Question

A stock has had returns of -26 percent, 12 percent, 34 percent, -8 percent, 27 percent, and 23 percent over the last six years. What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Arithmetic average return Geometric average return

Answer 1

Solution:
	Arithmetic Average return	10.33	%
	Geometric average return	8.10	%
Working Notes:
	Stock returns for the last six years
Year 1	-26%   or -0.26          r1
Year 2	12% or 0.12                 r2
Year 3	34% or 0.34                 r3
Year 4	-8% or - 0.08             r4
Year 5	27% or 0.27                   r5
Year 6	23% or 0.23                  r6
	Arithmetic Average return
	=(sum of all returns/ No period taken)
	= (r1 + r2 + r3 + r4 + r5 + r6)/6
	= (-26% + 12% + 34% + (-8%)+ 27% + 23%)/6
	= 62%/6
	=10.3333333%
	=10.33%
	Geometric average return
	=((1+r1) x ( 1+ r2) x ( 1 +r3) x (1+ r4) x (1+r5) x (1 + r6))^(1/6) - 1
	=(( 1- 0.26) x ( 1 + 0.12) x (1+ 0.34) x (1- 0.08) x (1 + 0.27) x ( 1 + 0.23) )^(1/6) - 1
	=1.081040256 - 1
	=0.081040256
	=8.10%
Notes:	Both the average returns are relevant in different cases like arithmetic method is used expected return of next period while Geometric is better measure of the change in wealth over the period.
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