Question

The rates of return on Cherry Jalopies, Inc., stock over the last five years were 16 percent, 11 percent, −1 percent, 6 percent, and 11 percent. What is the geometric return for Cherry Jalopies, Inc.? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Solution:

The formula for calculation of geometric return is

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

Where

Return 1 % = Return in year 1 = 16 % = 0.16

Return 2 % = Return in year 2 = 11 % = 0.11

Return 3 % = Return in year 3 = - 1 % = - 0.01

Return 4 % = Return in year 4 = 6 % = 0.06

Return 5 % = Return in year 5 = 11 % = 0.11

n = No. of years = 5

Applying the values in the formula we have

= [ ( 1 + 0.16 ) * ( 1 + 0.11 ) * ( 1 - 0.01 ) * ( 1 + 0.06 ) * ( 1 + 0.11 ) ] ^1/5 - 1

= [ ( 1.16 ) * ( 1.11 ) * ( 0.99 ) * ( 1.06 ) * ( 1.11 ) ] ^1/5 - 1

= [ 1.499840 ] ^1/5 - 1            

= [ 1.499840 ] ^0.20 - 1          

= 1.084449 - 1

= 0.084449

= 8.4449 %

= 8.44 % ( when rounded off to two decimal places )

Thus the geometric return for the stock of Cherry Jalopies, Inc.= 8.44 %

Note: The value of ( 1.499840 ) ^0.20   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.499840,0.20) = 1.084449