Question

EXCEL FILE ONLY

Refer to the table below. The table below shows the annual returns (in percentages) for 2 major market indices. For each index, calculate the arithmetic mean return and the geometric mean return of full-year returns from 2005-2015. What is the relationship between the arithmetic and geometric mean returns?

	2015	2014	2013	2012	2011	2010	2009	2008	2007	2006	2005
Nasdaq Composite Index	1.37	8.59	50.0	-31.5	-21.1	-39.3	85.6	39.6	21.6	22.7	39.9
Dow Jones Industrial Average	-0.61	3.15	25.3	-16.8	-7.1	-6.2	25.2	16.1	22.6	26.0	33.5

Answer 1

Arithmetic and Geometric mean returns have a relation in common between them, while arithmetic mean refers to the average returns of the stocks, geometric mean returns multiply the returns and find the nth root of those return.

Also, it is a proven fact that if the numbers are positive between them then the arithmetic mean is higher than geometric mean,

Let us suppose an example, consider two returns 5%, 10%

So Arithmetic Mean being average returns hence the values will be (5%+10%)/2 = 7.5%

Now with same values the geometric returns would be (5*10)^ (1/2) = 7.07% (approx)

So AM> GM (proved)