Question

Chapter 6 Q2

Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Probability 0.10 0.20 0.30 0.40 Stock Fund Rate of Return -44% -16.0% 10% 30% Bond Fund Rate of Return -13% 11% 4% -3% 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 4 decimal places.) Mean return 7.4 % Variance %-Squared b. Calculate the value the 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 4 decimal places.) Covariance %-Squared

Answer 1

a. Mean return= 0.10*(-44%)+0.2*(-16%)+0.3*10%+0.4*30%=7.4%

Variance= 0.1*(-44%-7.4%)^2+0.2*(-16%-7.4%)^2+0.3^(10%-7.4%)^2+0.4*(30%-7.4%)^2=99.71%

b.

Probability Scenario Severe Recession Mild Recession Normal growth Boom 0.1 0.2 M. N. Stock Fund Return Bond Fund Return -44% -13% -16% 11% 10% 4% 30% -3% =COVARIANCE.S(L2:15,M2:M5) COVARIANCE.S(array1, array2) 0.3 0.4 Covariance

Probability Scenario Severe Recession Mild Recession Normal growth Boom 0.1 0.2 0.3 0.4 M N Stock Fund Return Bond Fund Return -44% -13% -16% 11% 10% 4% 30% -3% 1.14% Covariance

Hence, covariance is 1.14% between stock fund and Bond Fund.