Economics
Yield to Maturity
Yield to maturity (YTM) is a measure of the total return anticipated on a bond if it is held until it matures. It takes into account the bond's current market price, its par value, the coupon interest rate, and the time to maturity. YTM is a crucial metric for investors as it helps in comparing and evaluating different bonds.
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9 Key excerpts on "Yield to Maturity"
eBook - PDFInvestments
Analysis and Management
- (Author)
- 2016(Publication Date)
- Wiley(Publisher)
So, your advisor recommends the bond because “it guarantees you a return of 6.25 percent if it is held to maturity.” Is your advisor’s statement accurate? ✓ The rate of return on bonds most often quoted is the Yield to Maturity (YTM) , a promised rate of return that occurs only under specific assumptions. YTM is the return an investor will receive from a bond purchased at the current market price if 1. The bond is held to maturity. 2. The coupons received while the bond is held are reinvested at the calculated YTM for the bond. In practice, YTM is thought of as the average annual return on the bond over its life. 7 However, an investor will actually earn this promised rate if and only if the two stated conditions are met. As we shall see, the likelihood of the second condition actually being met is extremely small. Thus, in our example above, your chances of earning exactly 6.25 percent over the 15‐year life of this bond are almost zero. The YTM is derived from Equation 17‐4 where the market price, the coupon, the num-ber of years to maturity, and the face value of the bond are known. The discount rate or YTM is the variable to be determined. Note in the following discussion that lowercase letters ytm, c, and n are used to denote semiannual variables, whereas capital letters YTM, C, and N are used to denote annual variables . ✓ Bond calculations in the United States usually involve semiannual periods, because bond interest is typically paid twice a year: P c t n t t n 1 1 1 ytm FV ytm (17-4) where P n the current market price of the bond the number of semiannual periods to maturity ytm the semiannual yield to mat urity to be solved for the semiannual coupon in dollars F c V the face value (or maturity value or par value), which in this discussion is always $ , 1 000 Yield to Maturity (YTM) The promised return on a bond purchased at the current market price and held to maturity Example 17-4 The current yield on our example bond is $100/$1,052.10 = 9.5 percent.
eBook - PDFInvestments
Analysis and Management
- Gerald R. Jensen, Charles P. Jones(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Your advisor recommends the bond stating, “it guarantees you a return of 6.25 per-cent if it is held to maturity.” Is your advisor’s statement accurate? • The bond return most often quoted is the Yield to Maturity (YTM) , a promised rate of return that occurs only under specific assumptions. YTM is the return an investor will receive from a bond purchased at the current market price if 1. The bond is held to maturity. 2. The coupons received are reinvested at the calculated YTM. In practice, YTM is the average annual return on the bond over its life. 6 However, an investor will actually earn this promised rate if and only if the two stated condi-tions are met. As we shall see, the likelihood of the second condition actually being met is extremely small. Thus, in our example, your chances of earning exactly 6.25 percent over the bond’s 15-year life are almost zero. The YTM is derived from Equation 17-4 where the market price, the coupon, the number of years to maturity, and the face value of the bond are known. The discount rate or YTM is the variable to be determined. Note in the following discussion that lowercase letters ytm, c, and n are used to denote semiannual variables, whereas capital letters YTM, C, and N are used to denote annual variables . • Bond calculations in the United States usually involve semiannual periods, because bond interest is typically paid twice a year: P c t n t t n 1 1 1 yt m y tm FV (17-4) where P n the current market price of the bond the number of semiannual periods to maturity yt m the semiannual yield to mat urity to be solved for the semiannual coupon in dollars F c V the face value maturity value or par value which in t ( ), his discussion is $1 000 , Since both the left-hand side of Equation 17-4 and the numerator values (cash flows) on the right-hand side are known, the equation can be solved for ytm.
eBook - PDFBonds
A Concise Guide for Investors
- M. Choudhry(Author)
- 2006(Publication Date)
- Palgrave Macmillan(Publisher)
An explanation of how we calculate the Yield to Maturity was given in Chapter 2. The curve itself is constructed by plotting the Yield to Maturity against the term to maturity for a group of bonds of the same class. We introduced a positively sloping yield curve earlier. Curves assume many different shapes, and in Figure 6.2 we show three hypothetical types. Bonds used in constructing the curve will only rarely have an exact number of whole years to redemption; however it is common to see yields plotted against whole years on the x-axis. This is because once a bond is desig- nated the benchmark for that term, its yield is taken to be the representative yield. For example, the ten-year benchmark bond in 2005 in the UK gilt market, the 4.75% Treasury 2015, will maintain its benchmark status throughout 2006, even as its term to maturity falls below ten years. It loses benchmark status once a new benchmark for that maturity is issued. The Yield to Maturity yield curve is the most commonly observed curve simply because Yield to Maturity is the most frequent measure of return used. The business sections of daily newspapers, where they quote bond yield at all, usually quote bond yields to maturity. Now the caveat This is one of those subjects that we need to be aware of and then promptly forget, a bit like in the world of cricket, when in the beginning your games master at school told you ‘you must always walk if you know you are out’ but in the real world you stand your ground until given out by the umpire! The Yield to Maturity yield curve contains some inaccuracies. This is because the Yield to Maturity measure has one large weakness, which is the assumption of a constant discount rate for coupons during the bond’s life at Bonds 116 the redemption yield level. In other words, we discount all the cash flows of the bond at one discount rate.
- Moorad Choudhry(Author)
- 2004(Publication Date)
- Butterworth-Heinemann(Publisher)
The Yield to Maturity yield curve is the most 42 Part I: Fixed Income Securities commonly observed curve simply because Yield to Maturity is the most frequent measure of return used. The business sections of daily newspapers, where they quote bond yields at all, usually quote bond yields to maturity. As we might expect, given the source data from which it is constructed, the Yield to Maturity yield curve contains some inaccuracies. We have already come across the main weakness of the Yield to Maturity measure, which is the assumption of a constant rate for coupon reinvestment during the bond's life at the redemption yield level. Since market rates will fluctuate over time, it will not be possible to achieve this (a feature known as reinvestment risk ). Only zero-coupon bondholders avoid reinvestment risk as no coupon is paid during the life of a zero-coupon bond. The Yield to Maturity yield curve does not distinguish between different payment pat-terns that may result from bonds with different coupons, that is, the fact that low-coupon bonds pay a higher portion of their cash flows at a later date than high-coupon bonds of the same maturity. The curve also assumes an even cash flow pattern for all bonds. Therefore in this case cash flows are not discounted at the appropriate rate for the bonds in the group being used to construct the curve. To get around this bond analysts may sometimes con-struct a coupon yield curve , which plots Yield to Maturity against term to maturity for a group of bonds with the same coupon. This may be useful when a group of bonds contains some with very high coupons; high coupon bonds often trade `cheap to the curve', that is they have higher yields than corresponding bonds of same maturity but lower coupon. This is usually because of reinvestment risk and, in some markets (including the UK), for tax reasons.
eBook - PDF- Moorad Choudhry, Graham "Harry" Cross, Jim Harrison(Authors)
- 2003(Publication Date)
- Butterworth-Heinemann(Publisher)
The business sections of daily newspapers, where they quote bond yields at all, usually quote bond yields to maturity. 3.00 4.00 5.00 7.00 6.00 Yield (%) Negative Positive Humped Years to maturity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Figure 9.1: Yield to Maturity yield curves. 194 The Gilt-Edged Market As we might expect, given the source data from which it is constructed, the Yield to Maturity yield curve contains some inaccuracies. In particular the assumption of a constant rate for coupon reinvestment during the bond's life at the redemption yield level. Since market rates will fluctuate over time, it will not be possible to achieve this (a feature known as reinvestment risk ). Only zero-coupon bondholders avoid reinvestment risk as no coupon is paid during the life of a zero-coupon bond. The Yield to Maturity yield curve does not distinguish between different payment patterns that may result from bonds with different coupons, that is, the fact that low-coupon bonds pay a higher portion of their cash flows at a later date than high-coupon bonds of the same maturity. The curve also assumes an even cash flow pattern for all bonds. Therefore in this case cash flows are not discounted at the appropriate rate for the bonds in the group being used to construct the curve. To get around this, bond analysts may sometimes construct a coupon yield curve , which plots Yield to Maturity against term to maturity for a group of bonds with the same coupon. This may be useful when a group of bonds contains some with very high coupons; high coupon bonds often trade ``cheap to the curve'', that is they have higher yields than corresponding bonds of the same maturity but lower coupon. This is usually because of reinvestment risk and, in some markets (including the UK), for tax reasons. For the reasons we have discussed the market often uses other types of yield curve for analysis when the Yield to Maturity yield curve is deemed unsuitable.
eBook - ePubIntroduction to Fixed Income Analytics
Relative Value Analysis, Risk Measures and Valuation
- Frank J. Fabozzi, Steven V. Mann(Authors)
- 2010(Publication Date)
- Wiley(Publisher)
CHAPTER 2Yield Curve AnalysisSpot Rates and Forward RatesA bond’s yield is a measure of its potential return given certain assumptions about how the future will unfold. The yield curve is the graphical depiction of the relationship between the Yield to Maturity and term to maturity for bonds that are alike in every other respect except term to maturity. When market participants refer to the “yield curve,” they usually mean the U.S. Treasury yield curve. A key function of the Treasury yield curve is to serve as a benchmark for pricing bonds and to determine yields in all other sectors of the debt market (e.g., corporate debt, mortgages, bank loans, etc.) This is also true in bond markets around the world where government securities often serve as benchmark securities for pricing other instruments. The purpose of this chapter is to develop the fundamental tools of yield curve analysis. We discuss par rates, spot rates, and forward rates—how they are computed, how they are related to each other, and how they are utilized by market participants.A BOND IS A PACKAGE OF ZERO-COUPON INSTRUMENTS
The traditional approach to valuation is to discount every cash flow of a fixed income security using the same interest or discount rate. The fundamental flaw of this approach is that it views each security as the same package of cash flows. For example, consider a 5-year U.S. Treasury note with a 6% coupon rate. The cash flows per $100 of par value would be nine payments of $3 every six months and $103 10 6-month periods from now. The traditional practice would discount every cash flow using the same discount rate regardless of when the cash flows are delivered in time and the shape of the yield curve. Finance theory tells us that any security should be thought of as a package or portfolio of zero-coupon bonds.7
eBook - PDFFundamentals of Financial Instruments
An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives
- Sunil K. Parameswaran(Author)
- 2022(Publication Date)
- Wiley(Publisher)
The current investment in the bond is $ P . An instant before the bond matures the investment in the security is $ M . Thus the average investment is ( M + P ) ÷ 2. The annual capital gain/loss computed by amortizing on a straight-line basis is M − P N 2 as we have seen in the case of the Japanese Yield. The approximate YTM is defined as: AYM = C + M − P N 2 M + P 2 The numerator in the expression represents the annual income for the investor, assuming of course that capital gains/losses are realized on a straight-line basis. The denominator, as we have explained, is the average investment during the life of the bond. Once the approximate yield is computed, we need to choose an interest rate band such that the upper limit gives a lower price than the observed price while the lower limit gives a higher price. The exact YTM is then obtained using linear interpolation. EXAMPLE 4.7 Consider a bond with a price of $925. The coupon is 7% per annum and the face value is $1,000. There are 10 years to maturity and the bond pays coupons on a semiannual basis. AYM = 70 + 1 , 000 − 925 20 2 1 , 000 + 925 2 = 0.08052 ≡ 8.052 % Let us choose a band of 7.75%–8.25%. The prices at the two extremes are 948.4675 and 915.9929. In this case the actual price lies in between the two extreme ( continued ) 150 BONDS ( continued ) prices. At times, however, we may end up choosing the interest rate band in such a way that the actual price is either higher than both the extreme values or lower than both. In such cases we have to redefine the band so that one of the corre-sponding prices is higher than the actual price while the other is lower. Now let us interpolate: 8.25%–7.75% corresponds to a price difference of 915.9929 – 948.4675. Thus 8.25% – y * should correspond to a price difference of 915.9929 – 925, where y * is the true YTM.
eBook - PDFBond and Money Markets
Strategy, Trading, Analysis
- Moorad Choudhry(Author)
- 2003(Publication Date)
- Butterworth-Heinemann(Publisher)
This feature can also be deduced from studying our convexity graph at Figure 7.1; when the initial yield level is high, a given change in interest rates produces a smaller change in 158 Part I: Introduction to the Bond Markets the price of the bond than when the initial yield level is lower. Market makers and portfolio managers are therefore aware of the fact that, when market yield levels are relatively high, the price volatility of bonds is comparatively low. 7.2 Duration 7.2.1 Basic concepts A plain vanilla coupon bond pays out a proportion of its return during the course of its life, in the form of coupon interest. If we were to analyse the properties of a bond, we should conclude quite quickly that its maturity gives us little indication of how much of its return is paid out during its life, nor any idea of the timing or size of its cash flows, and hence its sensitivity to moves in market interest rates. For example, if comparing two bonds with the same maturity date but different coupons, the higher coupon bond provides a larger proportion of its return in the form of coupon income than does the lower coupon bond. The higher coupon bond provides its return at a faster rate; its value is theoretically therefore less subject to subsequent fluctuations in interest rates. We may wish to calculate an average of the time to receipt of a bond’s cash flows, and use this measure as a more realistic indication of maturity. However cash flows during the life of a bond are not all equal in value, so a more accurate measure would be to take the average time to receipt of a bond’s cash flows, but weighted by the cash flows’ present value. This is, in effect, duration . We can measure the speed of payment of a bond, and hence its price risk relative to other bonds of the same maturity by measuring the average maturity of the bond’s cash flow stream.
eBook - PDF- Timothy Mayes(Author)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
13 Duration is a weighted average of the time to receive the cash flows of the bond in present value terms. Duration combines the effects of maturity, coupon rate, and yield into a single num- ber that we can use to measure the interest rate sensitivity of a bond. The longer the duration, the greater the interest rate risk of the bond. As you might imagine, this allows investors to quickly determine which bond will better suit their portfolio, given their expectations about future interest rate movements. Mathematically, Macaulay’s duration is calculated as: D Mac 5 a N t 5 1 Pmt t (1 1 YTM) t (t) V B (10-5) where Pmt t is the cash flow in period t, YTM is the per period (usually semiannual) Yield to Maturity, and V B is the current price. The fractional part of the numerator is the present value of each cash flow as a percentage of the bond’s price, which serves as the weighting in the average, and t is the number of periods until each cash flow is received. As with equation (10-1), this formula is only accurate on a payment date. 13. F. R. Macaulay, Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. New York: National Bureau of Economic Research, 1938. Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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