Question

You are given the returns for the following three stocks:

Year	Stock A	Stock B	Stock C
1	14%	15%	-20%
2	14%	20%	35%
3	14%	13%	35%
4	14%	8%	15%
5	14%	14%	5%

Calculate the arithmetic return, geometric return, and standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Answer 1

Calculation of arithmetic return of Stocks:

Arithmetic return = sum of returns of all years/No.of years

No.of years = 5

Arithmetic return of Stock A= 14%+14%+14%+14%+14%/5

= 70%/5

= 14

Arithmetic return of Stock B= 15%+20%+13%+8%+14%/5

= 70%/5

= 14

Arithmetic return of Stock C = -20%+35%+35%+15%+5%/5

= 70%/5

= 14

Calculation of geometric returns of stocks:

Geometric return= (1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)^1/n-1

r1 = return of 1st year

r2 = return of 2nd year

r3 = return of 3rd year

r4= return of 4th year

r5 = return of 5th year

Geometric return of Stock A = (1.14)*(1.14)*(1.14)*(1.14)*(1.14)^1/5-1

= (1.14)^5*1/5-1

= 1.14-1

= 0.14

Geometric return of Stock B = (1.15)*(1.2)*(1.13)*(1.08)*(1.14)^1/5-1

= 1.1393-1

= 0.1393 or

= 0.14 (rounded to 2 decimals)

Geometric return of Stock C = (-1.2)*(1.35)*(1.35)*(1.15)*(1.05)^1/5-1

= -1.214-1

= -2.214 or

= -2.21 (rounded to two decimals)

Calculation of Standard deviation of stocks:

Standard deviation of Stock A:

Year	Return- Expected return (1)	Square of Return-Expected return /Variance(2)
1	14%-14%=0	(0)^2 =0
2	14%-14%=0	(0)^2=0
3	14%-14%=0	(0)^2=0
4	14%-14%=0	(0)^2=0
5	14%-14%=0	(0)^2=0
	Variance	0

Standard deviation = Square root of Variance

= Square root of 0

= 0

Standard deviation of Stock B:

Arithmetic return/Expected return = 14% or 0.14

Year	Return-Expected return (1)	Square of Return-Expected return/Variance (2)
1	0.15-0.14=0.01	(0.01)^2 =0.0001
2	0.20-0.14=0.06	(0.06)^2=0.0036
3	0.13-0.14=-0.01	(-0.01)^2 =0.0001
4	0.08-0.14=-0.06	(-0.06)^= 0.0036
5	0.14-0.14= 0	(0)^2 =0
	Variance	0.0074

Standard deviation = Square root of Variance

= Square root of 0.0074

= 0.086

Standard deviation of Stock C:

Arithmetic mean/Expected return = 14% or 0.14

Year	Return-Expected return (1)	Square of Return-Expected return/Variance (2)
1	-0.2-0.14=-0.34	(-0.34)^2 =0.1156
2	0.35-0.14=0.21	(0.21)^2 =0.0441
3	0.35-0.14=0.21	(0.21)^2 = 0.0441
4	0.15-0.14=0.01	(0.01)^2 = 0.0001
5	0.05-0.14=-0.09	(-0.09)^2 = 0.0081
	Variance	0.212

Standard deviation = Square root of Variance

= Square root of 0.212

= 0.4604