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{{refimprove|date=July 2008}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


==Definition==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
The difference between the [[Bond duration|duration]] of [[asset]]s and [[liability (financial accounting)|liabilities]] held by a financial entity.<ref name="LeeLee2006">{{cite book|last1=Lee|first1=Cheng-Few|last2=Lee|first2=Alice C.|title=Encyclopedia of Finance|url=http://books.google.com/books?id=I6BH-RKYVG4C&pg=PA423|accessdate=15 February 2013|date=2006-05-05|publisher=Springer|isbn=9780387262840|pages=423–}}</ref>
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Overview==
Registered users will be able to choose between the following three rendering modes:
The '''duration gap''' is a financial and [[accounting]] term and is typically used by banks, pension funds, or other financial institutions to measure their risk due to changes in the interest rate. This is one of the mismatches that can occur and are known as [[asset liability mismatch]]es.


Another way to define Duration Gap is: it is the difference in the price sensitivity of interest-yielding assets and the price sensitivity of liabilities (of the organization) to a change in market interest rates (yields).<ref name="Skinner2004">{{cite book|last=Skinner|first=Frank|title=Pricing and Hedging Interest and Credit Risk Sensitive Instruments|url=http://books.google.com/books?id=2OAkxj2hAkgC&pg=PA218|accessdate=15 February 2013|date=2004-10-29|publisher=Butterworth-Heinemann|isbn=9780080473956|pages=218–}}</ref>
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


The duration gap measures how well matched are the timings of [[Cash flow|cash inflows]] (from assets) and cash outflows (from liabilities).
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


When the duration of assets is larger than the duration of liabilities, the duration gap is positive. In this situation, if [[Interest|interest rates]] rise, assets will lose more value than liabilities, thus reducing the value of the firm's equity. If interest rates fall, assets will gain more value than liabilities, thus increasing the value of the firm's equity.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


Conversely, when the duration of assets is less than the duration of liabilities, the duration gap is negative. If interest rates rise, liabilities will lose more value than assets, thus increasing the value of the firm's equity. If interest rates decline, liabilities will gain more value than assets, thus decreasing the value of the firm's equity.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


By duration matching, that is creating a zero duration gap, the firm becomes [[immunization (finance)|immunized]] against [[interest rate risk]]. Duration has a double-facet view. It can be beneficial or harmful depending on where interest rates are headed.
==Demos==


Some of the limitations of duration gap management include the following:
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
* the difficulty in finding assets and liabilities of the same duration
* some assets and liabilities may have patterns of cash flows that are not well defined
* customer prepayments may distort the expected cash flows in duration
* customer defaults may distort the expected cash flows in duration
* convexity can cause problems.


<math>Duration \ gap = duration \ of \ earning \ assets \ - \ duration \ of \ paying \ liabilities \ \times \ \frac{paying \ liabilities}{earning \ assets}</math>


When the duration gap is zero, the firm is immunized only if the size of the liabilities equals the size of the assets. In this example with a two-year loan of one million and a one-year asset of two millions, the firm is still exposed to [[rollover risk]] after one year when the remaining year of the two-year loan has to be financed.
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


<math>0 = 1 - 2 \times \frac{1,000,000}{2,000,000}</math>
==Test pages ==


==See also==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
* [[List of finance topics]]
*[[Displaystyle]]
* [[Bond convexity]]
*[[MathAxisAlignment]]
* The duration difference is also shown by sorting into maturity buckets as in the table [[Fractional-reserve banking#How the example bank manages its liquidity|How the example bank manages its liquidity]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


==References==
*[[Inputtypes|Inputtypes (private Wikis only)]]
{{Reflist}}
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
[[Category:Finance]]
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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