Question

Consider the following table:

   

		Stock Fund	Bond Fund
Scenario	Probability	Rate of Return	Rate of Return
Severe recession	0.05	−32%	−11%
Mild recession	0.25	−12%	17%
Normal growth	0.40	17%	10%
Boom	0.30	22%	−7%

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.

Answer 1

a

Stock
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Severe	0.05	-32	-1.6	-40.8	0.0083232
Recession	0.25	-12	-3	-20.8	0.010816
Normal	0.4	17	6.8	8.2	0.0026896
Boom	0.3	22	6.6	13.2	0.0052272
	Expected return %=	sum of weighted return =	8.8	Sum=Variance Stock=	0.02706=27.1% squared

b

Bond
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Severe	0.05	-11	-0.55	-16.6	0.0013778
Recession	0.25	17	4.25	11.4	0.003249
Normal	0.4	10	4	4.4	0.0007744
Boom	0.3	-7	-2.1	-12.6	0.0047628
	Expected return %=	sum of weighted return =	5.6	Sum=Variance Bond=	0.01016
			Standard deviation of Bond%	=(Variance)^(1/2)	10.08
Covariance Stock Bond:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Severe	0.05	-40.8	-16.6	0.0033864
Recession	0.25	-20.8	11.4	-0.005928
Normal	0.4	8.2	4.4	0.0014432
Boom	0.3	13.2	-12.6	-0.0049896
			Covariance=sum=	-0.006088
		Correlation A&B=	Covariance/(std devA*std devB)=	-0.36712