Question

conomic State	Probability	B	C	D
Very poor	0.1	30%	-25%	15%
Poor	0.2	20%	-5%	10%
Average	0.4	10%	15%	0%
Good	0.2	0%	35%	25%
Very good	0.1	-10%	55%	35%

a. Based on the table above, construct an equal-weighted (50/50) portfolio of Investments B and C. What is the expected rate of return and standard deviation of the portfolio?

b. Now construct an equal-weighted (50/50) portfolio of Investments B and D. What is the expected rate of return and standard deviation of the portfolio?

Part A:

   E(R) for BC portfolio: Note: format answer is 12.3%

   SD for BC portfolio: Note: format answer is 1.2%

Part B:

   E(R) for BD portfolio: Note: format answer is 12.3%

   SD for BD portfolio: Note: format answer is 1.2%

Answer 1

A	B	C=A*B	DEV=(B-10)	X=DEV^2	Y=X*A
Probability	Return of B in percentage	Probabity*Return	Deviation from expected	Deviation Squared	Deviation squared*Probability
0.1	30.00	3.00	20.00	400	40
0.2	20.00	4.00	10.00	100	20
0.4	10.00	4.00	-	-	-
0.2	-	-	(10.00)	100	20
0.1	(10.00)	(1.00)	(20.00)	400	40
	SUM	10		SUM	120
			VARIANCE	120
			STANDARD DEVIATION	10.95445	(Square Root (Variance)

Expected Return of B=10%

Standard Deviation of return of B=10.95%

D	E	F=D*E	DEV=(E-15)	X=DEV^2	Y=X*A
Probability	Return of C in percentage	Probabity*Return	Deviation from expected	Deviation Squared	Deviation squared*Probability
0.1	(25.00)	(2.50)	(40.00)	1,600	160
0.2	(5.00)	(1.00)	(20.00)	400	80
0.4	15.00	6.00	-	-	-
0.2	35.00	7.00	20.00	400	80
0.1	55.00	5.50	40.00	1,600	160
	SUM	15.00		SUM	480
			VARIANCE	480
			STANDARD DEVIATION	21.9089	(Square Root (Variance)

Expected Return of C=15%

Standard Deviation of return of C=21.91%

G	H	I=G*H	DEV=(H-12)	X=DEV^2	Y=X*A
Probability	Return of D	Probabity*Return	Deviation from expected	Deviation Squared	Deviation squared*Probability
0.1	15.00	1.50	3.00	9.00	0.90
0.2	10.00	2.00	(2.00)	4.00	0.80
0.4	-	-	(12.00)	144.00	57.60
0.2	25.00	5.00	13.00	169.00	33.80
0.1	35.00	3.50	23.00	529.00	52.90
	SUM	12.00		SUM	146.00
			VARIANCE	146
			STANDARD DEVIATION	12.08305	(Square Root (Variance)

Expected Return of D=12%

Standard Deviation of return of D=12.08%

If w1, w2 , are weight in the portfolio for assets 1 and 2

Then,w1+w2=1

R1, R2 are the return of the assets 1and2

S1, S2 are the standard deviation of the assets 1, 2

Portfolio Return=w1R1+w2R2

PortfolioVariance=(w1^2)*(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)

Cov(1,2)=Covariance of returns of asset1 and asset2

Portfolio Standard Deviation =Square root of Portfolio variance

a.PORTFOLIO OF B AND C

Return of assetB=Rb=10%%

Return of assetC=Rc=15%

Standard deviation of asset B=Sb=10.95%%

Standard deviation of asset C=Sc=21.91%

Correlation of asset Band C=0

Covariance(1,2)=0

wb=wc=0.5

Portfolio Return;

0.5*10+0.5*15=12.5%

Portfolio Variance=(0.5^2)*(10.95^2)+(0.5^2)*(21.91^2)=149.9877

Portfolio Standard Deviation=Square root of Variance=(149.9877^0.5)= 12.25%

b..PORTFOLIO OF B AND D

Return of assetB=Rb=10%

Return of assetD=Rd=12%

Standard deviation of asset B=Sb=10.95%

Standard deviation of asset D=Sd=12.08%

Correlation of asset Band C=0

Covariance(1,2)=0

wb=wd=0.5

Portfolio Return;

0.5*10+0.5*12=11%

Portfolio Variance=(0.5^2)*(10.95^2)+(0.5^2)*(12.08^2)=66.45723

Portfolio Standard Deviation=Square root of Variance=(66.45723^0.5)= 8.15%

	ExpectedReturn(E(R)	Std Deviation
a) Portfolio of B and C	12.50%	12.25%
b) Portfolio of B and D	11%	8.15%