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Topic: Bond convexity

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	Bond Calculator Help
		In return for purchasing a bond, the investor is guaranteed to a receive a periodic (usually annual or semi-annual) coupon payment over the life of the bond and a larger redemption payment when the bond matures.
		Bond prices and coupon amounts are expressed as a percentage of the bond's notional face value, so an investor holding a 1000000 DM German Government Bond with a coupon of 5% and a 100% redemption would receive an annual coupon payment of 50000 DM and a redemption payment of 1000000 DM.
		A bond's Convexity is its change in PVBP given a unit increase in yield; it indicates the degree of curvature in the price/yield graph.
	www.act365.com /avalon/Bondhelp.htm (968 words)

	CMS BondEdge-fixed income portfolio and credit risk analytics
		Therefore, when we see a bond's convexity changing from positive to negative and wonder why this is so, we should think about what is happening to the security's expected future cash flows as interest rates change; therein lies the answer.
		"Convexity" is a term that describes the degree and type of curvature observed.
		With a callable bond, as interest rates rally it becomes more likely that the issuer will call the bond, thereby providing the investor with a set of cash flows to the call date that are worth less than the cash flows to the maturity date.
	www.cmsbondedge.com /b2b/bb_convexposneg.html (959 words)

	BONDTALK.com: Bond Basics - Fixed Income Glossary
		The larger the convexity, the steeper the curvature of the price/yield curve.
		If a bond is viewed as a series of cash flows, this concept measures sensitivity (in years) as the present value-weighted average of the cash flows of the bond.
		A bond swap in which the weighting of the two bonds is made according to the respective values of the yield values of a 32nd.
	www.bondtalk.com /global.cfm?S=rultra&SS=fixedinc (6154 words)

	Bonds
		This computes the bond payment of a 9% coupon bond paying semiannually with 20 years to maturity and a par value of $1,000 if the required yield is 12%.
		It is the slope of the price-yield curve of a bond.
		The yield to maturity of the bond is 15%.
	documents.wolfram.com /applications/finance/Bonds.html (953 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: 2007-10-18)
		This measure is closely related to the derivative of the bond's price function with respect to the interest rate, and some authors consider the duration to be this derivative, with the weighted average maturity simply being an easy method of calculating the duration for a non-callable bond.
		Bonds that have embedded options should be analyzed using "effective duration." Effective duration is a discrete approximation of the slope of the bond's value as a function of the interest rate.
		Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=bond_duration (1384 words)

	Duration (Site not responding. Last check: 2007-10-18)
		Duration is a measure of the average (cash-weighted) term-to-maturity of a bond.
		In the section showing a bonds price as the present value of its cash flows, the bond shown was priced initially at par (100), when the YTM was 7.5%, with a Macaulay Duration of 4.26 years.
		The discrepancy between the estimated change in the bond price and the actual change is due to the convexity of the bond, which must be included in the price change calculation when the yield change is large.
	www.finpipe.com /duration.htm (647 words)

	TheStreet.com: Practical Uses of Duration and Convexity for Bond Buyers
		If you're buying an individual bond or assembling a portfolio of them, the duration of the individual securities and of the entire portfolio should at least be of interest to you, since it gives you an approximate idea of their sensitivity to changes in interest rates.
		And the indices, being composed of bonds, have durations.
		That's because most long-term muni bonds are callable 10 years from their issue date, and loads of closed-end muni funds came into existence in the late 1980s and early 1990s, when muni yields were much higher than they are now.
	www.thestreet.com /funds/bondforum/751721.html (1080 words)

	Bond Risk Statistic Calculations (Site not responding. Last check: 2007-10-18)
		The standard measures of Macaulay's duration, modified duration, convexity, and PVBP (present value of a basis point), are presented.
		Note that because bond price is a negative function of yield, the first derivative of price with respect to yield will also be negative, and the negative sign is therefore used in the above equation to ensure that the duration is always expressed as a positive number.
		Convexity is used to approximate the percentage change in the bond price that is not explained by the duration measure (resulting from the curvature in the bond price and yield relationship).
	www.derivativepricing.com /helpfiles/1330.htm (283 words)

	Interest Rate Risk Management
		The bond increases in value at the end of the year to 1030.58 (1.039) = 1070.77, while the $50 coupon is reinvested at an annual yield of 7.8% and grows to 50 (1.039) = 51.95, for a total of 1122.72.
		The convexity of the two portfolios differs: The bullet portfolio has a dollar convexity of 55.4506, while that of the barbell portfolio is 71.7846.
		Assume that this bond has a 6% annual default probability and that it is estimated that if the bond does default, each bondholder willl receive an amount equal to 60% of the bond's market price a year earlier.
	webpage.pace.edu /pviswanath/notes/investments/fixportf.html (4415 words)

	Advanced Bond Concepts: Convexity
		A bond with greater convexity is less affected by interest rates than a bond with less convexity.
		Remember that as bond yields increase, bond prices are decreasing and thus interest rates are increasing.
		Convexity is the final major concept you need to know for gaining insight into the more technical aspects of the bond market.
	www.investopedia.com /university/advancedbond/advancedbond6.asp (948 words)

	chaps11-15
		Bond B has a higher yield to maturity than bond A since its coupon payments and maturity are equal to those of A, while its price is lower.
		Bond A has a lower yield and a lower coupon, both of which cause it to have a longer duration than B. Moreover, A cannot be called, which makes its maturity at least as long as that of B, which generally increases duration.
		This can be seen to be a general property by noting from the duration-with-convexity formula that the duration effect on the two bonds due to any change in rates will be equal (since their durations are equal), but the convexity effect, which is always positive, will always favor the higher convexity bond.
	www.auburn.edu /~pughwi1/ansbodie2c.html (7639 words)

	Origins of bond convexity
		I am in the process of writing a paper about convexity measure of fixed income securities.
		I want to know who was the first person who proposed "convexity" or "convexity measure" as a way to adjust "modified duration" so that it would better measure the percentage change in the bond price when the yield changes.
		You see everywhere mentioned that "the Macaulay Duration was first proposed by Frederick Macaulay, in "Some Theoretical Problems Suggested by the Movement of Interest Rates, Bond Yields, and Stock Prices in the U.S. Since 1856 (New York: National Bureau of Economic Research, 1938).
	www.suite101.com /discussion.cfm/fixed_income_bonds/61157 (201 words)

	WWWFinance - Bond Valuation: Campbell R. Harvey
		A zero coupon bond is a bond that pays $1 at time T and no coupons prior to this period.
		If this was a six year bond bought at par and held for one year, then the return on holding the bond is 8.52% if the rates go to 13% and 5.13% if the rates go to 14%.
		Bond A has a 10 year maturity with a 12% coupon and Bond B has a 5 year maturity with a 12% coupon.
	www.duke.edu /~charvey/Classes/ba350/bondval/bondval.htm (6414 words)

	Convexity and Options Pricing(Put/Call Parity)
		This means that for a given increase/decrease in rates (say 10 bps) you will make more in relative/absolute terms when rates drop than you will lose when rates increase, assuming you have a long position in the Bond.
		The reverse would be true for a short position.
		Wouldn't this imply that Bond calls should be priced higher than Bond puts since you would make more for a given drop in the level of interest rates (due to the convexity of the underlying bond), than you would make on a Bond put for a same-magnitude increase in the level of interest rates?
	www.contingencyanalysis.com /archive/archive98-3/000000ba.htm (136 words)

	DURATION, IMMUNIZATION & CONVEXITY (Site not responding. Last check: 2007-10-18)
		The change in the bond price due to convexity: (convexity on bonds with no embedded options is always positive).
		As yields increase (decrease) the convexity decreases (increases).
		Two bonds that have equal duration but different convexity, the bond with the greater convexity will be more valuable because no matter whether yields increase or decrease the bond will have a higher price.
	www.umsl.edu /~busahanc/DURATION.htm (399 words)

	TheStreet.com: Noncallable Bonds Provide the Joy of Convexity
		Moreover, the longer the duration of a bond, the greater the margin of error.
		A bond only gets called when interest rates are lower than they were when the bond was issued.
		Because as an investor you'd much rather have a noncallable bond, callable bonds are cheaper (their yields are higher) than noncallables, all else being equal.
	www.thestreet.com /funds/bondforum/749419.html (866 words)

	non-callable bond Definition
		A bond that is not able to be redeemed prior to maturity.
		Learn the basics about corporate bonds as well as how to evaluate the yield, maturity, duration, rating, callability and convertibility.
		Here we explain how bonds work, and we describe the different types of bonds, including corporate, municipal, treasury, agency, zero-coupon, and junk bonds.
	www.investorwords.com /3306/non_callable_bond.html (140 words)

	bndconvy (Financial Toolbox)
		Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.
		is the periodic convexity reported on a semi-annual bond basis (in accordance with SIA convention).
		Find the convexity of a bond at three different yield values.
	www.weizmann.ac.il /matlab/toolbox/finance/bndconvy.html (385 words)

	bndconvy :: Functions (Financial Toolbox)
		This function determines the convexity for a bond whether or not the first or last coupon periods in the coupon structure are short or long (i.e., whether or not the coupon structure is synchronized to maturity).
		This function also determines the convexity of a zero coupon bond.
		is the periodic convexity reported on a semiannual bond basis (in accordance with SIA convention).
	www.mathworks.com /access/helpdesk/help/toolbox/finance/bndconvy.html (428 words)

	Soln Ch 16
		In this example, the percentage error using convexity with duration is less than one-tenth the error using only duration to estimate the price change.
		The price of the zero coupon bond ($1000 face value) selling at a yield to maturity of 8% is $374.84 and that of the coupon bond is $774.84.
		This can be seen to be a general property by noting from the duration-with-convexity formula that the duration effect on the two bonds due to any change in rates will be equal (since their durations are virtually equal), but the convexity effect, which is always positive, will always favor the higher convexity bond.
	www.uky.edu /~sjordan/fin650/spring99/ch16sol.html (900 words)

	Bond Calculator Software for Portfolio Management.
		All at the individual bond level, and at the overall bond portfolio level.
		For example, if you need to calculate duration as part of year-end reporting in January, and the bond's valuation date needs to be the last day of the previous year, you can do that.
		For example, if you need to calculate yield to maturity as part of year-end reporting in January, and the bond's valuation date needs to be the last day of the previous year, you can do that.
	www.toolsformoney.com /bond_calculator.htm (1487 words)

	Writing User-Defined Functions: The Other Side of Excel
		As most readers of FEN know, duration should be adjusted by a convexity factor to better estimate bond price changes with interest rate changes of greater than 50 basis points (especially for longer maturity, lower coupon bonds where the price-yield relationship is more pronounced in its convex nature).
		There are only three independent variables: c, the coupon rate; I, the bond yield; and N, the number of periods to maturity.
		Being able to create, just once, a user-defined function for convexity and have it available when needed is another valuable use of user-defined functions.
	www.fenews.com /fen43/back_to_basics/back_to_basics.htm (1802 words)

	Infotech Financials Pvt. Ltd. - Financial Solutions
		The Government of India (GOI) Bond Index system has been developed to arrive at a standard measure of the government bond market and its movement.
		The GOI bond index is a real number that measures the performance of a portfolio that is invested purely in government bonds.
		Calculate the number of bonds that the index fund would have to be holding to be invested in the index portfolio.
	www.infofin.com /INFOFIN/bondindex.htm (180 words)

	[No title]
		However, with a zero-coupon bond the Macaulay duration is equal to maturity and the modified duration is less.
		An adjustment to the percentage change estimated using duration is Convexity adjustment = 0.5(convexity)(yield change in basis points)2 Using both convexity and duration provides a good approximation of the actual price change for large movements ¡hSC nó¨Positive convexity¡¨ Positive convexity - As the required yield increases (decreases), the convexity of the bond decreases (increases).
		Insert Figure 24-4 ¡4 ÷ó¨The value of convexity¡¨µ Insert Figure 24-5 Given two bonds with the same duration and yield, there can be two different convexities.
	home.ubalt.edu /ntsbmors/FABOZZIPPT/chapter24.ppt (682 words)

	Bonds 5
		When we first talked about Bonds, we considered how the Bond Value varied with the Years to Maturity, Yield, etc.
		That curvature is Bond Convexity, which describes the convex shape of the curve.
		Now try the calculator with Years = 18, 12, 8, 6, 1 and watch the convexity decrease.
	www.gummy-stuff.org /bonds-5.htm (857 words)

	Advanced Bond Concepts: Introduction
		In their simplest form, bonds are pretty straightforward.
		However, like many securities, trading and analyzing bonds involves some more complicated underlying concepts.
		We'll reinforce and review bond fundamentals such as pricing and yield, explore the term structure of interest rates, and delve into the topics of duration and convexity.
	www.investopedia.com /university/advancedbond (262 words)

	Amazon.com: Duration, Convexity, and Other Bond Risk Measures (Frank J. Fabozzi Series): Books: Frank J. PhD,CFA, CPA ... (Site not responding. Last check: 2007-10-18)
		Duration, Convexity and other Bond Risk Measures offers the most comprehensive coverage of bond risk measures available.
		Financial expert Frank Fabozzi walks you through every aspect of bond risk measures from the price volatility characteristics of option-free bonds and bonds with embedded options to the proper method for calculating duration and convexity.
		Lucid on all aspects of bond convexity and a very good analysis of option embedded bonds with negative convexity.
	www.amazon.com /Duration-Convexity-Other-Measures-Fabozzi/dp/1883249635 (1100 words)

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