Rose Berry is attempting to evaluate 2 possible portfolios, which consist of the
ID: 2712190 • Letter: R
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?
Explanation / Answer
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
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 1.11Related Questions
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