Calculate covariance between stock A, B. Expected returns are Stock A .10 and B

Question

Calculate covariance between stock A, B. Expected returns are Stock A .10 and B .19

                          PROBABILITY.                    RETURN (A)                        RETURN (B)

GOOD                 .35                                            .30                                            .50

OK                        .50                                             .10                                           .10

POOR                  .15                                             -.25                                          -.30

Explanation / Answer

Ra and Rb denote returns on stock A and B respectively.

E(Ra) = 0.10, E(Rb) = 0.19

Covariance(Ra,Rb) = E[ Ra - E( Ra) * ( Rb-E(Rb) ]

= 0.35*(0.3-0.1)*(0.50-0.19) + 0.50*(0.1-0.1)*(0.10-0.19) + 0.15*(-0.25-0.1)*(-0.30-0.19)

Covariance(Ra,Rb) = 0.047425

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