Question

Consider the following table:

		Stock Fund	Bond Fund
Scenario	Probability	Rate of Return	Rate of Return
Severe recession	0.10	−32%	−10%
Mild recession	0.15	−10%	6%
Normal growth	0.35	22%	10%
Boom	0.40	37%	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

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

Answer a.

Computation of mean return of Stock fund

Calculation of mean return of Stock
Possible returns	Probability	Product
Xᵢ	p(Xᵢ)	Xᵢ p(Xᵢ)
-0.32	0.1	-0.032
-0.1	0.15	-0.015
0.22	0.35	0.077
0.37	0.4	0.148
	X̅	0.178

Mean return of stock fund(X̅)= 17.8%

Calculation of variance of
Possible returns	Probability	Deviation	(Deviation)^2	Product
Xᵢ	p(Xᵢ)	X̅	(Xᵢ-X̅)^2	(Xᵢ-X̅)^2 ˣ p(Xᵢ)
-0.32	0.1	-0.498	0.248004	0.0248004
-0.1	0.15	-0.278	0.077284	0.0115926
0.22	0.35	0.042	0.001764	0.0006174
0.37	0.4	0.192	0.036864	0.0147456
			Variance	0.051756

Variance = .05 ( Round to two decimal places)

Standard deviation = variance

                               =.05

                               =.2236

                               = 22.36%

Answer b.

Calculation of mean return of Bond
Possible returns	Probability	Product
Xᵢ	p(Xᵢ)	Xᵢ p(Xᵢ)
-0.1	0.1	-0.01
0.06	0.15	0.009
0.1	0.35	0.035
0.07	0.4	0.028
	Mean (X̅)	0.062

Calculation of Deviation of Bond
Possible returns	Probability	Deviation
Xᵢ	p(Xᵢ)	(Xᵢ-X̅)
-0.1	0.1	-0.162
0.06	0.15	-0.002
0.1	0.35	0.038
0.07	0.4	0.008

Calculation of Covariance of stock and bond

Stock fund			Bond fund			Stcok ˣ Bond
Probability	Deviation	Product	Probability	Deviation	Product
0.1	-0.498	-0.0498	0.1	-0.162	-0.0162	0.00080676
0.15	-0.278	-0.0417	0.15	-0.002	-0.0003	0.00001251
0.35	0.042	0.0147	0.35	0.038	0.0133	0.00019551
0.4	0.192	0.0768	0.4	0.008	0.0032	0.00024576
					Cov	0.00126054

Covariance = .001