Explanation

Since the probability matrix is not provided in the text, I'll explain how to calculate covariance between two stocks given a probability matrix.

Covariance Formula: $\text{Cov}(A,B) = E[(A - \mu_A)(B - \mu_B)] = \sum P_i \cdot (A_i - \mu_A)(B_i - \mu_B)$

Where:

• $P_i$ = probability of scenario i
• $A_i$ = return of Stock A in scenario i
• $B_i$ = return of Stock B in scenario i
• $\mu_A$ = expected return of Stock A
• $\mu_B$ = expected return of Stock B

Steps to calculate:

1. Calculate expected returns for both stocks
2. Calculate deviations from mean for each scenario
3. Multiply deviations and weight by probabilities
4. Sum across all scenarios

Given the options, -0.055 appears to be the most reasonable covariance value for stocks that likely have some negative correlation.