Question

Assume that you set up a portfolio composed of Stock A and Stock B. You invested 40% of your capital on Stock A whereas 60% of your capital on Stock B. During the last 3 years, your portfolio showed the following performance.

	Stock A	Stock B
2016	0.1	-0.1
2017	0.2	0
2018	0.3	0.4

What are your average portfolio return and risk (standard deviation or variance) during last three years? (20 points)

Answer 1

Calculation of Expected return:

Stock A = 0.1+0.2+0.3/3=0.6/3=0.2

Stock B = -0.1+0+0.4/3 = 0.3/3 = 0.1

Calculation of Expected return of portfolio:

Particulars	Probability (1)	Return (2)	Expected return (3) (1*2)
Stock A	0.4	0.2	0.08
Stock B	0.6	0.1	0.06
		Expected return	0.14

Calculation of Standard deviation of Stock A:

Year	Return	Return-Expected return	Square of Return-Expected return/Variance
2016	0.1	0.1-0.2=-0.1	(-0.1)^2=0.01
2017	0.2	0.2-0.2=0	(0)^2=0
2018	0.3	0.3-0.2=0.1	(0.1)^2=0.01
		Variance	0.02

Standard deviation = Square root of Variance

= Square root of 0.02

= 0.14

Calculation of Standard deviation of Stock B:

Year	Return	Return-Expected return	Square of Return-Expected return/Variance
2016	-0.1	-0.1-0.1=-0.2	(-0.2)^2=0.04
2017	0	0-0.1=-0.1	(-0.1)^2=0.01
2018	0.4	0.4-0.1=0.3	(0.3)^2=0.09
		Variance	0.14

Standard deviation = Square root of Variance

= Square root of 0.14

= 0.37

Calculation of Covariance:

Return-Expected return of Stock A (1)	Return-Expected return of Stock B (2)	Covariance (3) (1*2)
-0.1	-0.2	0.02
0	-0.1	0
0.1	0.3	0.03
	Covariance	0.05

Correlation coefficient = Covariance/ Std deviaA*Std deviaB

= 0.05/0.14*0.37

= 0.05/0.0518

= 0.05/0.0518

= 0.96

Calculation of standard deviation of portfolio:

Variance = (wA)^2*(std deviaA)^2+(wB)^2*(std deviaB)^2+2*wA*wB*std deviaA*std deviaB*correlation coefficient

wA = 0.4

wB = 0.6

Std deviaA = 0.14

Std deviaB = 0.37

Correlation coefficient = 0.96

Variance = (0.4)^2*(0.14)^2+(0.6)^2*(0.37)^2+2*0.4*0.6*0.14*0.37*0.96

= 0.003136+0.049284+0.023870

= 0.07629

Standard deviation = Square root of Variance

= Square root of 0.07629

= 0.27

Summary:

Portfolio return. = 0.14

Portfolio Risk. = 0.27