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

Question

Quizplus · Accepted Answer

The standard deviation of a portfolio of two stocks is given by the formula:σp = √(wA^2 * σA^2 + wB^2 * σB^2 + 2 * wA * wB * σA * σB * ρ)where:σp is the standard deviation of the portfoliowA is the weight of stock A in the portfolioσA is the standard deviation of stock AwB is the weight of stock B in the portfolioσB is the standard deviation of stock Bρ is the correlation coefficient between the two stocksIn this case, we have:wA = 40% = 0.4σA = 18% = 0.18wB = 60% = 0.6σB = 14% = 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)= √(0.02592 + 0.01512 - 0.02016)= √0.02088= 0.1445= 14.45%Therefore, the standard deviation of the portfolio is 14.45%, which is closest to choice A, 9.7%.

What Is the Standard Deviation of a Portfolio of Two