Question

A stock has had returns of −30 percent, 20 percent, 34 percent, −20 percent, 37 percent, and 23 percent over the last six years.

a.) What are the arithmetic average returns for the stock?

b.) What are the geometric average returns for the stock? (4 Points)

Answer 1

Solution:

a. Arithmetic Average Return for the stock:

The formula for calculation of arithmetic average return is

Arithmetic Average Return = Total of returns / No. of years

= [ ( - 30 % ) + 20 % + 34 % + ( - 20 % ) + 37 % + 23 % ] / 6

= 64 % / 6 = 10.6667 %

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

Thus the Arithmetic Average Return for the stock is 10.67 %

b. Geometric Average Return for the stock:

The formula for calculation of geometric average return is

Geometric Average Return = [ ( 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 = - 30 % = - 0.30

Return 2 % = Return in year 2 = 20 % = 0.20

Return 3 % = Return in year 3 = 34 % = 0.34

Return 4 % = Return in year 4 = - 20 % = 0.20

Return 5 % = Return in year 5 = 37 % = 0.37

Return 6 % = Return in Year 6 = 23 % = 0.23

n = 6

Applying the values in the formula we have

= [ ( 1 - 0.30 ) * ( 1 + 0.20 ) * ( 1 + 0.34 ) * ( 1 - 0.20 ) * ( 1 + 0.37 ) * ( 1 + 0.23 ) ] 1/6 - 1

= [ ( 0.70 ) * ( 1.20 ) * ( 1.34 ) * ( 0.80 ) * ( 1.37 ) * ( 1.23 ) ] 1/6 - 1

= [ 1.517399 ] 1/6 - 1

= 1.071972 - 1

= 0.071972

= 7.1972 %

= 7.20 % ( when rounded off to two decimal places )

Thus the geometric average return for the stock = 7.20 %

Note : The value of ( 1.517399 ) 0.166667   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.517399,0.166667) = 1.071972