imported>Doug Williamson |
imported>Doug Williamson |
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| Geometric mean returns or growth are calculated by taking account of compounding.
| | A situation in which market interest rates for longer term funds are lower than those for shorter maturities. |
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| (Contrasted with the arithmetic mean, which ignores compounding).
| | Also known as a negative yield curve or a falling yield curve. |
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| ===<span style="color:#4B0082">Example 1: Positive returns or growth</span>===
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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.)
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| == See also == | | == See also == |
| * [[Arithmetic mean]] | | * [[Negative yield curve]] |
| * [[CAGR]] | | * [[Phillips curve]] |
| | * [[Yield curve]] |
