Modified convexity - Revision history

imported>Doug Williamson: Layout.

2016-11-16T21:43:05Z

Layout.

← Older revision		Revision as of 21:43, 16 November 2016
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	Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.		Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.


	It is also possible to estimate the MD and the C<sub>MOD</sub> from given observations of Price and Yield, by rearranging them to solve for MD and C<sub>MOD</sub> - effectively running the price change estimation formulae in the other direction.		It is also possible to estimate the MD and the C<sub>MOD</sub> from given observations of Price and Yield, by rearranging them to solve for MD and C<sub>MOD</sub> - effectively running the price change estimation formulae in the other direction.

imported>Doug Williamson: Removed link

2016-11-16T14:05:22Z

Removed link

← Older revision		Revision as of 14:05, 16 November 2016
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	== See also ==		== See also ==
	* [[CertFMM]]
	* [[Convexity]]		* [[Convexity]]
	* [[Matching]]		* [[Matching]]

imported>Doug Williamson: Layout.

2016-04-05T09:45:14Z

Layout.

← Older revision		Revision as of 09:45, 5 April 2016
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	Price change estimation using Modified Convexity (C<sub>MOD</sub>):		Price change estimation using Modified Convexity (C<sub>MOD</sub>):

	= - ( Price x MD x (Change in yield) ) + ½ x ( Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup> )		= - (Price x MD x (Change in yield) ) + ½ x (Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup> )

imported>Doug Williamson: Added more space around calculations and changed square brackets

2015-04-07T15:17:27Z

Added more space around calculations and changed square brackets

← Older revision		Revision as of 15:17, 7 April 2015
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	The estimation of price change for a given small change in yield can then be calculated as follows:		The estimation of price change for a given small change in yield can then be calculated as follows:


	Price change estimation using Modified Duration (MD) only:		Price change estimation using Modified Duration (MD) only:

	= - Price x MD x Change in yield		= - Price x MD x Change in yield


	Price change estimation using Modified Convexity (C<sub>MOD</sub>):		Price change estimation using Modified Convexity (C<sub>MOD</sub>):

	= - [Price x MD x (Change in yield)] + ½ x [Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup>]		= - ( Price x MD x (Change in yield) ) + ½ x ( Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup> )

imported>Doug Williamson: Updated entry. Source ACT Glossary of terms

2014-11-26T10:21:09Z

Updated entry. Source ACT Glossary of terms

← Older revision		Revision as of 10:21, 26 November 2014
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	* [[Matching]]		* [[Matching]]
	* [[Modified duration]]		* [[Modified duration]]
			* [[Nominal annual rate]]
			* [[Portfolio]]

	[[Category:Manage_risks]]		[[Category:Manage_risks]]
	[[Category:Risk_frameworks]]		[[Category:Risk_frameworks]]

imported>Doug Williamson: Link with qualifications page.

2014-11-01T14:48:24Z

Link with qualifications page.

← Older revision		Revision as of 14:48, 1 November 2014
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	== See also ==		== See also ==
			* [[CertFMM]]
	* [[Convexity]]		* [[Convexity]]
	* [[Matching]]		* [[Matching]]

imported>Doug Williamson: Align with Convexity page definition, to mention portfolios as well as instruments.

2014-07-29T10:13:53Z

Align with Convexity page definition, to mention portfolios as well as instruments.

← Older revision		Revision as of 10:13, 29 July 2014
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	(MC).		(MC).

	Broadly speaking, modified convexity measures the curvature of an instrument’s price function, as yields change - from a given starting point - by a small amount.		Broadly speaking, modified convexity measures the curvature of an instrument’s or a portfolio's price function, as yields change - from a given starting point - by a small amount.

	More strictly, it is the rate of change of modified duration with respect to yield - at the given starting yield.		More strictly, it is the rate of change of modified duration with respect to yield - at the given starting yield.
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	* [[Modified duration]]		* [[Modified duration]]

	[[Category:~~Interest_Rate_Risk~~]]		[[Category:Manage_risks]]
	[[Category:~~Managing_Risk~~]]		[[Category:Risk_frameworks]]

imported>Doug Williamson: Categorise the page and align with ACT glossary.

2014-07-29T08:59:31Z

Categorise the page and align with ACT glossary.

← Older revision		Revision as of 08:59, 29 July 2014
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	'''Modified Convexity = C<sub>MOD</sub> = Convexity / (1+r)<sup>2</sup>'''		'''Modified Convexity = C<sub>MOD</sub> = Convexity / (1+r)<sup>2</sup>'''


			Where:

			r = periodic yield = [[Nominal annual rate]] / compounding frequency per year


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	* [[Matching]]		* [[Matching]]
	* [[Modified duration]]		* [[Modified duration]]

			[[Category:Interest_Rate_Risk]]
			[[Category:Managing_Risk]]

imported>Doug Williamson: Spacing 22/8/13

2013-08-22T08:55:11Z

Spacing 22/8/13

← Older revision		Revision as of 08:55, 22 August 2013
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	(MC). Broadly speaking, modified convexity measures the curvature of an instrument’s price function, as yields change - from a given starting point - by a small amount.		(MC).

			Broadly speaking, modified convexity measures the curvature of an instrument’s price function, as yields change - from a given starting point - by a small amount.

	More strictly, it is the rate of change of modified duration with respect to yield - at the given starting yield.		More strictly, it is the rate of change of modified duration with respect to yield - at the given starting yield.


	Modified convexity can be calculated from Convexity as follows:		Modified convexity can be calculated from Convexity as follows:

	'''Modified Convexity = C<sub>MOD</sub> = Convexity / (1+r)<sup>2</sup>'''		'''Modified Convexity = C<sub>MOD</sub> = Convexity / (1+r)<sup>2</sup>'''


	The estimation of price change for a given small change in yield can then be calculated as follows:		The estimation of price change for a given small change in yield can then be calculated as follows:
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	= - [Price x MD x (Change in yield)] + ½ x [Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup>]		= - [Price x MD x (Change in yield)] + ½ x [Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup>]

	Because the value v yield relationship is a curve and not a straight line (values do not change linearly as yields change) the estimate of change in value using only modified duration will generally underestimate the new value (because the curve lies above its tangent). Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.
			Because the value v yield relationship is a curve and not a straight line (values do not change linearly as yields change) the estimate of change in value using only modified duration will generally underestimate the new value (because the curve lies above its tangent).

			Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.

	It is also possible to estimate the MD and the C<sub>MOD</sub> from given observations of Price and Yield, by rearranging them to solve for MD and C<sub>MOD</sub> - effectively running the price change estimation formulae in the other direction.		It is also possible to estimate the MD and the C<sub>MOD</sub> from given observations of Price and Yield, by rearranging them to solve for MD and C<sub>MOD</sub> - effectively running the price change estimation formulae in the other direction.


	== See also ==		== See also ==

imported>Kmacharla at 14:35, 28 May 2013

2013-05-28T14:35:27Z

← Older revision		Revision as of 14:35, 28 May 2013
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	Price change estimation using Modified Duration (MD) only:		Price change estimation using Modified Duration (MD) only:
	= - Price x MD x Change in yield
			= - Price x MD x Change in yield

	Price change estimation using Modified Convexity (C<sub>MOD</sub>):		Price change estimation using Modified Convexity (C<sub>MOD</sub>):
	= - [Price x MD x (Change in yield)] + ½ x [Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup>]
			= - [Price x MD x (Change in yield)] + ½ x [Price x C<sub>MOD</sub> x (Change in yield)<sup>2</sup>]

	Because the value v yield relationship is a curve and not a straight line (values do not change linearly as yields change) the estimate of change in value using only modified duration will generally underestimate the new value (because the curve lies above its tangent). Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.		Because the value v yield relationship is a curve and not a straight line (values do not change linearly as yields change) the estimate of change in value using only modified duration will generally underestimate the new value (because the curve lies above its tangent). Therefore the modified convexity adjustment is always positive - it always adds to the estimate of the new price whether yields increase or decrease.
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	* [[Matching]]		* [[Matching]]
	* [[Modified duration]]		* [[Modified duration]]