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 -25% -5% 10% 15% Bond Fund Rate of Return -103 16% -68 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 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

Answer 1

a) Calculation of mean return and variance return of stock bond

Mean return calculation

Scenario	Probability (P)	Rate of return (R)	PxR
Severe Rec.	0.05	-0.25	-1.25%
Mild	0.25	-0.05	-1.25%
Normal growth	0.40	0.10	4%
Boom	0.30	0.15	4.5%
		Mean Return=	6%

Variance return calculation

Scenario	P	R	D	D2	PxD2
Severe	0.05	-25%	-31%(-0.31)	0.0961	0.004805
Mild	0.25	-5%	-11%	0.0121	0.003025
Normal	0.40	10%	4%	0.0016	0.00064
Boom	0.30	15%	9%	0.0081	0.00243
				Variance Return=	0.0109

b) Calculation of covariance between stock and bond fund

Covariance between stock and bond fund = Correlation between stock and bond x Standard deviation of Stock x Standard deviation of Bond

For this calculation, we need to calculate mean return and variance of bond also

Calculation of mean return of bond

Scenario	Probability (P)	Rate of return (R)	PxR
Severe Rec.	0.05	-0.10	-.5%
Mild	0.25	0.16	4%
Normal growth	0.40	0.09	3.6
Boom	0.30	-0.06	-1.8
		Mean Return=	5.3%

Calculation of variance of bond

Scenario	P	R	D	D2	PxD2
Severe	0.05	-10%	-15.3%	0.023409	0.00117045
Mild	0.25	16	10.7%	0.011449	0.00286225
Normal	0.40	9	3.7%	0.001369	0.0005476
Boom	0.30	-6%	-11.3%	0.012769	0.0038307
				Variance Return=	0.008411

Variance of stock = 0.0109
Therefore Standard deviation(SD) of Stock =  Square root of stock variance = 0.1044

Variance of bond = 0.008411
Standard deviation(SD) of Bond = square root of bond variance = 0.091711

Correlation = Covariance between stock and bond
SD of Stock x SD of Bond

Therefor Covariance = Correlation between Stock and bond x SD of stock x SD of bond
= 0.1044 x 0.091711
=0.009574