Difference between revisions of "Geometric mean"

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Geometric mean returns are calculated by taking account of compounding.
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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).
  
For example, the geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:
 
  
(1.04 x 1.05 x 1.06)<sup>(1/3)</sup> -1
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===<span style="color:#4B0082">Example 1: Positive returns or growth</span>===
  
= 4.9968%.
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The geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:
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(1.04 x 1.05 x 1.06)<sup>(1/3)</sup> - 1
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= '''4.9968%'''.
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===Relationship between geometric mean and arithmetic mean===
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When returns or growth are positive, geometric means are smaller figures than arithmetic means.
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In Example 1 above, the arithmetic mean is:
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(4% + 5% + 6%) / 3 = '''5.0000%'''
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''The geometric mean of +4.9968% is a smaller positive number than the [[arithmetic mean]] of +5.0000%.''
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On the other hand, when returns or growth are ''negative'', the geometric mean is a larger negative number - further away from zero - than the arithmetic mean.
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===<span style="color:#4B0082">Example 2: Negative returns or decline</span>===
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The geometric mean return calculated from three ''negative'' sample returns of -(4)%, -(5)% and -(6)% is given by:
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( (1 - 0.04) x (1 - 0.05) x (1 - 0.06) )<sup>(1/3)</sup> - 1
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(0.96 x 0.95 x 0.94)<sup>(1/3)</sup> - 1
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= '''-(5.0035)%'''.
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The negative geometric mean of -(5.0035)% is a larger negative number - further away from zero - than the arithmetic mean of -(5.0000)%.
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(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]]
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* [[CAGR]]

Latest revision as of 20:31, 15 January 2016

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, the geometric mean is a larger negative number - further away from zero - than the arithmetic mean.


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 larger negative number - further away from zero - 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