Question

You are trying to form portfolios based on the following information:

State	Probability	Return A	Return B
Poor	20.0%	-4.0%	-4.0%
Normal	40.0%	3.0%	8.0%
Good	30.0%	10.0%	8.0%
Very Good	10.0%	30.0%	10.0%

You also know the risk-free rate is 5%.

Question 4: Calculate the Covariance between Stock A and B

Question 5: Calculate the Correlation Coefficient between Stock A and B

Answer 1

Expected return of Stock A = Probability * Return A

Expected return of Stock A = (20% * (-4%)) + (40% * 3%) + (30% * 10%) + (10% * 30%)

Expected return of Stock A = 6.4%

Expected return of Stock B = Probability * Return B

Expected return of Stock B = (20% * (-4%)) + (40% * 8%) + (30% * 8%) + (10% * 10%)

Expected return of Stock B = 5.8%

Variance of Stock A =  Probability * (Return A - Expected return of Stock A)²

Variance of Stock A = 20% * (-4% - 6.4%)² + 40% * (3% - 6.4%)² + 30% * (10% - 6.4%)² + 10% * (30% - 6.4%)²

Variance of Stock A = 0.8584%

Standard Deviation of Stock A = Variance of Stock A

Standard Deviation of Stock A = 0.8584%

Standard Deviation of Stock A = 9.2650%

Variance of Stock B =  Probability * (Return A - Expected return of Stock A)²

Variance of Stock B = 20% * (-4% - 5.8%)² + 40% * (8% - 5.8%)² + 30% * (8% - 5.8%)² + 10% * (10% - 5.8%)²

Variance of Stock B = 0.2436%

Standard Deviation of Stock B = Variance of Stock A

Standard Deviation of Stock B = 0.2436%

Standard Deviation of Stock B = 4.9356%

Covariance between Stock A & B = Probability * (Return A - Expected return of Stock A) * (Return A - Expected return of Stock A)

Covariance between Stock A & B = 20% * (-4% - 6.4%) * (-4% - 5,8%) + 40% * (3% - 6.4%) * (8% - 5,8%) + 30% * (10% - 6.4%) * (8% - 5,8%) + 10% * (30% - 6.4%) * (10% - 5,8%)

Covariance between Stock A & B = 0.2968%

Correlation between Stock A & B = Covariance between Stock A & B / (Standard Deviation of Stock A * Standard Deviation of Stock B)

Correlation between Stock A & B = 0.2968% / (9.2650% * 4.9356%)

Correlation between Stock A & B = 0.6491