Question

Consider the following table:

			Stock Fund			Bond Fund
Scenario	Probability		Rate of Return			Rate of Return
Severe recession	0.05		–26	%		–11	%
Mild recession	0.25		–6	%		17	%
Normal growth	0.40		11	%		10	%
Boom	0.30		16	%		–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.)

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.)

Answer 1

a)

Probability (P)	Stock return (S)	P * S	(S - Mean return)	(S - Mean return)^2	P * (S - Mean return)^2
0.05	-26	-1.3	-32.4	0.104976	0.0052488
0.25	-6	-1.5	-12.4	0.015376	0.003844
0.4	11	4.4	4.6	0.002116	0.0008464
0.3	16	4.8	9.6	0.009216	0.0027648
	Mean Return =	6.4	Variance=	0.012704

Mean return for stock fund = 6.4%

Variance for stock fund =0.0127 or 1.27%

b)

Probability (P)	Stock return (S)	P * S	X=(S - Mean stock return)	Bond return (B)	P*B	Y=(B - Mean bond return)	P *X *Y
0.05	-26	-1.3	-32.4	-11	-0.55	-16.6	0.002689
0.25	-6	-1.5	-12.4	17	4.25	11.4	-0.00353
0.4	11	4.4	4.6	10	4	4.4	0.00081
0.3	16	4.8	9.6	-7	-2.1	-12.6	-0.00363
	Mean stock return	6.4		Mean bond return	5.6		-0.003664

Covariance = -0.003664 or -0.3664 % or -0.37%