Question

Consider the following table: Bond Fund Rate of Return -138 Scenario Severe recession Mild recession Normal growth Boom Probability 0.10 0.20 0.40 0.30 Stock Fund Rate of Return -40% -20% 25% 30% 19% 12% -9% 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.) 11.01% 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

Using excel formula

		A	B	C	D	E	F
		Probability	Stock Fund Rate of Return		Excel Formula	Varinaces	Excel Formula
1	Severe Recession	0.1	-40%	-0.04	A1*B1	0.02601	A1*(C1-11%)^2
2	Mild Recession	0.2	-20%	-0.04	A2*B2	0.01922	A2*(C2-11%)^2
3	Normal Growth	0.4	25%	0.1	A3*B3	0.00784	A3*(C3-11%)^2
4	Boom	0.3	30%	0.09	A4*B4	0.01083	A4*(C4-11%)^2
			Mean Return	11.00%	SUM(D1:D4)	0.0639	SUM(F1:F4)
			Variance	0.0639

Expected return of Bond = 0.1*-13%+0.2*19%+0.4*12%+0.3*-9% =4.60%

Covariance =0.1*(-40%-11%)*(-13%-4.60%)+0.2*(-20%-11%)*(19%-4.6%)+0.4*(25%-11%)*(12%-4.60%)+0.3*(30%-11%)*(-9%-4.60%) =-0.00356 or -3.56%