A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35%, while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is 0.75. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is _________. Group of answer choices17.74%21.59%20.39%19.11%
Question
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35%, while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is 0.75. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is _________. Group of answer choices17.74%21.59%20.39%19.11%
Solution
The standard deviation of a two-asset portfolio is calculated using the following formula:
σp = sqrt[(wA^2 * σA^2) + (wB^2 * σB^2) + 2wAwBσAσB*ρAB]
where: σp is the standard deviation of the portfolio, wA and wB are the weights of the assets in the portfolio, σA and σB are the standard deviations of the assets, and ρAB is the correlation coefficient between the returns of the two assets.
Given that wA=0.4, σA=0.35, wB=0.6, σB=0.15, and ρAB=0.75, we can substitute these values into the formula:
σp = sqrt[(0.4^2 * 0.35^2) + (0.6^2 * 0.15^2) + 20.40.60.350.15*0.75] σp = sqrt[(0.16 * 0.1225) + (0.36 * 0.0225) + 0.063] σp = sqrt[0.0196 + 0.0081 + 0.063] σp = sqrt[0.0907]
Therefore, the standard deviation of the return on the portfolio is sqrt[0.0907] = 0.3012 or 30.12% when expressed as a percentage.
So, the correct answer is not among the provided answer choices. Please check the calculations and the provided data.
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