Question

A stock had returns of 15 percent, 2 percent, 10 percent, 12 percent, -7 percent, and -3 percent over the past six years. What is the geometric average return for this time period?

Answer 1

Geometric Average return			=	(((1+0.15)*(1+0.02)*(1+0.10)*(1+0.12)*(1-0.07)*(1-0.03))^(1/6))-1
			=	4.52%
There are two types of average return-(a) Simple average return and anoter is (b) Geometric Average return
Suppose we have $ 100 to invest at the beginning of 6 year investment period.
Simple Average Return			=	(15%+2%+10%+12%-7%-3%)/6
			=	4.83%
It shows that investment has earned avrerage 4.83% over last 6 years.But, that was not true picture.
We understand with the example of investment of 100 over 6 years.
Now, Future Value as per simple average return over last 6 years							=	100*(1+0.0483)^6		=	132.71
But, we can see from below table the actual return:
Year	Beginning Value		return %		Return earned		Ending Value
1	100.00		15%		15.00		115.00
2	115.00		2%		2.30		117.30
3	117.30		10%		11.73		129.03
4	129.03		12%		15.48		144.51
5	144.51		-7%		-10.12		134.40
6	134.40		-3%		-4.03		130.37
Actual Return is 130.37 in 6 years.It means simple return was giving the wrong picture.
Now, as per geometric mean,
Future Value		=	100*(1+0.0452)^6		=	130.376
Thus, Geometric average return shows the actual return.