Question

Rose Berry is attempting to evaluate 2 possible portfolios, which consist of the same 5 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                               1.30                             10%                         30%

2                               .70                                30                           10

3                               1.25                              10                           20

4                               1.10                              10                           20

5                                .90                               40                           20

Totals                                                            100%                     100%

a. Calculate the betas for portfolio 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

Asset	Beta	Portfolio A	Portfolio B
1	1.3	10%	30%
2	0.7	30%	10%
3	1.25	10%	20%
4	1.1	10%	20%
5	0.9	40%	20%
a) Beta A	0.935
Beta B	1.11

Beta can be found out using the sumproduct function of excel:

Beta A = 1.3 * 10% + 0.7 * 30% + 1.25 * 10% + 1.1 * 10% + 0.9 * 40% = 0.935

Beta B = 1.3 * 30% + 0.7 * 10% + 1.25 * 20% + 1.1 * 20% + 0.9 * 20% = 1.11

b) Beta measures the systematic risk of the portfolio, that is, the senistivity of the portfolio to the market.

Since Beta of portfolio B is more than that of portfolio A, Portfolio B is more risky than Portfolio A.

Comparison with the market

Market Beta = 1

Beta A = 0.935

Beta B = 1.11

Since Beta of portfolio A is less than the market beta, portfolio A is less risky than the market portfolio.

Since Beta of portfolio B is more than the market beta, portfolio B is more risky than the market portfolio.

The order/ranking of portfolios in terms of riskiness measured using Beta is as follows:

1) Portfolio B

2) Market Portfolio

3) Portfolio A