Question

Consider the following table:

		Stock Fund	Bond Fund
Scenario	Probability	Rate of Return	Rate of Return
Severe recession	0.20	−28%	−10%
Mild recession	0.25	−8.0%	12%
Normal growth	0.35	4%	2%
Boom	0.20	42%	−7%

a. Calculate the values of mean return (1 decimal) and variance for the stock fund (4 decimals).

b. Calculate the value of the covariance between the stock and bond funds (4 decimals).

Answer 1

a

Stock fund
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Severe recession	0.2	-28	-5.6	-30.2	0.0182408
Mild recession	0.25	-8	-2	-10.2	0.002601
Normal	0.35	4	1.4	1.8	0.0001134
Boom	0.2	42	8.4	39.8	0.0316808
	Expected return %=	sum of weighted return =	2.2	Sum=Variance Stock fund=	0.0526
			Standard deviation of Stock fund%	=(Variance)^(1/2)	22.94

b

Covariance Stock fund Bond fund:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Severe recession	0.2	-30.2	-10.3	0.0062212
Mild recession	0.25	-10.2	11.7	-0.0029835
Normal	0.35	1.8	1.7	0.0001071
Boom	0.2	39.8	-7.3	-0.0058108
			Covariance=sum=	-0.0025