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Topic: Macaulay Duration

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	Duration
		Duration is a measure of the average (cash-weighted) term-to-maturity of a bond.
		Macaulay duration is useful in immunization, where a portfolio of bonds is constructed to fund a known liability.
		Modified duration is an extension of Macaulay duration and is a useful measure of the sensitivity of a bond's price (the present value of it's cash flows) to interest rate movements.
	www.finpipe.com /duration.htm (647 words)

	Bond duration - Wikipedia, the free encyclopedia
		That means that the duration gives the opposite of the relative variation of the value of a bond respect to a variation of the rate of the bond, forgetting the quadratic terms.
		Macaulay duration, named for Frederick Macaulay who introduced the concept, is the weighted average maturity of a bond where the weights are the relative discounted cash flows in each period.
		Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative.
	en.wikipedia.org /wiki/Macaulay_Duration (1092 words)

	Bond Market Tutorial: Duration - Dana Investment Advisors (Site not responding. Last check: 2007-10-08)
		Macaulay duration is a measurement of the average time to receipt of all of the cash flows for a given security weighted by the size of each cash flow.
		Macaulay duration is often used to compare the relative risk of two bonds.
		The Macaulay duration would be the point in the life of the bond where the cash flows were in balance; a wedge could be put under the plank at this point and all of the cash flows would be balanced.
	www.danainvestment.com /duration.asp (374 words)

	TheStreet.com: Finally, We Have the Maturity to Explain Duration
		Duration -- which is always shorter than maturity except in the case of zero-coupon bonds, for which duration equals maturity -- measures the amount of time it will take for the investor to receive half of the present value of all future payments from the bond.
		The plank is essentially a timeline, and duration is the point along the plank where a fulcrum would go to balance the whole system.
		As the yield drops, the duration lengthens; as the yield rises, the duration shortens.
	www.thestreet.com /funds/bondforum/746354.html (1085 words)

	DURATION ANALYSIS AND ITS APPLICATIONS: A REVIEW
		Duration analysis is most well known for its use in bond portfolio management where billions in fixed income funds are managed using duration as a measure of interest rate sensitivity.
		Macaulay’s duration is defined as a weighted average of the times at which cash flows from an asset are obtained.
		The duration of a particular class of property, hospitals for example, is computed as a value-weighted average of the durations of the land and buildings comprising the asset.
	www.yorku.ca /groberts/WorkingPaper3.htm (10384 words)

	Macaulay Duration
		Macaulay in fact gave two definitions of duration: Stricly speaking, he defined duration to be the present value weighted average maturity, using the full term structure of zero-coupon interest rates on bonds of comparable quality and terms.
		The exact duration of a bond portfolio is the value-weighted average of the exact durations of its component bonds.
		However, the internal duration of a portfolio is not, strictly speaking, the value-weighted average of the internal durations.
	www.econ.ohio-state.edu /jhm/ts/duration.htm (1117 words)

	Duration and Convexity
		Duration is the slope of the curve multiplied by minus one.
		Duration is defined to be the slope of that tangent line, multiplied by negative one.
		Duration captured the fact that the graph in Exhibit 2 was downward sloping.
	www.riskglossary.com /articles/duration_and_convexity.htm (1582 words)

	[No title]
		At the 4% yield, the bond’s duration would be 4.56 and at 8%, the duration would be 4.52; neither duration matches the remaining horizon period of 5 years.
		To reestablish an immunized position when the bond's duration is no longer equal to the duration of the liability requires resetting the bond position such that the durations are again matched.
		For multiple-period liabilities, bond immunization strategies can be done either by matching the duration of each liability with the appropriate bond or bullet bond portfolio or by constructing a portfolio with a duration equal to the weighted average of the durations of the liabilities.
	www.blackwellpublishing.com /bonds/Solutions/ch8solmanual.doc (4746 words)

	FRBSF: Economic Letter - Measuring Interest Rate Risk for Mortgage-Related Assets (01/14/2000)
		Also, modified duration is lower for amortizing bonds, on which some principal is scheduled to be returned before final maturity, than for non-amortizing bonds, on which principal is returned only at final maturity.
		The prepayment of principal is particularly important to measuring the duration of mortgage-related assets.
		To put this number in perspective, note that this is equivalent to the modified duration and Macaulay duration of a zero-coupon (non-amortizing, noncallable) bond with a term to maturity of 6-1/2 years.
	www.frbsf.org /econrsrch/wklyltr/2000/el2000-01.html (1761 words)

	WWWFinance - Duration Measures: Historical Perspective
		He gave the name duration to the measure, but it is now often called Macaulay duration.
		However, it was noticed that there is a relationship between Macaulay duration and the first derivative of the price/yield function.
		The modified duration of a Eurobond showed its interest rate sensitivity to a change in the annualized rate, but a Treasury bond's modified duration showed its sensitivity to a change in the semiannual rate.
	www.duke.edu /~charvey/Classes/ba350/bondval/duration.htm (1194 words)

	SOA6: Immunization question - Actuarial Outpost
		I don't believe that there is a "right" duration measure to use, other than the one that best captures the interest rate sensitivity of your assets or liabilities.
		Effective duration is different from itself depending on the amount of change in interest rate (and thus changes in prices) used in the calculation.
		But to calculate effective duration you plug in a non-zero number, so it is only approximately equal to the modified duration.
	actuarialoutpost.com /actuarial_discussion_forum/showthread.php?t=3404 (1213 words)

	Advanced Bond Concepts: Duration
		Duration increases immediately on the day a coupon is paid, but throughout the life of the bond, the duration is continually decreasing as time to the bond's maturity decreases.
		The four types of durations are Macaulay duration, modified duration, effective duration and key-rate duration.
		Macaulay duration is calculated by adding the results of multiplying the present value of each cash flow by the time it is received and dividing by the total price of the security.
	www.investopedia.com /university/advancedbond/advancedbond5.asp (2123 words)

	Tutorial (Financial Toolbox) (Site not responding. Last check: 2007-10-08)
		The Macaulay duration of an income stream, such as a coupon bond, measures how long, on average, the owner waits before receiving a payment.
		It is the weighted average of the times payments are made, with the weights at time T equal to the present value of the money received at time T. The modified duration is the Macaulay duration discounted by the per-period interest rate; i.e., divided by (1+rate/frequency).
		To illustrate, the following example computes the annualized Macaulay and modified durations, and the periodic Macaulay duration for a bond with settlement (12-Jan-2000) and maturity (01-Oct-2001) dates as above, a 5% coupon rate, and a 4.5% yield to maturity.
	www.weizmann.ac.il /matlab/toolbox/finance/fintu24a.html (202 words)

	SSRN-The Duration Derby: A Comparison of Duration Based Strategies in Asset Liability Management by Harry Zheng, Lyn ...
		Macaulay duration matched strategy is a key tool in bond portfolio immunization.
		In this paper the approximate duration is proposed to measure the bond price sensitivity to changes of interest rates of non-flat term structures.
		Approximate duration turns out to be a possible contender in asset liability management: it does not assume any particular structures or patterns of changes of interest rates, it does not need short selling of bonds, and it is easy to set up and rebalance the optimal portfolio with linear programming.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=266690 (345 words)

	Macaulay Duration Definition
		The weighting is based on the present value of each cash flow divided by the price.
		This is one of two ways to calculate duration, the other being modified duration.
		Learn the basics about corporate bonds as well as how to evaluate the yield, maturity, duration, rating, callability and convertibility.
	www.investorwords.com /2911/Macaulay_Duration.html (155 words)

	Dictionary - M (Site not responding. Last check: 2007-10-08)
		It is equal to the Macaulay Duration divided by (1+ (bond yield/k)) where k represents the number of compounding periods per annum.
		Thus, it is inversely related to the approximate percentage change in price for a given change in yield.
		This is one of two ways in which duration can be calculated, the other method being Macaulay Duration.
	www.kbsh.ca /dictionary/m (1790 words)

	modified duration Definition
		Equal to the Macaulay Duration divided by (1+ (bond yield/k)) where k is the number of compounding periods per year.
		It is therefore inversely proportional to the approximate percentage change in price for a given change in yield.
		This is one of two ways to calculate duration, the other being Macaulay duration.
	www.investorwords.com /3087/modified_duration.html (171 words)

	Macaulay Duration
		In 1938, Frederick R. Macaulay defined Duration as the total weighted average time for recovery of the interest payments and principal in relation to the current market price of the bond.
		This is one of two ways to calculate duration, the other being modified duration.
		The calculation of a bond duration is a valuable strategic tool in the hands of bond investors because by measuring the average time to receipt of cash from a bond, it allows investors to measure a bond's price sensitivity to changes in market interest rates.
	www.fxwords.com /m/macaulay-duration.html (122 words)

	DD K-M
		The idea is that life insurance companies are good at underwriting insurance risks, collecting premiums, and servicing the policies, but needn’t tie up their money for the duration.
		Macaulay Duration is an overestimate, and Modified Duration (q.v.
		However, as a practical matter their duration should be close to that of the U.S. Treasury’s Long Bond.
	www.margrabe.com /Dictionary/DictionaryKM.html (2598 words)

	[No title]
		However, with a zero-coupon bond the Macaulay duration is equal to maturity and the modified duration is less.
		Note that with the small change in the required yield, modified duration is a close figure.
		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).
	home.ubalt.edu /ntsbmors/FABOZZIPPT/chapter24.ppt (682 words)

	UoE:SoBE:BEM6252:Exam98 (Site not responding. Last check: 2007-10-08)
		Explain why Macaulay's duration for a zero-coupon bond is equal to the maturity interval (n) of the bond.
		State what are the limitations of using duration as a measure of bond's price sensibility to interest-rate changes.
		Find the option-adjusted duration of a deep-discount bond, where the coupon rate is substantially below the current market yield, and of a premium callable bond, where the coupon rate is substantially higher than the current market yield.
	ex.ac.uk /sobeinternal/DeadCourses/BEM6252/Exam98B/BEM6252Exam98.html (269 words)

	[No title]
		Many applications are not sensitive to the difference, and modified and Macaulay duration numbers are often used interchangeably.
		See also Macaulay Duration, Duration, Effective Duration, Partial Duration, Option-Adjusted Duration.
		If Macaulay duration is 6, yield is 7% (0.07), and the bond pays interest twice a year:
	www.amex.com /servlet/AmexFnDictionary?pageid=display&titleid=4062 (108 words)

	Macaulay Duration
		The weight of each cash flow is determined by dividing the present value of the cash flow by the price.
		The metric is named after its creator, Frederick Macaulay.
		Macaulay duration is frequently used by portfolio managers who use an immunization strategy.
	www.investopedia.com /terms/m/macaulayduration.asp (192 words)

	Financial Dictionary — Meaning for Macaulay duration
		With fixed-interest securities, or any known set of cashflows, it is the sum of the time to each cashflow (eg, coupon payment) weighted by the ratio of the market value of each cashflow to the total market value of the security.
		The concept was devised in the US in 1938 by Frederick Macaulay, as a measure to capture the characteristics of bonds rather than merely classifying them by maturity.
		Copyright Australia and New Zealand Banking Group Limited 100 Queen street, Melbourne 3000 (ABN 11 005 357 522), 1996-2007.
	www.anz.com /edna/dictionary.asp?action=content&content=macaulay_duration (175 words)

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