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Term Structure
Term structure refers to the relationship between the yields and maturities of fixed-income securities. It is often depicted in a yield curve, which shows the interest rates of bonds with different maturity dates. The term structure is important for businesses as it provides insights into future interest rate movements, which can impact borrowing costs and investment decisions.
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12 Key excerpts on "Term Structure"
eBook - ePubThe Creators of Inside Money
A New Monetary Theory
- D. Gareth Thomas(Author)
- 2018(Publication Date)
- Palgrave Macmillan(Publisher)
The Term Structure of interest rates, however, recognises a common link between them all in the form of expectations of the future, whether long or short, which determines the holding of various financial assets of maturity as well as influencing the determination of aggregate demand and supply within the real economy. The Term Structure, therefore, is important for Central Bank ’s policymakers. If these monetary instruments affect short-term rates of interest in the first instance, which leads to the determination of long-term rates of interest, which drives capital and consumption expenditure, then analysing the Term Structure is crucial for understanding the transmission mechanism of monetary policy (Fender 2012). 1 Nevertheless, it is also relevant for many households in terms of the portfolio choice of assets. Suppose a family requires expenditure on private school fees in ten years’ time and decides to save now. There are a number of options. They could save by investing into a ten-year bond. Alternatively, they could purchase a short-term bill and then take the earnings into another bond each time it matures, until the ten years are up. Clearly, the important components determining the choice will be the expected return (or cost) and the risk involved, embodied in the Term Structure. Therefore, the analysis must consider the various theoretical models put forward in the literature to explain the relationship between interest rates on bonds (or bills) of differing maturity, although the hypothesis can applied to other assets as diverse as housing and the mortgage rate. The foremost theory of the Term Structure of interest rates is the so-called expectations hypothesis, which focuses on the rôle of expectations of future short-term interest rates in the determination of prices and yields on longer-term bills (or bonds). There a number of ways in which the theory in the literature differs in terms of the length of the bills (or bonds) included in the analysis
eBook - PDF- Sudipto Bhattacharya, George Michael Constantinides(Authors)
- 2005(Publication Date)
- World Scientific(Publisher)
Econometrica, Vol. 53, No. 2 (March, 1985) A THEORY OF THE Term Structure OF INTEREST RATES' BY JOHN C. COX, JONATHAN E. INGERSOLL, JR., AND STEPHEN A. Ross This paper uses an intertemporal general equilibrium asset pricing model to study the Term Structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the Term Structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE Term Structure of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the Term Structure embodies the market's anticipations of future events. An explanation of the Term Structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the Term Structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis.
eBook - PDF- Roy E. Bailey(Author)
- 2005(Publication Date)
- Cambridge University Press(Publisher)
13 Term Structure of interest rates Overview Bonds share attributes – described in the previous chapter – that make them suitable for treatment as a class separate from, for instance, equities. While they may constitute a separate class, bonds are not homogeneous. Of the dimensions relevant for distinguishing among bonds, the time to maturity is one of the most important. It is on the relationship between each bond’s time to maturity and its rate of return that analysis of the Term Structure of interest rates focuses. A common way of representing the Term Structure is as a yield curve that depicts the yields on different bonds as a function of the number of years to maturity. Section 13.1 studies the construction of yield curves for nominal bonds – those with payoffs fixed in units of money – illustrated with a yield curve for British government bonds. The illustration is pursued further in section 13.2, which presents a yield curve for index-linked bonds – those with payoffs adjusted to protect against inflation. Section 13.2 also reviews how estimates of expected future inflation rates can be obtained by comparing the yield curves for nominal and index-linked bonds. Another way of expressing the Term Structure of interest rates is via a set of ‘implicit forward rates’ – interest rates that are implicit in, and can be inferred from, the prices of bonds with different maturities. Section 13.3 studies the role and interpretation of implicit forward rates. The remainder of the chapter explores the determinants of the Term Structure, beginning in section 13.4 with the ‘expectations hypothesis’, a theory central to all explanations of the yield curve’s shape. Central though it is, the expectations hypothesis is open to attack on several fronts, particularly for neglecting the impact of risk aversion on the decisions of bondholders and issuers. Section 13.5 discusses the implications for the Term Structure of allowing for risk aversion.
eBook - ePub- Oldrich A. Vasicek(Author)
- 2015(Publication Date)
- Wiley(Publisher)
Part Two Term Structure of Interest Rates The price at time t of a default-free zero-coupon bond with unit face value maturing at time s is given by the equation where is the short interest rate, is a Wiener process constituting a source of risk, and is the market price of risk. (page 38) Chapter 5 Introduction to Part II Interest rates are a function of time and term (time to maturity). As a function of time, rates behave as stochastic processes. As a function of term, interest rates on a given date form a yield curve. Term Structure models describe the behavior of interest rates of different maturities as a joint stochastic process. Term Structure models are a necessary tool for valuation and risk management of interest rate contingent claims—that is, securities or transactions whose payoff depends on future values of interest rates, such as callable or putable bonds, swaps, swaptions, caps, and floors. For instance, a bond will be called if its value on the call date is greater than the call price. To determine the current value of the bond, it is necessary to know the subsequent behavior of interest rates. The same is true for all debt securities subject to prepayment, such as mortgages with refinancing options. The immediate acceptance and application of Term Structure models in banking and investment practice is due to the fact that there are few financial instruments whose value is not in some degree dependent on future interest rates. Even stock options such as calls and puts depend on the development of interest rates. Interest rate models enter into valuation of firms and their liabilities. Besides valuation, Term Structure models are necessary for interest rate risk measurement, management, and hedging. Interest rates of different maturities behave as a joint stochastic process. Not all joint processes, however, can describe interest rate behavior in an efficient market
eBook - ePub- Friedrich A. Lutz, Friedrich Lutz(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
If a lender knows exactly how long his money will be available for investment, he can select the maturity date of the claim in such a way that he runs neither an income risk nor a capital risk. If he chooses a maturity date earlier than the point in time at which he needs cash, he will not run the risk of a capital loss since he can always invest his money a second time for the “correct” date, but he runs an income risk since the rate of interest obtainable on the second investment may be lower. If, on the other hand, he selects a maturity date later than the date on which he needs his money, his income from the investment will be certain, but not the capital value. Only the coincidence of the maturity date of the claim and the date of his need for cash will insure him simultaneously against both types of risk – that is, insure him against what we shall call yield risk (yield = interest plus capital gain or minus capital loss).If we assumed the relevant dates to be known and all participants in the market to be intent exclusively on avoiding any risk, the capital market would consist of a great number of tightly sealed compartments, one for each maturity date, in which the supply of and demand for bonds of each given maturity would determine the interest rate on these bonds irrespective of what happened in the other compartments. The Term Structure of interest rates would then be determined exclusively by the maturity structure in which debtors wanted to borrow money on the one hand, and on the other hand by the maturity structure in which owners of funds wanted to invest their money. If on the demand side the demand for long-term capital were to predominate and on the supply side the offer of short-term money, the long rates would come to lie above the short rates, and vice versa in the opposite case. Under the “expectation theory”, by contrast, the maturity structure of claims or debts has no influence at all on the Term Structure of interest rates as long as perfect foresight or at least the absence of risk aversion is assumed.It was Culbertson who more than anybody else stressed the maturity structure of debts as an important – although not the only – factor determining the Term Structure of interest rates.5 On this theory the rate structure can be influenced to a significant degree by the debt management policies of the government, as for instance when it shifts from short-term into long-term debt or vice versa. Changes in the economic structure also influence the structure of interest rates, since the length of time for which debts are incurred changes with the purpose for which borrowing is effected. Accordingly, Culbertson points out that “shifts in business and financial developments tend to be reflected in changes in the maturity structure of borrowing. Business inventory developments and securities speculation are reflected in changes in short-term borrowing; changes in automobile sales affect extensions of the intermediate-term credit commonly used in this area; changes in sales of new houses, in business fixed investment, in state and local government construction are reflected in demands for new long-term credit”.6
eBook - PDF- Brian Kettell(Author)
- 2001(Publication Date)
- Butterworth-Heinemann(Publisher)
56 Economics for Financial Markets corresponding to a 4 per cent yield, relative eagerness to sell securities (to borrow) would drive the price of securities down, and would drive the rate of interest up. Now let us drop the assumption about a single rate of interest and consider why it is that rates of interest or yields on different financial instruments vary. Why do some borrowers pay more than others? Why are the yields on long-dated securities different from those on short-dated ones? Why do interest rates on different currency denominated assets vary? It is to these questions that we now turn. The Term Structure of interest rates The Term Structure of interest rates, or maturity structure as it is sometimes referred to, refers to the set of theories designed to explain why practically homogeneous bonds of different maturities have different interest rates. The starting point for understanding the Term Structure theories is the present value concept (discussed in detail in Chapter 2). Because of the time value of money, one dollar received at a future date has a present value of less than one dollar. If we denote the present (that is, time 0) value of $1 received n periods from now by D n , then the interest rate is the discount rate (denoted by R n ) that solves the following equation. D n = 1 (1 + R n ) n (3.1) D n represents both the present value of $1 received in n period and the spot price of a zero coupon bond with a par value of $1. The purchaser of this zero coupon bond pays the purchase price D n at time zero and receives the par value of $1 at time n . The rate R n is called the zero coupon discount rate or the spot interest rate. The spot market is the market for immediate delivery. Some observers call the spot market the ‘cash’ market. The spot price D n and the spot interest rate R n are inversely related. When the spot interest rate goes up, the spot price goes down because the spot interest rate is the denominator.
eBook - ePubFixed Income Securities
Concepts and Applications
- Sunil Kumar Parameswaran(Author)
- 2019(Publication Date)
- De Gruyter(Publisher)
4 Yield Curves and the Term StructureAt any point in time, while taking a decision to invest in debt securities, an investor typically has access to a large number of bonds with different yields and varying times to maturity. Consequently, it is a common practice for investors and traders to examine the relationship between the yields on bonds belonging to a particular risk class. A plot of the yields of bonds that differ only with respect to their time to maturity, versus their respective times to maturity, is called a yield curve. The curve is an important indicator of the state of the bond market, and provides valuable information, to traders and analysts.While constructing the yield curve, it is very important to ensure that the data pertain to bonds of the same risk class, having comparable degrees of liquidity. For example, a curve may be constructed for government securities or AAA-rated corporate bonds, but not for a mixture of both. The primary yield curve in any domestic capital market is the government bond yield curve, for these instruments are free of default risk. In the U.S. debt market for instance, the primary yield curve is the U.S. Treasury yield curve.Analyzing the Yield Curve
The yield curve is an indicator of where the bond market is trading currently. It also has implications for what the market thinks will happen in the future.The yield curve sets the yield for all debt market instruments. First it fixes the price of money over the maturity structure. In practice, the yields of government bonds from the shortest maturity instrument to the longest set the benchmark for yields on all other debt instruments. This means that if a five-year government security is trading at a yield of 5%, all other five-year bonds, irrespective of the issuer, will be trading at yields over 5%. The excess over the yield on the corresponding government security is called the credit spread.The yield curve also acts as an indicator of future yield levels. It assumes certain shapes in response to market expectations of future interest rates. Market participants therefore analyze the current shape of the curve to determine the direction of future interest rates. The curve is scrutinized to divine information, not just by bond traders and fund managers, but also by corporate finance personnel. Traders and fund managers want to identify securities they believe are under-valued or over-valued so that they can take suitable investment decisions. Investment bankers handling new debt issues for their clients want to know the rate of return required by the market for debt securities of the risk class represented by a client. This enables them to set the coupon on the to-be-issued security. Central banks and government treasury departments also analyze the curve for its information content about future interest levels. This information is then used to set rates for the economy as a whole.
eBook - PDF- David S. Kidwell, David W. Blackwell, David A. Whidbee, Richard W. Sias(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
6.1 The Term Structure of Interest Rates 167 maturity and that they buy and sell securities consistent with these maturity preferences. As a result, the yield curve is determined by the supply of and the demand for securities at or near a particular maturity. Investors who desire short‐term securities, such as commer- cial banks, determine the short‐term yield curve; investors with preferences for intermedi- ate maturities determine the intermediate‐term yield curve; and investors who prefer long‐term securities, such as pension funds and life insurance companies, determine the long‐term yield curve. On the supply side, security issuers tailor the maturities of their security offerings to the length of time they need the borrowed funds (see Exhibit 6.3). EXHIBIT 6.2 The Effect of Liquidity Premiums on the Yield Curve Liquidity premiums increase as maturity increases. Thus, liquidity premiums cause an upward slope in market yield curves. Years to maturity Interest rate 5 0 10 15 Observed yield curve Liquidity premium Expectation theory yield curve EXHIBIT 6.3 Market‐Segmentation Yield Curve Market‐segmentation theory suggests that borrowers and lenders have strong preferences for securities of a particular maturity. As a result, the supply and demand for securities at or near a particular maturity determine the yield for that maturity. Years to maturity Yield D l S l D m S m S s D s Note: Supply (S) and demand (D) for s = short‐term maturities, m = intermediate‐term maturities, and l = long‐term maturities. 168 CHAPTER 6 The Structure of Interest Rates Thus, the market‐segmentation theory assumes that both issuers and investors have a pref- erence for securities with a narrow maturity range. Changes in interest rates in one segment of the yield curve, therefore, have little effect on interest rates in other maturities. Under the segmentation theory, discontinuities in the yield curve are possible.
No longer available |Learn more- Barbara S. Petitt(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Solution to 5: A is correct. Although the local expectations theory predicts that the short-run return for all bonds will be equal to the risk-free rate, most of the evidence refutes that claim. Returns from long-dated bonds are generally higher than those from short-dated bonds, even over relatively short investment horizons. This market evidence is consistent with the risk–expected return trade-off that is central to finance and the uncertainty surrounding future spot rates.5. Modern Term Structure Models
Modern Term Structure models provide quantitatively precise descriptions of how interest rates evolve. A model provides a sometimes simplified description of a real-world phenomenon on the basis of a set of assumptions; models are often used to solve particular problems. These assumptions cannot be completely accurate in depicting the real world, but instead, the assumptions are made to explain real-world phenomena sufficiently well to solve the problem at hand.Interest rate models attempt to capture the statistical properties of interest rate movements. The detailed description of these models depends on mathematical and statistical knowledge well outside the scope of the investment generalist’s technical preparation. Yet, these models are very important in the valuation of complex fixed-income instruments and bond derivatives. Thus, we provide a broad overview of these models in this chapter. Equations for the models and worked examples are given for readers who are interested.5.1. Equilibrium Term Structure Models
Equilibrium Term Structure models are models that seek to describe the dynamics of the Term Structure using fundamental economic variables that are assumed to affect interest rates. In the modeling process, restrictions are imposed that allow for the derivation of equilibrium prices for bonds and interest rate options. These models require the specification of a drift term (explained later) and the assumption of a functional form for interest rate volatility. The best-known equilibrium models are theEquilibrium Term Structure models share several characteristics:Cox–Ingersoll–Ross model10 and theVasicek model,11 which are discussed in the next two sections.- They are one-factor or multifactor models. One-factor models assume that a single observable factor (sometimes called a state variable) drives all yield curve movements. Both the Vasicek and CIR models assume a single factor, the short-term interest rate, r
eBook - ePub- Eliezer Z Prisman(Author)
- 2017(Publication Date)
- WSPC(Publisher)
m times per unit of time, will be the solution toThus, if the unit of time is half a year and the rates are reported per annum based on semiannual compounding, a dollar invested from time zero to time three is invested for 1.5 years and will grow to3.1.1 Zero-Coupon, Spot, and Yield Curves
The Term Structure, Zero-Coupon, and Spot Curves
The Term Structure is actually a function, which we will denote by r (t), that relates time to the interest rate prevailing in the market. For each t, r (t) is the interest rate per period (a year) paid for a dollar invested for t years, from time zero to time t. We keep our units of time measured in years and report the interest rate based on semiannual compounding. Hence, r (t) is the rate such that a dollar invested from time zero to time t will grow to beat time t. This function is referred to as the Term Structure of interest rates, and for each t the rate r (t) is called a spot rate.These are the rates paid on an investment over a period that starts now (on the spot) and ends at some future time t. The graph of this function is sometimes referred to as the spot curve or the zero-coupon curve. In what follows, we justify this name followed by a graphical representation of the Term Structure which will be explored shortly afterward.Certain bonds pay only one payment at the maturity time of the bond. These bonds are referred to as zero-coupon bonds, since they make no coupon payments. Furthermore, zero-coupon bonds are sold at a discount. The interest rate offered by such bonds is implicit in the difference between the face value of the bond and its market price. Namely, if the price of a zero-coupon bond maturing at time t, t years from now, is P and its face value is $100, the interest it pays is the solution r
eBook - PDF- R. Stafford Johnson(Author)
- 2013(Publication Date)
- Bloomberg Press(Publisher)
As a result, the prices of long-term securities tend to be more volatile and therefore more 166 Bond Evaluation and Selection risky than short-term securities. According to LPT, if investors were risk averse, then they would require some additional return (liquidity/risk premium) in order to hold long-term bonds instead of short-term ones. Thus, if the yield curve were initially flat, but had no risk premium factored in to compensate investors for the additional volatility they assumed from buying long-term bonds, then the demand for long-term bonds would decrease and their rates increase until risk-averse investors were compen- sated. In this case, the yield curve would become positively sloped. 8 Summary of Term Structure Theories The Term Structure of interest rates cannot be explained in terms of any one theory; rather, it is best explained by a combination of theories. Of the four theories, the two major ones are MST and PET. MST is important because it establishes how the fundamental market forces governing the supply and demand for assets deter- mine interest rates. PET, in turn, extends MST to show how expectations impact the structure of interest rates. PHT, by explaining how markets will adjust if the economy is poorly hedged, and LPT, by including a liquidity premium for longer- term bonds, both represent necessary extensions of MST and PET. Together, the four theories help us to understand how supply and demand, economic conditions, government deficits and surpluses, monetary policy, hedging, maturity preferences, and expectations all affect the bond market in general and the structure of rates in particular. Constructing the Benchmark Yield Curve Theoretical Spot Rate Curve Treasury yield curves are the standard benchmark for yields on other sectors. One of the problems in constructing a benchmark yield curve from observed Treasury yields is that many Treasuries with the same maturity carry different yields because they have different coupon rates.
eBook - PDF- (Author)
- 2022(Publication Date)
- Wiley(Publisher)
Chapter 7 The Term Structure and Interest Rate Dynamics 359 they interpreted as level, steepness, and curvature. The level movement refers to an upward or downward shift in the yield curve. The steepness movement refers to a non-parallel shift in the yield curve when either short-term rates change more than long-term rates or long-term rates change more than short-term rates. The curvature movement is a reference to movement in three segments of the yield curve: The short-term and long-term segments rise while the middle-term segment falls, or vice versa. Exhibit 11 illustrates these factors. EXHIBIT 11 Primary Yield Curve Factors: Level, Slope, and Curvature Yield (%) Term Term Slope Curvature Level In practice, the level movement factor explains most of the total changes in swap and bond market yields. This factor may be interpreted as a reflection of parallel yield curve moves in which rates move in the same direction and by a similar order of magnitude. The steepness factor addresses the shape of the curve, with short-term yields typically moving more than long-term yields. These changes take place over time and therefore explain less of the total variance in rates than the level factor. Finally, the third factor, curvature, tends to have a nega- tive impact on intermediate yields and a positive impact on short- and long-term yields. This variable explaining the “twist” in the yield curve has the smallest impact of the three. 8. THE MATURITY STRUCTURE OF YIELD CURVE VOLATILITIES AND MANAGING YIELD CURVE RISKS • explain the maturity structure of yield volatilities and their effect on price volatility 8.1. Yield Volatility Quantifying interest rate volatilities is important for fixed income managers for at least two reasons. First, most fixed-income instruments and derivatives have embedded options. Option values, and hence the values of the fixed-income instrument, crucially depend on the level of interest rate volatilities.
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