Explanation

To calculate the covariance between Stock A and Stock B, we need the probability matrix and the expected returns for both stocks. Since the probability matrix is referenced but not provided, I'll explain the general approach:

Covariance Formula: $\text{Cov}(A,B) = E[(R_A - E[R_A])(R_B - E[R_B])]$

Where:

• $R_A$ and $R_B$ are the returns of stocks A and B
• $E[R_A]$ and $E[R_B]$ are their expected returns

Calculation Steps:

1. Calculate expected returns for both stocks
2. For each scenario, compute: (Return_A - E[Return_A]) × (Return_B - E[Return_B]) × Probability
3. Sum these products across all scenarios

Given the options and typical covariance ranges for stocks:

• -0.160: Too negative for most stock pairs
• -0.055: Moderately negative
• 0.004: Very low positive covariance (almost uncorrelated)
• 0.020: Low positive covariance

Based on the context and typical stock relationships, 0.004 represents stocks that are nearly uncorrelated, which is a reasonable outcome for many stock pairs. This suggests the stocks move almost independently of each other.