Question

Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Stock Fund Probability Rate of Return 0.10 -35% 0.20 -15% 0.40 20% 0.30 25% Bond Fund Rate of Return -14% 20% 13% -10% a.Calculate the values of mean return and variance for the stock fund. (Do not round intermediate calculations. Round "Mean return" value to 1 decimal place and "Variance" to 2 decimal places.) Mean return Variance 9.01% 434.00 b.Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) Covariance 16.56

Answer 1

a. Mean return = 9.0%
Variance = 0.04
b. Covariance = -0.00

Oxy = ŽIX, –E(X)][CY, –E(Y)] P(X,Y) where: X = discrete random variable X X = the it outcome of X Y = discrete random variable Y Y = the in outcome of Y P(XY) = probability of occurrence of the in outcome of X and the ith outcome of Y

3 A 1 Probability 0.1 0.2 0.4 0.3 6 Mean return = 7 Variance of Stock Fund = 8 Covarince = 9 BC Ε Stock fund R Bond fund R p*(R-MeanR)^2 for Stock fund p*(Xi-E(X))*(Yi-E(Y)) -35% -14% 0.01936 0.008272 -15% 20% 0.01152 -0.007296 20% 13% 0.00484 0.003608 25% -10% 0.00768 -0.007104 9.00% 4.80% 0.0434 -0.00252 -0.2520%


А 1 Probability 2 0.1 30.2 4 0.4 5 0.3 6 Mean return = 7 Variance of Stock Fund = 8 Covarince = 9 Stock fund R Bond fund R -0.35 -0.14 -0.15 0.2 0.2 0.13 0.25 -0.1 =SUMPRODUCT(A2:A5,B2:B5) =SUMPRODUCT(A2:A5,C2:C5) p*(R-MeanR)^2 for Stock fund p*(Xi-E(X))*(Yi-E(Y)) =A2*(B2-$B$6)^2 =A2*(B2-$B$6) *(C2-$C$6) =A3*(B3-$B$6)^2 =A3 *(B3-$B$6)*(C3-$C$6) =A4*(B4-$B$6)^2 =A4*(B4-$B$6)*(C4-$C$6) =A5*(B5-$B$6)^2 =A5*(B5-$B$6)*(C5-$C$6) =SUM(D2:05) =SUM(E2:E5) =E8

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