Question

A stock had returns of 13 percent, 17 percent, 17 percent, -4 percent, 13 percent, and 8 percent over the last six years.

  

Required:
(a)	What is the arithmetic return for the stock?
	(Click to select)  10.87%  10.77%  10.67%  12.80%  11.20%

  

(b)	What is the geometric return for the stock?
	(Click to select)  10.52%  10.22%  10.42%  12.63%  10.91%

rev: 09_20_2012

Answer 1

Solution :

a. Arithmetic Return for the stock:

The formula for calculation of arithmetic return is

Arithmetic Return = Total of returns / No. of years

= [13 % + 17 % + 17 % + ( - 4 % ) + 13 % + 8 % ) ] / 6

= 64 % / 6 = 10.6667 %

= 10.67 % ( when rounded off to two decimal places )

Thus the arithmetic return for the stock = 10.67%

Thus the solution is option 3 = 10.67 %          

b. Geometric Return for the stock:

The formula for calculation of geometric return is

Geometric mean = [ ( 1 + Return 1 % ) * ( 1 + Return 2 % ) * .( 1 + Return 3 % ) * ( 1 + Return 4 % ) * ( 1 + Return 5 % ).. ( 1 + Return n % ) ] ^1/n - 1

Where Return 1 % = Return in year 1 = 13 % = 0.13

Return 2 % = Return in year 2 = 17 % = 0.17

Return 3 % = Return in year 3 = 17 % = 0.17

Return 4 % = Return in year 4 = ( - 4 % ) = - 0.04

Return 5 % = Return in year 5 = 13 % = 0.13

Return 6 % = Return in Year 6 = 8 % = 0.08

n = 6

Applying the values in the formula we have

= [ ( 1 + 0.13 ) * ( 1 + 0.17 ) * ( 1 + 0.17 ) * ( 1 - 0.04 ) * ( 1 + 0.13 ) * ( 1 + 0.08 ) ] ^1/6 - 1

= [ ( 1.13 ) * ( 1.17 ) * ( 1.17 ) * ( 0.96 ) * ( 1.13 ) * ( 1.08 ) ] ^1/6 - 1

= [ 1.812273 ] ^1/6 - 1

= [ 1.812273 ] ^0.1667 - 1

= 1.104195 - 1 = 0.104195

= 10.4195 %

= 10.42 % ( when rounded off to two decimal places )

Thus the geometric return for the stock = 10.42 %

Thus the solution is option 3 = 10.42 %         

Note : ( 1.812273 ) ^0.1667 is calculated using the excel formula

=POWER(Number,Power) = POWER(1.812273,0.1667) = 1.104195