### Bond coupon and duration

The duration also called "Macaulay duration" is the average period of capital commitment. Unlike the simple term to maturity, it takes account of the capital commitment of all the individual payment flows.

## Macaulay Duration vs. Modified Duration

Duration analysis can be applied to entire bond portfolios. It can also be used to hedge bonds against unfavourable yield trends. There is an inverse relationship between market rates and bond prices - the direct result of rising yields is dropping prices. On the other hand, coupon payments can be invested more profitably, which increases the future value of the portfolio. The duration is usually expressed in years and indicates the period after which these two effects cancel each other out.

This figure allows investors to compare bonds with different terms to maturity, interest coupons and repayment frequencies.

The concept of duration suggests that investors should choose the average commitment period of a bond or bond portfolio in accordance with their individual investment horizons. As the positive and negative effects of interest rate changes cancel each other out at the time of the duration, interest rate changes have no bearing on the value of the investment at this point in time.

It should be noted that the concept assumes a flat yield curve and a parallel movement of the curve, i. The duration expresses the interest-rate sensitivity of a bond issue in a single figure. The relative risk of a bond is indicated by changes in the duration or differences between the durations of different bonds. The duration of a bond depends on the features that determine its price. It will be shorter. The shorter the term to maturity, the higher the market yield, and the higher the coupon,. The duration can be used to calculate an approximative price change:.

Calculation of an approximative price change in the event of a rate increase by 0. Management Network Banner Advertisement. Cookie notification Our website uses cookies. Money and Capital Market. Primary and Secondary Market. Monetary Market. Derivative Financial Market.

## Duration Definition & Example | InvestingAnswers

Financial Market. Securities Trading. Tasks of the Stock Exchange. Exchange Knowledge. IPOs and the secondary market. Types of Shares. Types of bonds. Table 6. Zero Coupon Bonds or Discounted Debt Instruments are the financial contracts with the simplest cash flow pattern: They involve two separate cash flows depicted in Figure 3. Figure 3. Cash flow pattern of a zero coupon or discount debt instrument. Cash flow payments are assumed to coincide with contract commencement not conclusion! The redemption payment to the investor usually consists of the principal amount plus some interest in return for lending the initial amount for the given period.

In practice, there is no distinction made between the interest and principal part of the redemption payment, when they are due on the same date. There is no element of optionality, discretion, or dependence on underlying cash flows or accumulated asset values embedded in this type of contract, and in the absence of credit risk the investor holding the instrument to maturity would have complete certainty as to the cash flow he or she will receive in return for his or her initial investment.

For the individual coupon period 3, Figure 3.

The cash flow is fixed at the beginning and accrues monotonously over the entire period. The cash flow amount to be paid accrues from the beginning of the coupon period and is paid out at the end of it. Cash flow of a zero coupon bond. As in this example all coupon periods have an identical coupon rate specified that is paid at regular intervals; the coupon schedule can be summarised in a single coupon stream.

Assuming that the interval between two successive coupon payments is exactly 0. Real world term sheet of a zero coupon bond. Table 3. Instrument cash flow schedule table in the zero coupon bond example. Redemption cash flow schedule not strictly needed. Instrument cash flow element table in the zero coupon bond example. A zero-coupon bond is the simplest fixed income security. It is an issue of debt, the issuer promising to pay the face value of the debt to the bondholder on the date the bond matures.

There are no coupon payments during the life of the bond, so it is a discount instrument, issued at a price that is below the face or principal amount. The price increases over time until the maturity date, when it reaches the maturity or par value. We have:. Analysts and researchers frequently work in terms of logarithms of yields and prices, or continuously compounded rates. One advantage of this is that it converts the non-linear relationship in 3. The expression in 3. A good definition of the term structure of interest rates is given in Sundaresan , who states that it:.

click For example, Figures 3. Each of the curves exhibit peculiarities in their shape, although the most common type of curve is gently upward-sloping, as is the French curve. The UK curve is inverted.

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We explore further the shape of the yield curve later in this chapter. US Treasury zero-coupon yield curve in September UK gilt zero-coupon yield curve.

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Yield source: Bloomberg. French OAT zero-coupon yield curve. Gregory Duffee, in Handbook of Economic Forecasting , Denote its time- t price and yield by. The yield on a bond can be related to future bond returns in two useful ways. The relation is. The second accounting identity links the current yield to the sum, during the life of the bond, of one-period yields and excess returns:.

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These conditional expectations are also identities. They hold regardless of the information set used for conditioning, as long as the set contains the yield y t n. A strip is a zero-coupon bond , that is a bond that makes no coupon payments during its life and has only one cash flow, its redemption payment on maturity. For example a ten-year gilt can be stripped into 21 zero-coupon bonds, comprised of one bond from the principal repayment and twenty from the semi-annual coupons.

Coupon payments due in six, twelve, eighteen and so on months from the stripping date would become six, twelve, eighteen and so on month zero-coupon bonds. In Chapter 6 of this book we explained how the prices of such bonds are related to the yield curve derived from conventional bonds. We also illustrated the general rule that if a yield curve is upward sloping positive , the theoretical zero-coupon yield curve will lie above the conventional bond yield curve, while if the conventional curve is inverted, the zero-coupon curve will lie below it.

The gilt strips market is a recent development, with trading having commenced only on 8 December Not all gilts are strippable; only stocks designated as being strippable by the BoE and subsequently the DMO may be stripped. The market began quietly with relatively low volumes of trading. Strips are fully fledged gilts; they remain registered securities and liabilities of HM Government, therefore they have identical credit risk compared to conventional gilts. There is no limit on the amount or proportion of a strippable gilt issue that can be stripped or reconstituted.

The Crest system, inherited from CGO, includes a forward input facility for stripping and reconstitution requests to be entered up to one month in advance. GEMMs will include strips trading as part of their general gilt market making obligations. We have noted that strips are fully-fledged gilts, registered securities and liabilities of the government. It is not possible to remove a strip from Crest and hold it in paper form. Private investors must buy and sell gilts through a stockbroker. This is because when strips were introduced the BoE believed that strips, which carried greater interest-rate risk than conventional gilts of similar maturity, should not be available for purchase by retail investors unless they were aware of their characteristics; therefore strips cannot be purchased through the post.

Stripped coupons from different gilts but with the same coupon dates are fully fungible; this increases their liquidity. At the moment there is no fungibility between coupon and principal strips, although this remains under review and may be possible at a later date. All strippable gilts have the same coupon dates, 7 June and 7 December each year, so that all strips mature on these dates each year. Strips are not deliverable into the LIFFE medium- and long-gilt futures contracts; for these it is necessary to deliver a coupon gilt from amongst those in the futures contract delivery basket.

In such models, it is assumed that the spot rate process r satisfies the stochastic differential equation. As, under wide conditions, a solution of SDE [3. Nathan Tintle, How much is the bond worth if you sell it in 4 years and: a. Suppose you buy a zero-coupon bond that has a yield rate of 2. How much is the bond worth if you sell it in 2 years and: a.