In: Finance
Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 0.12 and 0.15, respectively. (Round your answer to 4 decimal places. For example .1244) Probability Return(A) Return(B) Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30
Covariance :
Covariance is a statistical tool that is used to determine the relationship between the movement of two assets/ Stocks.
If Past data is given:
Assume stock A = X
stock B = Y
Covariance = Sum [ prob * (X-Avg X)(Y-Avg Y) ]
Expected Ret:
Scenario | Prob | Ret (X) | Prob* Ret(X) | Ret (Y) | Prob* Ret(Y) |
Good | 0.3500 | 30.00% | 10.50% | 50% | 17.50% |
OK | 0.5000 | 10.00% | 5.00% | 10% | 5.00% |
Poor | 0.1500 | -25.00% | -3.75% | -30% | -4.50% |
Expected Ret | 11.75% | 18.00% |
Covaraince:
Scenario | Prob | Ret (X) | (X-AvgX) | Ret (Y) | (Y-AvgY) | (X-AVgX)(Y-AvgY) | Prob* (X-AVgX)(Y-AvgY) |
Good | 0.3500 | 30.00% | 18.25% | 50.00% | 32.00% | 0.0584 | 0.02044 |
OK | 0.5000 | 10.00% | -1.75% | 10.00% | -8.00% | 0.0014 | 0.00070 |
Poor | 0.1500 | -25.00% | -36.75% | -30.00% | -48.00% | 0.1764 | 0.02646 |
Covariance = Sum [Prob * (X-AvgX)(Y-AvgY) ] | 0.04760 |