Question

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:

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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?

ASSET ASSET BETA PORTFOLIO 1 PORTFOLIO 2

1 1.43 15% 25%

2 0.52 30% 10%

3 1.52 15% 35%

4 1.78 5% 15%

5 0.31 35% 15%

Answer 1

a) Portfolio Beta = Sum [ portfolio weight * asset beta ]

Asset	Asset Beta	Portfolio 1	Portfolio 2	Asset Beta * Portfolio 1	Asset Beta * Portfolio 2
1	1.43	15%	25%	0.2145	0.3575
2	0.52	30%	10%	0.156	0.052
3	1.52	15%	35%	0.228	0.532
4	1.78	5%	15%	0.089	0.267
5	0.31	35%	15%	0.1085	0.0465
Portfolio Beta				0.796	1.255

Beta for Portfolio A is 0.796 and Portfolio B is 1.255

b) By definition, beta is volatility if portfolio with change in market, i.e. a beta of 1 means that a portfolio's volatility matches up exactly with the markets. A higher beta indicates great volatility, and a lower beta indicates less volatility.

Given this, Portfolio A has lesser volatility than market (beta = 1), and hence, lower risk. Further, Portfolio B has higher volatility than market (beta = 1), and hence, higher risk.

On comparing Portfolio A and B, clearly, portfolio B is riskier than portfolio A.