Question

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 26%, while stock B has a standard deviation of return of 20%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is 0.046, the correlation coefficient between the returns on A and B is __________.?

Answer 1

To find the correlation coefficient between two stocks, one must use the variance formula of a two-asset portfolio which incorporates the weights, variances, and the correlation coefficient. Substituting the given values and solving for the correlation coefficient, we find it to be approximately 0.49.

Step-by-step explanation:

To find the correlation coefficient between stocks A and B, we use the formula for the variance of a two-asset portfolio:

Variance portfolio = (WeightA² * Variance A) + (Weight B² * Variance B) + (2 * Weight A * Weight B * Standard Deviation A * Standard Deviation B * Correlation Coefficient AB)

Substituting the given values:

0.046 = (0.60² * 0.26² ) + (0.40² * 0.20² ) + (2 * 0.60 * 0.40 * 0.26 * 0.20 * Correlation Coefficient AB)

Solve for the correlation coefficient:

Correlation Coefficient AB = (0.046 - (0.60² * 0.26² ) - (0.40² * 0.20² )) / (2 * 0.60 * 0.40 * 0.26 * 0.20)

After calculating the values, we find that the correlation coefficient is approximately 0.49.

Answer 2

The correlation coefficient between the returns on stock A and stock B is approximately -0.0163.

Step-by-step explanation:

To find the correlation coefficient between the returns on stock A and stock B, we need to use the formula:

r = (σAB)/(σAσB)

Since the variance of return on the portfolio is given as 0.046, we can use the following formula to find the covariance:

Var(Portfolio) = wA2Var(A) + wB2Var(B) + 2wAwBCov(A,B)

Where:

wA is the weight of stock A in the portfolio (60%)

wB is the weight of stock B in the portfolio (40%)

Cov(A,B) is the covariance between the returns on stock A and stock B

Substituting the given values, we get:

0.046 = (0.6)2(0.26)2 + (0.4)2(0.20)2 + 2(0.6)(0.4)Cov(A,B)

Simplifying the equation and solving for Cov(A,B), we find:

Cov(A,B) = -0.000852

Now, we can substitute the values of σA = 0.26, σB = 0.20, and Cov(A,B) = -0.000852 into the correlation coefficient formula:

r = (-0.000852)/(0.26)(0.20)

r ≈ -0.0163

Therefore, the correlation coefficient between the returns on stock A and stock B is approximately -0.0163.