Question

Please answer the questions in the space provided below each question. Show all of your work and circle your final answer.

1. You forecast there are three potential scenarios for the economy: a bull, flat, and bear market. You also estimate the returns for a stock and bond mutual fund as follows:

Economic Scenario	Stock Fund	Bond Fund	Probability of Scenario
Recession	-18%	6%	0.3
Flat	8%	4%	0.45
Boom	20%	-8%	0.25

Using this information, you find for the stock fund: E(r_S)=0.032 and σ_S=0.1469, and for the bond fund: E(r_B)=0.016 and σ_B=0.0561.

1. Compute the covariance between the stock and bond fund. (Record your answer to at least four decimal places) (10 points)

2. Compute the correlation coefficient between the stock and bond fund. (Record your answer to at least four decimal places) (10 points)

You put 70% of your portfolio in the stock fund and the remaining 30% in the bond fund.

3. Compute the standard deviation of your portfolio. (Record your answer to at least four decimal places) (10 points)

Answer 1

Stock
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
Recession	0.3	-18	-5.4	-21.2	0.0134832
Flat	0.45	8	3.6	4.8	0.0010368
Boom	0.25	20	5	16.8	0.007056
	Expected return %=	sum of weighted return =	3.2	Sum=Variance Stock=	0.02158
			Standard deviation of Stock%	=(Variance)^(1/2)	14.69
Bond
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
Recession	0.3	6	1.8	4.4	0.0005808
Flat	0.45	4	1.8	2.4	0.0002592
Boom	0.25	-8	-2	-9.6	0.002304
	Expected return %=	sum of weighted return =	1.6	Sum=Variance Bond=	0.00314
			Standard deviation of Bond%	=(Variance)^(1/2)	5.61
Covariance Stock Bond:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
Recession	0.3	-21.2	4.4	-0.0027984
Flat	0.45	4.8	2.4	0.0005184
Boom	0.25	16.8	-9.6	-0.004032
		A.	Covariance=sum=	-0.006312
		B. Correlation A&B=	Covariance/(std devA*std devB)=	-0.766373104
	C.
	Variance=	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
	Variance=	0.0082
	Standard deviation=	(variance)^0.5
	Standard deviation%=	9.06