Difference between revisions of "Geometric mean"

From ACT Wiki
Jump to: navigation, search
(Standardise appearance of page)
(Link with CAGR page and expand page.)
Line 1: Line 1:
Geometric mean returns are calculated by taking account of compounding.
+
Geometric mean returns or growth are calculated by taking account of compounding.
  
 
(Contrasted with the arithmetic mean, which ignores compounding).
 
(Contrasted with the arithmetic mean, which ignores compounding).
  
  
'''Example'''
+
===<span style="color:#4B0082">Example 1: Positive returns or growth</span>===
  
 
The geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:
 
The geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:
Line 10: Line 10:
 
( 1.04 x 1.05 x 1.06 )<sup>(1/3)</sup> - 1  
 
( 1.04 x 1.05 x 1.06 )<sup>(1/3)</sup> - 1  
  
= 4.9968%.
+
= '''4.9968%'''.
 +
 
 +
 
 +
===Relationship between geometric mean and arithmetic mean===
 +
 
 +
When returns or growth are positive, geometric means are smaller figures than arithmetic means.
 +
 
 +
In Example 1 above, the arithmetic mean is:
 +
 
 +
(4% + 5% + 6%) / 3 = '''5.0000%'''
 +
 
 +
 
 +
''The geometric mean of +4.9968% is a smaller positive number than the [[arithmetic mean]] of +5.0000%.''
 +
 
 +
 
 +
 
 +
On the other hand, when returns or growth are ''negative'', this relationship is reversed.
 +
 
 +
 
 +
===<span style="color:#4B0082">Example 2: Negative returns or decline</span>===
 +
 
 +
The geometric mean return calculated from three ''negative'' sample returns of -(4)%, -(5)% and -(6)% is given by:
 +
 
 +
( (1 - 0.04) x (1 - 0.05) x (1 - 0.06) )<sup>(1/3)</sup> - 1
 +
 
 +
( 0.96 x 0.95 x 0.94 )<sup>(1/3)</sup> - 1
 +
 
 +
= '''-(5.0035)%'''.
 +
 
 +
 
 +
''The negative geometric mean of -(5.0035)% is a bigger negative number than the arithmetic mean of -(5.0000)%.''
 +
 
 +
''(The arithmetic mean of the negative returns of -(4)%, -(5)% and -(6)% is the three items added together and divided by 3.)''
  
  
 
== See also ==
 
== See also ==
 
* [[Arithmetic mean]]
 
* [[Arithmetic mean]]
 +
* [[CAGR]]

Revision as of 08:46, 1 December 2015

Geometric mean returns or growth are calculated by taking account of compounding.

(Contrasted with the arithmetic mean, which ignores compounding).


Example 1: Positive returns or growth

The geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:

( 1.04 x 1.05 x 1.06 )(1/3) - 1

= 4.9968%.


Relationship between geometric mean and arithmetic mean

When returns or growth are positive, geometric means are smaller figures than arithmetic means.

In Example 1 above, the arithmetic mean is:

(4% + 5% + 6%) / 3 = 5.0000%


The geometric mean of +4.9968% is a smaller positive number than the arithmetic mean of +5.0000%.


On the other hand, when returns or growth are negative, this relationship is reversed.


Example 2: Negative returns or decline

The geometric mean return calculated from three negative sample returns of -(4)%, -(5)% and -(6)% is given by:

( (1 - 0.04) x (1 - 0.05) x (1 - 0.06) )(1/3) - 1

( 0.96 x 0.95 x 0.94 )(1/3) - 1

= -(5.0035)%.


The negative geometric mean of -(5.0035)% is a bigger negative number than the arithmetic mean of -(5.0000)%.

(The arithmetic mean of the negative returns of -(4)%, -(5)% and -(6)% is the three items added together and divided by 3.)


See also