Geometric mean and Primary financial statements: Difference between pages

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imported>Doug Williamson
(Clarify that larger negative number here means further away from zero.)
 
imported>Doug Williamson
(Add link.)
 
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Geometric mean returns or growth are calculated by taking account of compounding.
''Financial reporting.''


(Contrasted with the arithmetic mean, which ignores compounding).
Under International Accounting Standards (IAS) 'primary' financial statements are the main accounting statements that must be presented.  




===<span style="color:#4B0082">Example 1: Positive returns or growth</span>===
These are:


The geometric mean return calculated from sample returns of 4%, 5% and 6% is given by:
* Statement of financial position (balance sheet).
* Income statement (profit or loss account), which can be included in the statement of comprehensive income.
* Statement of comprehensive income.
* Statement of changes in equity.
* Statement of cash flows.


( 1.04 x 1.05 x 1.06 )<sup>(1/3)</sup> - 1


= '''4.9968%'''.
The primary financial statements are supported by Notes to the accounts, providing additional and more detailed financial information.




===Relationship between geometric mean and arithmetic mean===
==See also==
* [[Entity]]
* [[Financial reporting]]
* [[Income statement]]
* [[International Accounting Standards]]
* [[Notes]]
* [[Statement of cash flows]]
* [[Statement of changes in equity]]
* [[Statement of comprehensive income]]
* [[Statement of financial position]]
* [[Statement of profit or loss and other comprehensive income]]


When returns or growth are positive, geometric means are smaller figures than arithmetic means.
[[Category:Accounting,_tax_and_regulation]]
 
[[Category:Compliance_and_audit]]
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.
 
 
===<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 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 ==
* [[Arithmetic mean]]
* [[CAGR]]

Revision as of 15:57, 5 May 2019

Financial reporting.

Under International Accounting Standards (IAS) 'primary' financial statements are the main accounting statements that must be presented.


These are:

  • Statement of financial position (balance sheet).
  • Income statement (profit or loss account), which can be included in the statement of comprehensive income.
  • Statement of comprehensive income.
  • Statement of changes in equity.
  • Statement of cash flows.


The primary financial statements are supported by Notes to the accounts, providing additional and more detailed financial information.


See also

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