Final answer:
The question cannot be answered precisely without additional information about the returns of A and B in each state or their probabilities. Covariance is calculated by the formula Cov(A, B) = E[(A - E[A])(B - E[B])], but specific return values or probabilities for A and B are required to perform the calculation.
Step-by-step explanation:
The student's question is regarding the calculation of covariance between the returns of two financial assets, A and B. However, to determine the covariance, we need more specific information about the returns of A and B in each state (good, bad, ugly) or the returns' respective probabilities. Without this information, it is not possible to calculate the exact value of covariance between A and B.
For illustrative purposes, if the returns of A and B in each state were known, you could use the formula:
Cov(A, B) = E[(A - E[A])(B - E[B])]
Where E[A] is the expected return of A, E[B] is the expected return of B, and E[(A - E[A])(B - E[B])] is the expected value of the product of the deviations of A and B from their respective means.
To calculate this, you would multiply the deviation of each asset's return from its mean by the deviation of the other asset's return from its mean for each state of the world. Each product is then weighted by the probability of that state occurring and all these weighted products are summed to get the covariance.