Security	Expected Return	Standard Deviation	Beta
A	12%	15%	0.8
B	16%	9%	1.4
Market Return	13%	10%
Risk-Free Rate	5%

1. 1. With regard to Securities A and B only, which security has the smaller total risk?  
2. 2. With regard to Securities A and B only, which security has the smaller systematic risk?  
   3. Compute the Jensen Alpha for Securities A and B.  
   4. Identify and justify which of the 2 stocks would be more appropriate for Karen who would like to make her very first investment in the financial market.
   5. Draw the Security Market Line (SML), labeling each axis, r_f, and the slope of the SML. Indicate where securities A and B are located on the graph.

Answer 1

Question A

Total risk for Security A = beta ^{2 *} standard deviation of market ² + Error term ²

= (0.8*0.8) * (0.1*0.1) = 0.0064

Total risk for Security A = beta ^{2 *} standard deviation of market ² + Error term ²

= (1.4*1.4) * (0.1*0.1) = 0.0196

Security A has lower risk compared security B

Error term is ignored since it is not given in the above information.

Question B

Since systematic risk is beta ² * Standard deviation of market ²

Security A will be of lower risk

Question C

Calculation of Jenson's alpha

For A :

Jenson's alpha = Return of the security - (Rf + beta * (Rm - Rf))

= 12 - (5 + 0.8(13-5)) = 0.6

For B :

Jensons alpha = 16 - (5+1.4(13-5)) = -0.2

Question D

Security A is of good option to invest on considering all the factors like risk and alpha.