What is the standard deviation of a portfolio of two stocks given the following data? Stock A has a standard deviation of 30%.Stock B has a standard deviation of 18%.The portfolio contains 60% of stock A and the correlation coefficient between the two stocks is -1.0.
A) 0.0%
B) 10.8%
C) 18.0%
D) 24.0%

Question

Quizplus · Accepted Answer

The standard deviation of a portfolio of two stocks 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 stock A in the portfolioσ1 is the standard deviation of stock Aw2 is the weight of stock B in the portfolioσ2 is the standard deviation of stock Bρ is the correlation coefficient between the two stocksIn this case, we have:w1 = 0.6σ1 = 0.3w2 = 0.4σ2 = 0.18ρ = -1.0Plugging these values into the formula, we get:σp = √(0.6^2 * 0.3^2 + 0.4^2 * 0.18^2 + 2 * 0.6 * 0.4 * 0.3 * 0.18 * -1.0) = 0.108Therefore, the standard deviation of the portfolio is 10.8%.

What Is the Standard Deviation of a Portfolio of Two