Question

Consider the following table: Scenario Severe recession Mild recession Normal growth Boom Probability 0.05 0.25 0.40 0.30 Stock Fund Rate of Return -40% -14% 17% 33% Bond Fund Rate of Return -9% 15% 8% -5% 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 %-Squared 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 %-Squared

Answer 1

a) Mean Return of the stock fund = 0.05 * -40% + 0.25* -14% + 0.40 *17% + 0.3*33% =11.2%

Variance = 0.05*(-40%-11.2%)^2+ 0.25*(-14%-11.2%)^2+ 0.40 *(17%-11.2%)^2+ 0.3 *(33%-11.2%)^2=4.46% or 445.86% Squared

b.Mean return of bond = 0.05*-9% + 0.25*15% + 0.40*8% + 0.30*-5% =  5%
Covariance =0.05*(-40%-11.2%)*(-9%-5%) + 0.25*(-14%-11.2%) *(15%-5%)+ 0.40 *(17%-11.2%)* (8%-5%)+ 0.3 *(33%-11.2%)*(-5%-5%) =-0.8560% or -85.60%