Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.61. If you invest 60% of your funds in Stock X and 40% in Stock Y.The standard deviation of your portfolio is, therefore ______%.
Question
Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.61. If you invest 60% of your funds in Stock X and 40% in Stock Y.The standard deviation of your portfolio is, therefore ______%.
Solution
To calculate the standard deviation of a two-stock portfolio, we use the formula:
σp = √[w1².σ1² + w2².σ2² + 2.w1.w2.σ1.σ2.ρ1,2]
where:
- σp is the standard deviation of the portfolio
- w1 and w2 are the weights of the two stocks in the portfolio
- σ1 and σ2 are the standard deviations of the two stocks
- ρ1,2 is the correlation coefficient between the two stocks
Substituting the given values into the formula:
σp = √[(0.6)².(0.3)² + (0.4)².(0.2)² + 2.(0.6).(0.4).(0.3).(0.2).(0.61)]
σp = √[(0.36)(0.09) + (0.16)(0.04) + 2*(0.6)(0.4)(0.3)(0.2)(0.61)]
σp = √[0.0324 + 0.0064 + 0.08832]
σp = √[0.12712]
σp = 0.3565
Therefore, the standard deviation of the portfolio is 35.65%.
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