Question

Portfolio betas  Personal Finance Problem   Rose Berry is attempting to evaluate two possible​ portfolios, which consist of the same five assets held in different proportions. She is particularly interested in using beta to compare the risks of the​ portfolios, so she has gathered the data shown in the following​ table:

Portfolio weights
Asset	Asset beta	Portfolio A			Portfolio B
1	1.75	15​%			20​%
2	0.72	30​%			15​%
3	1.73	15​%			25​%
4	1.54	15​%			20​%
5	0.46	25%			20%
Totals		100%			100%

a. Calculate the betas for portfolios A and B.

b.Compare the risks of these portfolios to the market as well as to each other. Which portfolio is more​ risky?

Answer 1

(a)-Beta for the Portfolio A & B

Beta for the Portfolio A

Beta for the Portfolio A = Sum(Asset Beta x Portfolio weights)

= (1.75 x 0.15) + (0.72 x 0.30) + (1.73 x 0.15) + (1.54 x 0.15) + (0.46 x .25)

= 0.26 + 0.22 + 0.26 + 0.23 + 0.12

= 1.08

Beta for the Portfolio B

Beta for the Portfolio B = Sum(Asset Beta x Portfolio weights)

= (1.75 x 0.20) + (0.72 x 0.15) + (1.73 x 0.25) + (1.54 x 0.20) + (0.46 x 0.20)

= 0.35 + 0.11 + 0.43 + 0.31 + 0.09

= 1.29

(b)-Comparison

Beta of the both Portfolio A (1.08) and the Portfolio B (1.29) is higher than the Market Beta of 1.0. Therefore, the Both Portfolio A & B is considered to the more risky than the overall Market.