Asset W has an expected return of 13.85 percent and a beta of 1.42. If the risk-
ID: 2646344 • Letter: A
Question
Asset W has an expected return of 13.85 percent and a beta of 1.42. If the risk-free rate is 4.67 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not include the percent signs (%). Leave no cells blank - be certain to enter "0" wherever required. Round your portfolio expected return answers to 2 decimal places (e.g., 32.16). Round your portfolio beta answers to 3 decimal places (e.g., 32.161).)
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Asset W has an expected return of 13.85 percent and a beta of 1.42. If the risk-free rate is 4.67 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not include the percent signs (%). Leave no cells blank - be certain to enter "0" wherever required. Round your portfolio expected return answers to 2 decimal places (e.g., 32.16). Round your portfolio beta answers to 3 decimal places (e.g., 32.161).)
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Explanation / Answer
The portfolio return can be calculated with the use of following formula:
Portfolio Return = Percentage of Portfolio in Asset W*Expected Return on Asset W + Percentage of Portfolio in Risk Free Asset*Expected Risk Free Rate where Percentage of Portfolio in Risk Free Asset = (100%- Percentage of Portfolio in Asset W)
Portfolio Beta = Percentage of Portfolio in Asset W*Expected Beta on Asset W + Percentage of Portfolio in Risk Free Asset*Beta on Risk Free Asset where Percentage of Portfolio in Risk Free Asset = (100%- Percentage of Portfolio in Asset W)
Beta on Risk Free Asset is 0.
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Solution:
Portfolio Return:
0% = 0%*13.85% + (100%-0%)*4.67% = 4.67%
25% = 25%*13.85% + (100%-25%)*4.67% = 6.97%
50% = 50%*13.85% + (100%-50%)*4.67% = 9.26%
75% = 75%*13.85% + (100%-75%)*4.67% = 11.56%
100% = 100%*13.85% + (100%-100%)*4.67% = 13.85%
125% = 125%*13.85% + (100%-125%)*4.67% = 16.15%
150% = 150%*13.85% + (100%-150%)*4.67% = 18.44%
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Portfolio Beta:
0% = 0%*1.42 + (100% - 0%)*0 = 0
25% = 25%*1.42 + (100% - 25%)*0 = .355
50% = 50%*1.42 + (100% - 50%)*0 = .71
75% = 75%*1.42 + (100% - 75%)*0 = 1.065
100% = 100%*1.42 + (100%-100%)*0 = 1.42
125% = 125%*1.42 + (100%-125%)*0 = 1.775
150% = 150%*1.42 + (100%-150%)*0 = 2.13
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Tabular Representation:
Percentage of Portfolio in Asset W Portfolio Expected Return Portfolio Beta 0.00% 4.67% 0 25.00% 6.97% 0.355 50.00% 9.26% 0.71 75.00% 11.56% 1.065 100.00% 13.85% 1.42 125.00% 16.15% 1.775 150.00% 18.44% 2.13