You are given the following return probability distribution for Stock X and Y:  Bear market Normal market Bull marketProbability 0.2 0.5 0.3Stock X -10% 10% 20%Stock Y -5% 20% 10%What is the return correlation between Stock X and Y?Group of answer choices0.41930.62250.54470.2071

To calculate the correlation between the returns of Stock X and Y, we first need to calculate the expected returns, variances, and covariance.

Step 1: Calculate the expected returns for each stock.

The expected return is calculated by multiplying each possible return by its probability and then summing these values.

For Stock X: Expected Return (X) = (0.2*-10%) + (0.510%) + (0.320%) = -2% + 5% + 6% = 9%

For Stock Y: Expected Return (Y) = (0.2*-5%) + (0.520%) + (0.310%) = -1% + 10% + 3% = 12%

Step 2: Calculate the variances for each stock.

The variance is calculated by multiplying the squared difference between each possible return and the expected return by its probability, and then summing these values.

For Stock X: Variance (X) = 0.2*(-10%-9%)^2 + 0.5*(10%-9%)^2 + 0.3*(20%-9%)^2 = 0.2361 + 0.51 + 0.3*121 = 72.2 + 0.5 + 36.3 = 109

For Stock Y: Variance (Y) = 0.2*(-5%-12%)^2 + 0.5*(20%-12%)^2 + 0.3*(10%-12%)^2 = 0.2289 + 0.564 + 0.3*4 = 57.8 + 32 + 1.2 = 91

Step 3: Calculate the covariance between the returns of Stock X and Y.

The covariance is calculated by multiplying the difference between each possible return and the expected return for Stock X by the difference between each possible return and the expected return for Stock Y, and then summing these values.

Covariance (X,Y) = 0.2*(-10%-9%)(-5%-12%) + 0.5(10%-9%)(20%-12%) + 0.3(20%-9%)(10%-12%) = 0.217 + 0.58 + 0.38 = 3.4 + 4 + 2.4 = 9.8

Step 4: Calculate the correlation between the returns of Stock X and Y.

The correlation is calculated by dividing the covariance by the square root of the product of the variances.

Correlation (X,Y) = Covariance (X,Y) / sqrt(Variance (X) * Variance (Y)) = 9.8 / sqrt(109 * 91) = 9.8 / 104.4 = 0.0938

So, the correlation between the returns of Stock X and Y is approximately 0.0938, which is not among the provided answer choices. Please check the calculations and the provided data.