Suppose you own a two-security portfolio.You have 35.0% of your money invested in Security X and the remainder in Security Y.The standard deviations of Securities X and Y are 10.0% and 15.0%, respectively.What is the correlation between the two securities if the portfolio variance is 0.013225?
A)0.0055
B)0.0137
C)0.3654
D)0.9148

Question

Quizplus · Accepted Answer

We can use the formula for portfolio variance:
Portfolio Variance = w1^2 * σ1^2 + w2^2 * σ2^2 + 2w1w2σ1σ2ρ12
where w1 and w2 are the proportions invested in Securities X and Y, σ1 and σ2 are the standard deviations of Securities X and Y, and ρ12 is the correlation between Securities X and Y.

Substituting the given values, we have:
0.013225 = (0.35)^2 * (0.1)^2 + (0.65)^2 * (0.15)^2 + 2 * 0.35 * 0.65 * 0.1 * 0.15 * ρ12

Simplifying and solving for ρ12, we get:
ρ12 = 0.3654

Therefore, the answer is C (0.3654).

Suppose You Own a Two-Security Portfolio