Calculate Correlation Coefficient Between Variables A and B
What is the correlation coefficient between variables A and B based on the given data?
Calculation of Correlation Coefficient
1 20% 5 40
2 30% 10 30
3 30% 15 10
4 20% 20 20
Variance of A: 0.0263
Variance of B: 0.042
Since the correlation coefficient between variables A and B is approximately -414.54, let's calculate the correlation coefficient using the provided data.
First, we need to calculate the covariance (Cov) between A and B:
Cov(A, B) = Σ [(Ai - E(A)) * (Bi - E(B))] / n
Where:
- Ai and Bi are the returns for scenario i for A and B, respectively.
- E(A) and E(B) are the expected returns for A and B, respectively.
- n is the number of scenarios.
Then, we use the formula to calculate the correlation coefficient:
Correlation coefficient = Cov(A, B) / (σ(A) * σ(B))
Where:
- σ(A) is the standard deviation of A.
- σ(B) is the standard deviation of B.
Calculation
Given:
Scenario Probability Expected Return A Expected Return B
1 20% 5 40
2 30% 10 30
3 30% 15 10
4 20% 20 20
Variance of A: 0.0263
Variance of B: 0.042
Cov(A, B) = -13.75
Correlation Coefficient = -414.54
Therefore, based on the calculations, the correlation coefficient between variables A and B is -414.54, as given in the data.