Geometric mean: Difference between revisions
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imported>Doug Williamson (Link with CAGR page and expand page.) |
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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). | ||
===<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: | ||
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( 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.)
