Question

Joe is attempting to evaluate two possible portfolios consisting of the same five assets but held in different proportions. She is particularly interested in using beta to compare the risk of the portfolios and, in this regard, has gathered the following data

       Portfolio Weights  
Asset   Asset Beta   Portfolio A   Portfolio B
1 1.25   12% 29%
2 0.67   30%   10%
3 1.29   6%   19%
4 1.13   11%   22%
5 0.87   41%   20%
   Total   100%   100%

.a. Calculate the betas for portfolios A and B.

b. Compare the risk of each portfolio to the market as well as to each other. Which portfolio is more risky?

Answer 1

Solution:

(A).Portfolio beta = weighted sum of individual asset betas.

Asset	Asset Beta	Portfolio A	Portfolio B
1	1.25	12%	29%
2	0.67	30%	10%
3	1.29	6%	19%
4	1.13	11%	22%
5	0.87	41%	20%
Total		100%	100%

Portfolio A Beta = 12% * 1.25 + 30% * 0.67 + 6%*1.29 + 11%*1.13 + 41%*0.87

                          = 0.15 + 0.201 + 0.0774 + 0.1243 + 0.3567

                          = 0.9094

Portfolio B Beta = 29% * 1.25 + 10% * 0.67 + 19%*1.29 + 22%*1.13 + 20%*0.87

                          = 0.3625 + 0.067+ 0.2451 + 0.2486 + 0.174

                          = 1.0972

(B) Compare the risks of portfolios to Market and each other

Portfolio A is less risky when it is compared to market

Portfolio B is more risky when it is compared to market.

Portfolio B is more risky when it is compared to Portfolio A.