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In: Finance

Given the returns and probabilities for the three possiblestates listed here, calculate the covariance between...

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

 

Solutions

Expert Solution

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

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