Question

Create a portfolio using the four stocks and information below:

	Expected Return	Standard Deviation	Weight in Portfolio
Stock A	23.00%	16.00%	10.00%
Stock B	18.00%	10.00%	25.00%
Stock C	28.00%	24.00%	23.00%
Stock D	14.00%	26.00%	42.00%
----------------------	----------------------	----------------------	----------------------
Correlation (A,B)	0.5100	----------------------	----------------------
Correlation (A,C)	0.3700	----------------------	----------------------
Correlation (A,D)	0.0600	----------------------	----------------------
Correlation (B,C)	0.8800	----------------------	----------------------
Correlation (B,D)	0.3500	----------------------	----------------------
Correlation (C,D)	0.6100	----------------------	----------------------

(Do not round intermediate calculations. Record your answers in decimal form and round your answers to 4 decimal places. Ex. x.xxxx)

What is the variance of A?

What is the variance of B?

What is the variance of C?

What is the variance of D?

What is the Correlation (A,A)?

What is the Correlation (B,B)?

What is the Correlation (C,C)?

What is the Correlation (D,D)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (A,C)?

What is the Covariance (A,D)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the Covariance (B,C)?

What is the Covariance (B,D)?

What is the Covariance (C,A)?

What is the Covariance (C,B)?

What is the Covariance (C,C)?

What is the Covariance (C,D)?

What is the Covariance (D,A)?

What is the Covariance (D,B)?

What is the Covariance (D,C)?

What is the Covariance (D,D)?

What is the expected return on the portfolio above?

What is the variance on the portfolio above?

What is the standard deviation on the portfolio above?

Answer 1

#1 Calculation of Variance

Variance = Standard Deviation²

Variance of A = 16² = 256

Variance of B = 10² = 100

Variance of C = 24² = 576

Variance of D = 26² = 676

#2 Calculation of Correlation

Correlation measures the relationship between two variables. Its value ranges from -1 to +1. Correlation of -1 means the two variables are perfect negative correlated, for example when one variable increases the other decreases in the same extend. Correlatio of 0 means the variaables are uncorrelated. Correlation of +1 means the two variables are perfect positive correlated.

Correlation of a single stock with itself is +1, which can be proved as follows-

Correlation (A,A) = Covariance (A,A) / (SD of A * SD of A)

Covariance of a sinlge stock with itself is the variance of that stock alone. Also variance is Standard Deviation²

Correlation (A,A) = Variance A / Variance A

+1

Correlation (A,A)= Correlation (B,B) = Correlation (C,C) = Correlation (D,D) =+1

#3 Calculation of Covariance

Covariance of a sinlge stock with itself is the variance of that stock alone.

Covariance (A,A) =Variance of stock A =256

Covariance (A,A) =Variance of stock B = 100

Covariance (A,A) =Variance of stock C = 576

Covariance (A,A) =Variance of stock D = 676

Covariance (A,B) = Correlation (A,B) * SD of A * SD of B = .5100*.16*.10= 0.0082

Covariance (A,C) = Correlation (A,C) * SD of A * SD of C = .3700*.16*.24 = 0.0142

Covariance (A,D) = Correlation (A,D) * SD of A * SD of D = .0600*.16*.26 = 0.0025

Covariance (B,C) = Correlation (B,C) * SD of B * SD of C = .8800*.1*.24 = 0.0211

Covariance (B,D) = Correlation (B,D) * SD of B * SD of D = .3500*.1*.26 = 0.0091

Covariance (C,D) = Correlation (C,D) * SD of C * SD of D = .6100*.24*.26 = 0.0381

#4 Calculation of expected return on the portfolio

The return of a portfolio is the weighted average return of the securities which constitute the porfolio

Stock	Weight	Expected Return (%)	Weight*Expected Return
A	0.10	23	2.3000
B	0.25	18	4.5000
C	0.23	28	6.4400
D	0.42	14	5.8800

Portfolio Return = 19.1200% (2.3000+4.5000+6.4400+5.8800)

#5 Calculation of variance on the portfolio

(WA*SDA)^2+(WB*SDB)^2+(2*WA*WB*SDA*SDB*correlationAB) + (WA*SDA)^2+(WC*SDC)^2+(2*WA*WC*SDA*SDC*correlationAC) +(WA*SDA)^2+(WB*SDD)^2+(2*WA*WD*SDA*SDD*correlationAD) + (WB*SDB)^2+(WC*SDC)^2+(2*WB*WC*SDB*SDC*correlationBC) + (WB*SDD)^2+(WC*SDD)^2+(2*WB*WD*SDB*SDD*correlationBD) + (WC*SDC)^2+(WD*SDD)^2+(2*WC*WD*SDC*SDD*correlationCD)

= (.1*.16)^2+(.25*.1)^2+(2*.1*.25*.16*.1*.51) + (.1*.16)^2+(.23*.24)^2+(2*.1*.23*.16*.24*.37)+ (.1*.16)^2+(.25*.26)^2+(2*.1*.42*.16*.26*.06) + (.25*.1)^2+(.23*.24)^2+(2*.25*.23*.1*.24*.88) + (.25*.26)^2+(.23*.26)^2+(2*.25*.42*.1*.26*.35) + (.23*.24)^2+(.42*.26)^2+(2*.23*.42*.24*.26*.61)

= .0481

#6 Calculation of standard deviation on the portfolio

standard deviation = Variance

= .0481

= .2193

= 21.9260%