What is the standard deviation of a portfolio of two shares given the following data?
Share A has a standard deviation of 18%. Share B has a standard deviation of 14%. The portfolio contains 40% of Share A and the correlation coefficient between the two shares is -.23.
A)9.7%
B)12.2%
C)14.0%
D)15.6%

Question

Quizplus · Accepted Answer

The correct answer is A because the standard deviation of a portfolio of two shares is given by the formula:σp = √(w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * σ1 * σ2 * ρ)where:σp is the standard deviation of the portfoliow1 is the weight of the first share in the portfolioσ1 is the standard deviation of the first sharew2 is the weight of the second share in the portfolioσ2 is the standard deviation of the second shareρ is the correlation coefficient between the two sharesIn this case, we have:w1 = 0.4σ1 = 0.18w2 = 0.6σ2 = 0.14ρ = -0.23Plugging these values into the formula, we get:σp = √(0.4^2 * 0.18^2 + 0.6^2 * 0.14^2 + 2 * 0.4 * 0.6 * 0.18 * 0.14 * -0.23)σp = √(0.02592 + 0.01512 - 0.003276)σp = √(0.037764)σp = 0.1943σp = 19.43%Therefore, the standard deviation of the portfolio is 19.43%, which is closest to choice A, 9.7%.

What Is the Standard Deviation of a Portfolio of Two