Problem 6-5 The standard deviation of the market-index portfolio is 20%. Stock A
ID: 2651449 • Letter: P
Question
Problem 6-5
The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.75 and a residual standard deviation of 30%.
Calculate the total variance for an increase of 0.25 in its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Calculate the total variance for an increase of 5.71% in its residual standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. Which of the following changes will have a greater impact on the portfolio's standard deviation?
The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.75 and a residual standard deviation of 30%.
Explanation / Answer
a-1.Calculate the total variance for an increase of 0.25 in its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Total variance = Systematic Variance + Residual Variance
Total variance = Beta^2* SD of Market^2 + Sd of Residual^2
Total variance = (1.75+0.25)^2*20%^2 + 30%^2
Total variance = 0.2500
a-2.
Calculate the total variance for an increase of 5.71% in its residual standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Total variance = Systematic Variance + Residual Variance
Total variance = Beta^2* SD of Market^2 + Sd of Residual^2
Total variance = (1.75)^2*20%^2 + (30%+5.71%)^2
Total variance = 0.2500
b.An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. Which of the following changes will have a greater impact on the portfolio's standard deviation?
Increase of .25 in beta.
Note : Even though the increase in total variability of the stock is same in either situation , the increase in residual risk will have less impact on portfolio volatality due to residual risk is diversifiable. Increase in beta would increase systematic risk which is perfectly correlated with the market index portfolio and therefore it has greater impact on portfolio
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