CH-5-6 Factors Affecting Bond Yields and the Term Structure of Interest Rates – Bond Markets, Analysis and Strategies : Book Guide

This Document Contains Chapters 5 to 6 CHAPTER 5 FACTORS AFFECTING BOND YIELDS AND THE TERM STRUCTURE OF INTEREST RATES CHAPTER SUMMARY In this chapter we look at the factors that affect the yield offered in the bond market. We begin with the minimum interest rate that an investor wants from investing in a bond, the yield on U.S. Treasury securities. Then we describe why the yield on a non-U.S. Treasury security will differ from that of a U.S. Treasury security. Finally, we focus on one particular factor that affects the yield offered on a security: maturity. The pattern of interest rates on securities of the same issuer but with different maturities is called the term structure of interest rates. BASE INTEREST RATE The securities issued by the U.S. Department of the Treasury are backed by the full faith and credit of the U.S. government. As such, interest rates on Treasury securities are the key interest rates in the U.S. economy as well as in international capital. The minimum interest rate that investors want is referred to as the base interest rate or benchmark interest rate that investors will demand for investing in a non-Treasury security. This rate is the yield to maturity (hereafter referred to as simply yield) offered on a comparable maturity Treasury security that was most recently issued (“on the run”). BENCHMARK SPREAD The difference between the yields of any two bonds is called a yield spread. For example, consider two bonds, bond A and bond B. The yield spread is then yield spread = yield on bond A – yield on bond B. The normal way that yield spreads are quoted is in terms of basis points. The yield spread reflects the difference in the risks associated with the two bonds. When bond B is a benchmark bond and bond A is a non-benchmark bond, the yield spread is referred to as a benchmark spread; that is, benchmark spread = yield on non-benchmark bond – yield on benchmark bond. The benchmark spread reflects the compensation that the market is offering for bearing the risks associated with the non-benchmark bond that do not exist for the benchmark bond. Thus, the benchmark spread can be thought of as a risk premium. Some market participants measure the risk premium on a relative basis by taking the ratio of the yield spread to the yield level. This measure, called a relative yield spread, is computed as follows: relative yield spread = (yield on bond A – yield on bond B) / yield on bond B. The yield ratio is the quotient of two bond yields: yield ratio = yield on bond A / yield on bond B. The factors that affect the yield spread include the type of issuer, the issuer’s perceived credit worthiness, the term or maturity of the instrument, provisions that grant either the issuer or the investor the option to do something, the taxability of the interest received by investors, the expected liquidity of the security. Types of Issuers The bond market is classified by the type of issuer, including the U.S. government, U.S government agencies, municipal governments, credit (domestic and foreign corporations), and foreign governments. These classifications are referred to as market sectors. Different sectors are generally perceived to represent different risks and rewards. Some market sectors are further subdivided into categories intended to reflect common economic characteristics. For example, within the credit market sector, issuers are classified as follows: industrial, utility, finance, and non-corporate. The spread between the interest rate offered in two sectors of the bond market with the same maturity is referred to as an intermarket sector spread. The spread between two issues within a market sector is called an intra market sector spread. Perceived Credit Worthiness of Issuer Default risk or credit risk refers to the risk that the issuer of a bond may be unable to make timely principal and/or interest payments. Most market participants rely primarily on commercial rating companies to assess the default risk of an issuer. The spread between Treasury securities and non-Treasury securities that are identical in all respects except for quality is referred to as a credit spread. Inclusion of Options It is not uncommon for a bond issue to include a provision that gives either the bondholder and/or the issuer an option to take some action against the other party. The presence of an embedded option has an effect on the spread of an issue relative to a Treasury security and the spread relative to otherwise comparable issues that do not have an embedded option. Taxability of Interest Because of the tax-exempt feature of municipal bonds, the yield on municipal bonds is less than that on Treasuries with the same maturity. The yield on a taxable bond issue after federal income taxes are paid is called the after-tax yield: after-tax yield = pretax yield × (1 – marginal tax rate) Alternatively, we can determine the yield that must be offered on a taxable bond issue to give the same after-tax yield as a tax-exempt issue. This yield, called the equivalent taxable yield: equivalent taxable yield = tax- exempt yield / (1 – marginal tax rate). The municipal bond market is divided into two major sectors: general obligations and revenue bonds. State and local governments may tax interest income on bond issues that are exempt from federal income taxes. Some municipalities’ exempt interest income from all municipal issues from taxation; others do not. Some states exempt interest income from bonds issued by municipalities within the state but tax the interest income from bonds issued by municipalities outside the state. Municipalities are not permitted to tax the interest income from securities issued by the U.S. Treasury. Thus part of the spread between Treasury securities and taxable non-Treasury securities of the same maturity reflects the value of the exemption from state and local taxes. Expected Liquidity of an Issue Bonds trade with different degrees of liquidity. Bonds with greater expected liquidity will have lower yields that investors would require. The lower yield offered on Treasury securities relative to non-Treasury securities reflects the difference in liquidity. Finance ability of an Issue A portfolio manager can use an issue as collateral for borrowing funds. By borrowing funds, a portfolio manager can create leverage. The typical market used by portfolio managers to borrow funds using a security as collateral for a loan is the repurchase agreement market or “repo” market. When a portfolio manager wants to borrow funds via a repo agreement, a dealer provides the funds. The interest rate charged by the dealer is called the repo rate. There is not one repo rate but a structure of rates depending on the maturity of the loan and the specific issue being financed. With respect to the latter, there are times when dealers are in need of particular issues to cover a short position. When a dealer needs a particular issue, that dealer will be willing to offer to lend funds at a lower repo rate than the general repo rate in the market. Term to Maturity The time remaining on a bond’s life is referred to as its term to maturity or simply maturity. The volatility of a bond’s price is dependent on its term to maturity. More specifically, with all other factors constant, the longer the term to maturity of a bond, the greater the price volatility resulting from a change in market yields. Generally, bonds are classified into three maturity sectors: Bonds with a term to maturity of between 1 to 5 years are considered short term; bonds with a term to maturity between 5 and 12 years are viewed as intermediate term; and long-term bonds are those with a term to maturity greater than 12 years. The spread between any two maturity sectors of the market is called a maturity spread. The relationship between the yields on otherwise comparable securities with different maturities is called the term structure of interest rates. TERM STRUCTURE OF INTEREST RATES The term structure of interest rates plays a key role in the valuation of bonds. Yield Curve The graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities is known as the yield curve. In the past, most investors have constructed yield curves from observations of prices and yields in the Treasury market. Two factors account for this tendency. First, Treasury securities are free of default risk, and differences in credit worthiness do not affect yields. Therefore, these instruments are directly comparable. Second, as the largest and most active bond market, the Treasury market offers the fewest problems of illiquidity or infrequent trading. The disadvantage, as noted previously, is that the yields may be biased downward because they reflect favorable financing opportunities. Market participants are coming to realize that the traditionally constructed Treasury yield curve is an unsatisfactory measure of the relation between required yield and maturity. The key reason is that securities with the same maturity may carry different yields. This phenomenon reflects the role and impact of differences in the bonds’ coupon rates. Why the Yield Curve Should Not Be Used to Price a Bond The price of a bond is the present value of its cash flow. The bond pricing formula assumes that one interest rate should be used to discount all the bond’s cash flows. Because of the different cash flow patterns, it is not appropriate to use the same interest rate to discount all cash flows. Instead, each cash flow should be discounted at a unique interest rate appropriate for the time period in which the cash flow will be received. The correct way to think about bonds is that they are packages of zero-coupon instruments. Each zero-coupon instrument in the package has a maturity equal to its coupon payment date or, in the case of the principal, the maturity date. The value of the bond should equal the value of all the component zero-coupon instruments. If this does not hold, it is possible for a market participant to generate riskless profits by stripping off the coupon payments and creating stripped securities. To determine the value of each zero-coupon instrument, it is necessary to know the yield on a zero-coupon Treasury with that same maturity. This yield is called the spot rate, and the graphical depiction of the relationship between the spot rate and maturity is called the spot rate curve. Because there are no zero-coupon Treasury debt issues with a maturity greater than one year, it is not possible to construct such a curve solely from observations of market activity on Treasury securities. Rather, it is necessary to derive this curve from theoretical considerations as applied to the yields of the actually traded Treasury debt securities. Such a curve is called a theoretical spot rate curve and is the graphical depiction of the term structure of interest rate. Constructing the Theoretical Spot Rate Curve for Treasuries A default-free theoretical spot rate curve can be constructed from the yield on Treasury securities. The Treasury issues that are candidates for inclusion are (i) on-the-run Treasury issues, (ii) on-the-run Treasury issues and selected off-the-run Treasury issues, (iii) all Treasury coupon securities, and bills, and (iv) Treasury coupon strips. After the securities that are to be included in the construction of the theoretical spot rate curve are selected, the methodology for constructing the curve must be determined. If Treasury coupon strips are used, the procedure is simple, because the observed yields are the spot rates. If the on-the-run Treasury issues with or without selected off-the-run Treasury issues are used, a methodology called bootstrapping is used. On-the-Run Treasury Issues The on-the-run Treasury issues are the most recently auctioned issue of a given maturity. These issues include the 3-month, 6-month, and 1-year Treasury bills; the 2-year, 5-year, and 10-year Treasury notes; and the 30-year Treasury bond. Treasury bills are zero-coupon instruments; the notes and the bond are coupon securities. There is an observed yield for each of the on-the-run issues. For the coupon issues, these yields are not the yields used in the analysis when the issue is not trading at par. Instead, for each on-the-run coupon issue, the estimated yield necessary to make the issue trade at par is used. The resulting on-the-run yield curve is called the par coupon curve. The goal is to construct a theoretical spot rate curve with 60 semiannual spot rates: 6 month rate to 30-year rate. Excluding the three-month bill, there are only six maturity points available when only on-the-run issues are used. The 52 missing maturity points are extrapolated from the surrounding maturity points on the par yield curve. The simplest interpolation method, and the one most commonly used, is linear extrapolation. Specifically, given the yield on the par coupon curve at two maturity points, the following is calculated: . Then, the yield for all intermediate semiannual maturity points is found by adding to the yield at the lower maturity the amount computed here. There are two problems with using just the on-the-run issues. First, there is a large gap between some of the maturities points, which may result in misleading yields for those maturity points when estimated using the linear interpolation method. Specifically, the concern is with the large gap between the five-year and 10-year maturity points and the 10-year and 30-year maturity points. The second problem is that the yields for the on-the-run issues themselves may be misleading because most offer the favorable financing opportunity in the repo market mentioned earlier. This means that the true yield is greater than the quoted (observed) yield. To overcome these problems, we convert the par yield curve into the theoretical spot rate curve using bootstrapping. To explain the process of estimating the theoretical spot rate curve from observed yields on Treasury securities, consider (i) a six-month Treasury bill where its annualized yield is the six-month spot rate and (ii) a one-year Treasury where its annualized yield is the one year spot rate. Given these two spot rates, we can compute the spot rate for a theoretical 1.5-year zero-coupon Treasury. The price of a theoretical 1.5-year zero-coupon Treasury should equal the present value of three cash flows from an actual 1.5-year coupon Treasury, where the yield used for discounting is the spot rate corresponding to the cash flow. We can solve for the theoretical 1.5-year spot rate. Doubling this rate, we can obtain the bond-equivalent yield, which is the theoretical 1.5-year spot rate. This rate is the rate that the market would apply to a 1.5-year zero-coupon Treasury security if, in fact, such a security existed. Given the theoretical 1.5-year spot rate, we can obtain the theoretical 2-year spot rate and so forth until we derive theoretical spot rates for the remaining 15 half-yearly rates. The spot rates using this process represent the term structure of interest rates. It would seem logical that the observed yield on strips could be used to construct an actual spot rate curve rather than go through the tedious computation procedure to get yields. There are three problems with using the observed rates on strips. First, the liquidity of the strips market is not as great as that of the Treasury coupon market. Thus, the observed rates on strips reflect a premium for liquidity. Second, the tax treatment of strips is different from that of Treasury coupon securities. Specifically, the accrued interest on strips is taxed even though no cash is received by the investor. Finally, there are maturity sectors in which non-U.S. investors find it advantageous to trade off yield for tax advantages associated with a strip. On-the-Run Treasury Issues and Selected Off-the-Run Treasury Issues One of the problems with using just the on-the-run issues is the large gaps between maturities, particularly after five years. To mitigate this problem, some dealers and vendors use selected off-the-run Treasury issues. All Treasury Coupon Securities and Bills Using only on-the-run issues, even when extended to include a few off-the-run issues, fails to recognize the information embodied in Treasury prices that are not included in the analysis. Thus, it is argued that it is more appropriate to use all Treasury coupon securities and bills to construct the theoretical spot rate curve. Treasury Coupon Strips Treasury coupon strips are zero-coupon Treasury securities. It would seem logical that the observed yield on strips could be used to construct an actual spot rate curve. There are three problems with using the observed rates on strips. First, the liquidity of the strips market is not as great as that of the Treasury coupon market. Second, the tax treatment of strips is different from that of Treasury coupon securities. Finally, there are maturity sectors in which non–U.S. investors find it advantageous to trade off yield for tax advantages associated with a strip. Using the Theoretical Spot Rate Curve Arbitrage forces a Treasury to be priced based on spot rates and not the yield curve. The ability of dealers to purchase securities and create value by stripping forces Treasury securities to be priced based on the theoretical spot rates. Spot Rates and the Base Interest Rate The base interest rate for a given maturity should not be seen as simply the yield on the on-the-run Treasury security for that maturity, but the theoretical Treasury spot rate for that maturity. To value a non-Treasury security, we should add a risk premium to the theoretical Treasury spot rates. Forward Rates From the yield curve we can extrapolate the theoretical spot rates. In addition, we can extrapolate what some market participants refer to as the market’s consensus of future interest rates. To illustrate, buying either a one-year instrument or a six-month instrument and when it matures in six months, buy another six-month instrument. Given the one-year spot rate, there is some rate on a six-month instrument six months from now that will make the investor indifferent between the two alternatives. We denote that rate by f which can be readily determined given the theoretical one-year spot rate and the six-month spot rate. Doubling f gives the bond-equivalent yield for the six-month rate six months from now in which we are interested. The market prices its expectations of future interest rates into the rates offered on investments with different maturities. This is why knowing the market’s consensus of future interest rates is critical. The rate that we determined for f is the market’s consensus for the six-month rate six months from now. A future interest rate calculated from either the spot rates or the yield curve is called a forward rate. Relationship Between Six-Month Forward Rates and Spot Rates In general, the relationship between a t-period spot rate (zt), the current six-month spot rate (z1), and the six month forward rates is zt = [(1 + z1) (1 + f1) (1 + f2) ··· (1 + ft –1)]1/t – 1 where ft is the six-month forward rate beginning t six-month periods from now. Other Forward Rates It is not necessary to limit ourselves to six-month forward rates. The spot rates can be used to calculate the forward rate for any time in the future for any investment horizon. Forward Rate as a Hedge able Rate A natural question about forward rates is how well they do at predicting future interest rates. The forward rate may never be realized but is important in what it tells investors about his expectation relative to what the market consensus expects. Some market participants prefer not to talk about forward rates as being market consensus rates. Instead, they refer to forward rates as being hedge able rates. For example, by buying the one-year security, the investor can hedge the six-month rate six months from now. Determinants of the Shape of the Term Structure If we plot the term structure—the yield to maturity, or the spot rate, at successive maturities against maturity—we find three typically shapes: an upward-sloping yield curve; a downward-sloping or inverted yield curve, or a flat yield curve. Two major theories have evolved to account for these observed shapes of the yield curve: expectations theories and market segmentation theory. There are several forms of the expectations theory: pure expectations theory, liquidity theory, and preferred habitat theory. Expectations theories share a hypothesis about the behavior of short-term forward rates and also assume that the forward rates in current long-term bonds are closely related to the market’s expectations about future short-term rates. These three theories differ, however, as to whether other factors also affect forward rates, and how. The pure expectations theory postulates that no systematic factors other than expected future short-term rates affect forward rates; the liquidity theory and the preferred habitat theory assert that there are other factors. Accordingly, the last two forms of the expectations theory are sometimes referred to as biased expectations theories. Pure Expectations Theory According to the pure expectations theory, the forward rates exclusively represent the expected future rates. Thus, the entire term structure at a given time reflects the market’s current expectations of the family of future short-term rates. Liquidity Theory The pure expectations theory states that investors will hold longer-term maturities if they are offered a long-term rate higher than the average of expected future rates by a risk premium that is positively related to the term to maturity. According to this theory, which is called the liquidity theory of the term structure, the implied forward rates will not be an unbiased estimate of the market’s expectations of future interest rates because they embody a liquidity premium. Preferred Habitat Theory The preferred habitat theory also adopts the view that the term structure reflects the expectation of the future path of interest rates as well as a risk premium. However, the preferred habitat theory rejects the assertion that the risk premium must rise uniformly with maturity. Market Segmentation Theory The market segmentation theory also recognizes that investors have preferred habitats dictated by the nature of their liabilities. However, the market segmentation theory differs from the preferred habitat theory in that it assumes that neither investors nor borrowers are willing to shift from one maturity sector to another to take advantage of opportunities arising from differences between expectations and forward rates. The Main Influences of the Shape of the Yield Curve Empirical evidence suggests that the three main influences on the shape of the Treasury yield curve are (1) the market’s expectations of future rate changes, (2) bond risk premiums, and (3) convexity bias. The convexity bias influence is the least well known of the three influences. The longer the maturity, the more convexity the security has. That is, longer-term Treasury securities have a more attractive feature due to convexity than shorter-term Treasury securities. As a result, investors are willing to pay more for longer-term Treasury securities and therefore accept lower returns. This influence on the shape of the Treasury yield curve is what is referred to as the convexity bias. RATE SWAP YIELD CURVE The basic elements of an interest rate swap are important for us to understand because it is a commonly used interest rate benchmark. In fact, the interest rate swap market in most countries is increasingly used as an interest rate benchmark despite the existence of a liquid government bond market. In a generic interest rate swap, the parties exchange interest rate payments on specified dates: one party pays a fixed rate and the other party pays a floating rate over the life of the swap. In a typical swap, the floating rate is based on a reference rate, and the reference rate is typically the London Interbank Offered Rate (LIBOR). LIBOR is the interest rate at which prime banks in London pay other prime banks on U.S. dollar certificates of deposits. The fixed interest rate that is paid by the fixed rate counterparty is called the swap rate. Dealers in the swap market quote swap rates for different maturities. The relationship between the swap rate and maturity of a swap is called the swap rate yield curve or, more commonly, the swap curve. Because the reference rate is typically LIBOR, the swap curve is also called the LIBOR curve. There is a swap curve for most countries. For Euro interest rate swaps, the reference rate is the Euro Interbank Offered Rate (Euribor), which is the rate at which bank deposits in countries that have adopted the euro currency and are member states of the European Union are offered by one prime bank to another prime bank. The swap curve is used as a benchmark in many countries outside the United States. Unlike a country’s government bond yield curve, however, the swap curve is not a default-free yield curve. Instead, it reflects the credit risk of the counterparty to an interest rate swap. One would expect that if a country has a government bond market, the yields in that market would be the best benchmark. That is not necessarily the case. There are several advantages of using a swap curve over a country’s government securities yield curve. First, there may be technical reasons why within a government bond market some of the interest rates may not be representative of the true interest rate but instead be biased by some technical or regulatory factor unique to that market. Second, to create a representative government bond yield curve, a large number of maturities must be available. Finally, the ability to compare government yields across countries is difficult because there are differences in the credit risk for every country. KEY POINTS • The price–yield relationship for all option-free bonds is convex. • There are three properties of the price volatility of an option-free bond: (1) for small changes in yield, the percentage price change is symmetric; (2) for large changes in yield, the percentage price change is asymmetric; and (3) for large changes in yield the price appreciation is greater than the price depreciation for a given change in yield. • In all economies, there is not just one interest rate but a structure of interest rates. • The difference between the yields on any two bonds is called the yield spread. When one of the two bonds is a benchmark bond, the yield spread is called a benchmark spread and reflects a risk premium. • The most commonly used benchmark in the United States is U.S. Treasury securities. • The factors that affect the spread include (1) the type of issuer (e.g., agency, corporate, municipality), (2) the issuer’s perceived credit worthiness as measured by the rating system of commercial rating companies, (3) the term or maturity of the instrument, (4) the embedded options in a bond issue (e.g., call, put, or conversion provisions), (5) the taxability of interest income at the federal and municipal levels, (6) the expected liquidity of the issue, and (7) the finance ability of an issue. • The credit spread is the yield spread or benchmark spread attributable to credit risk. The option-adjusted spread is the measure that is used to adjust for any options embedded in a bond issue. • The relationship between yield and maturity is referred to as the term structure of interest rates. The graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities is known as the yield curve. • There is a problem with using the Treasury yield curve to determine the one yield at which to discount all the cash payments of any bond. Each cash flow should be discounted at a unique interest rate that is applicable to the time period when the cash flow is to be received. Because any bond can be viewed as a package of zero-coupon instruments, its value should equal the value of all the component zero-coupon instruments. The rate on a zero-coupon bond is called the spot rate. The relationship between the spot rate and maturity is called the term structure of interest rates. • A default-free theoretical spot rate curve can be constructed from the yield on Treasury securities using either (1) only on-the-run Treasury issues, (2) on-the-run Treasury issues and selected off-the-run Treasury issues, (3) all Treasury coupon securities and bills, and (4) Treasury coupon strips. When the securities used are either (1) or (2), a method known as bootstrapping is used. More complex statistical techniques are used when all Treasury coupon securities and bills are used. • Under certain assumptions, the market’s expectation of future interest rates can be extrapolated from the theoretical Treasury spot rate curve. The resulting forward rate is called the implied forward rate. The spot rate is related to the current six-month spot rate and the implied six-month forward rates. • Several theories have been proposed about the determination of the term structure: pure expectations theory, the biased expectations theory (the liquidity theory and preferred habitat theory), and the market segmentation theory. All the expectation theories hypothesize that the one-period forward rates represent the market’s expectations of future actual rates. The pure expectations theory asserts that it is the only factor. The biased expectations theories assert that there are other factors. • Empirical evidence suggests that the three main influences on the shape of the Treasury yield curve are (1) the market’s expectations of future rate changes, (2) bond risk premiums, and (3) convexity bias. • The swap rate yield curve also provides information about interest rates in a country and is used as an interest rate benchmark. The swap rate yield curve, or simply swap curve or LIBOR curve, is not a default-free yield curve but rather reflects inter-bank credit risk. In many countries, market participants use the country’s swap curve as the benchmark interest rates rather than the country’s government bond yield curve. ANSWERS TO QUESTIONS FOR CHAPTER 5 (Questions are in bold print followed by answers.) 1. Following are U.S. Treasury benchmarks available on December 31, 2007: US/T 3.125 11/30/2009 3.133 US/T 3.375 11/30/2012 3.507 US/T 4.25 11/15/2017 4.096 US/T 4.75 02/15/2037 4.518 On the same day, the following trades were executed: Issuer Issue Yield (%) Time Warner Cable Inc. TWC 6.55 05/01/2037 6.373 McCormick & Co. Inc. MKC 5.75 12/15/2017 5.685 Goldman Sachs Group Inc. GS 5.45 11/01/2012 4.773 Based on the above, complete the following table: Issue Yield (%) Treasury Benchmark Benchmark Spread (bps) Relative Yield Spread Yield Ratio TWC 6.55 05/01/2037 6.373 MKC 5.75 12/15/2017 5.685 GS 5.45 11/01/2012 4.773 To finish the above table we first put in the Treasury benchmarks as given in the problem. For 05/01/2037, it is 4.518%; for 12/15/2017, it is 4.096%; and, for 11/01/2012, it is 3.507%. We can now compute the benchmark spread (bps) given as: benchmark spread = yield on issuer – yield on benchmark bond Inserting our values give the following benchmark spreads: benchmark spread (05/01/2037) = 6.373% – 4.518% = 1.855% benchmark spread (12/15/2017) = 5.685% – 4.096% = 1.589% benchmark spread (11/01/2012) = 4.773% – 3.507% = 1.266% We can now compute the relative yield spread given as: relative yield spread = (yield on issuer – yield on benchmark) / yield on benchmark Inserting our values give the following relative yield spreads: relative yield spread (05/01/2037) = (6.373% – 4.518%) / 4.518% = 41.085% or about 41% relative yield spread (12/15/2017) = (5.685% – 4.096%) / 4.096% = 38.794% or about 39% relative yield spread (11/01/2012) = (4.773% – 3.507%) / 3.507% = 36.099% or about 36% We can now compute the yield ratio given as: yield ratio = yield on issuer / yield on benchmark Inserting our values give the following relative yield spreads: yield ratio (05/01/2037) = 6.373% / 4.518% = 1.41058 (or about 1.41) yield ratio (12/15/2017) = 5.685% / 4.096% = 1.38794 (or about 1.39) yield ratio (11/01/2012) = 4.773% / 3.507% = 1.36099 (or about 1.36) Below we fill in the missing spaces in bold-face print. We have: Issue Yield (%) Treasury Benchmark Benchmark Spread (bps) Relative Yield Spread Yield Ratio TWC 6.55 05/01/2037 6.373 4.518 1.855 41% 1.41 MKC 5.75 12/15/2017 5.685 4.096 1.589 39% 1.39 GS 5.45 11/01/2012 4.773 3.507 1.266 36% 1.36 2. The yield spread between two corporate bond issues reflects more than just differences in their credit risk. What other factors would the spread reflect? In addition to the perceived riskiness of the issuer, other factors that affect the spread include the type of issuer, the term or maturity of the issue, embedded options, taxability of interest received by investors, and expected liquidity of the issue. 3. Why is an option-adjusted spread more suitable for a bond with an embedded option than a yield spread? A bond with an option can be broken down into both a bond and an option. Thus, it stands to reason that a spread for this type of bond should take into consideration the aspects of an option that can impact the spread. The option-adjusted spread is the measure that is used to adjust for any options embedded in a bond issue. For a bond with embedded options, its option-adjusted spread is the spread at which it presumably would be trading over a benchmark if it had no embedded optionality. More precisely, it is the instrument's current spread over the benchmark minus that component of the spread that is attributable to the cost of the embedded options. An option-adjusted spread can be calculated with respect to various benchmarks: Treasuries, swap rates, a short-term “risk-free” rate, and so forth. 4. Suppose a client observes the following two benchmark spreads for two bonds: Bond issue U rated A: 150 basis points Bond issue V rated BBB: 135 basis points Your client is confused because he thought the lower-rated bond (bond V) should offer a higher benchmark spread than the higher-rated bond (bond U). Explain why the benchmark spread may be lower for bond U. One would expect that absent any embedded options, the lower rated bond (bond V) would have a higher benchmark spread. For our situation, the opposite is observed in the market as the lower rated bond (bond V) has a lower benchmark spread. The reason could be one or both of the following. First, the higher rated bond (bond U) is callable. Hence, the benchmark spread reflects compensation for the call risk. Second, the lower rated bond (bond V) may be put able or may be convertible. Either of these embedded option features could result in a lower benchmark spread relative to the higher rated bond. For example, suppose bond V is a convertible bond. It is possible that if converted it could give the owner a much greater value and in fact could conceivably give more dividend than is currently being paid to the bondholder. These aspects in turn explain why the benchmark spread may be lower for bond V. 5. In the May 29, 1992, Weekly Market Update published by Goldman, Sachs & Co., the following information was reported in an exhibit for high-grade, tax-exempt securities as of the close of business Thursday, May 28, 1992: Maturity (years) Yield (%) Yield (%) as a Percentage of Treasury Yield 1 3.20 76.5 3 4.65 80.4 5 5.10 76.4 10 5.80 78.7 30 6.50 82.5 Answer the below questions. (a) What is meant by a tax-exempt security? A tax-exempt security is a security in which the investor is exempt from paying certain taxes. For example, purchasers of municipal bond issues are exempt from paying federal taxes. The tax-exempt aspect can affect the spread. For example, part of the spread between Treasury securities and taxable non-Treasury securities of the same maturity reflects the value of the exemption from state and local taxes. (b) What is meant by high-grade issue? By high-grade issue, we mean a security issue that has low credit risk. Higher bond ratings such as triple A, double A, and single A are associated with high quality and would be considered having low credit risk relative to lower ratings such as triple B, double B, single B and below. (c) Why is the yield on a tax-exempt security less than the yield on a Treasury security of the same maturity? The yield on a tax-exempt security is less because investors are excused from paying certain taxes (e.g., federal, state, or local). Thus, they can require a lower rate of return. (d) What is the equivalent taxable yield? The equivalent taxable yield is the yield that must be offered on a taxable bond issue to give the same after-tax yield as a tax-exempt issue. In equation form, we have: equivalent taxable yield = . (e) Also reported in the same issue of the Goldman, Sachs report is information on intra market yield spreads. What are these? An intra market yield spread is the spread between two issues within a market sector. Examples of market sectors include the U.S. government, U.S. government agencies, municipal governments, credit (domestic and foreign corporations), and foreign governments. 6. Answer the below questions. (a) What is an embedded option in a bond? An embedded option is an option found in a bond that includes a provision giving either the bondholder and/or the issuer an option to take some action against the other party. The action can involve an option that gives a right (but not the obligation) to buy or sell an asset at a price often called the exercise or strike price. The right to buy is called a call option while the right to sell is called a put option. (b) Give three examples of an embedded option that might be included in a bond issue. Below are three examples of an embedded option. Example one is a callable bond. A bond with a call provision gives the issuer the right to call the issue by redeeming it as a designated price. Example two is a bond convertible into common stock of the issuing company. A bond with a convertibility feature gives the lender the right to convert the bond into stock. Example three is a sinking fund bond. A sinking fund provision gives the issuing company the power to periodically retire part of the bond issue. It is like a call option except not all of the bonds are callable at once. The redemption schedule associated with a sinking fund provision involves a sequence of principal repayments prior to the maturity date. (c) Does an embedded option increase or decrease the risk premium relative to the base interest rate? An embedded option that works in favor of the issuer increases the risk premium relative to the base interest rate. An embedded option that works in favor of the borrower decreases the risk premium. Thus, an embedded option can either increase or decrease the risk premium relative to the base interest rate depending on who it favors. 7. Answer the below questions. (a) What is a yield curve? The yield curve is the graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities. The yield curve is usually constructed from observations of prices and yields in the Treasury market. (b) Why is the Treasury yield curve the one that is most closely watched by market participants? The Treasury yield curve is the yield curve most closely watched by market participants for several reasons. First, Treasury securities are free from default risk and so differences in credit worthiness do not affect yields making these instruments directly comparable. Second, the Treasury market is the largest and most active bond market offering the fewest problems in terms of illiquidity and infrequent trading. 8. What is a spot rate? The spot rate for a certain maturity is the yield on a zero-coupon Treasury of the same maturity. The graphical depiction of the relationship between the spot rate and maturity is called the spot rate curve. 9. Explain why it is inappropriate to use one yield to discount all the cash flows of a financial asset. Because cash flows from a financial asset can occur at different points in time, it is not correct to assume they will all have the same yield and thus should be discounted at the same interest rate. Each cash flow should be discounted at a unique interest rate appropriate for the period in which the cash flow will be received. Thus, the correct way to think about an asset is as a package of cash flows with each cash flow discounted by a rate appropriate for the period received. 10. Explain why a financial asset can be viewed as a package of zero-coupon instruments. A financial asset generates cash flows over time. The value of the asset is the present value of all the cash flows. Since each cash flow can occur at a different point in time, each cash flow should be valued in today’s dollar using a discount rate that reflects the required rate of return associated with that time period. Thus, each cash flow is like a zero-coupon bond where today’s value for the zero-coupon bond is the discounted value of the zero-coupon’s promised maturity value (e.g., cash flow at a point in time). The discount rate for the zero-coupon bond is its spot rate which can differ from one time period to the next. So too, the cash flows generated by the financial asset should have discount rates that differ from one time period to the next. 11. How are spot rates related to forward rates? Forward rates and spot rates are related because forward rates can be derived from spot rates. Forward rates are expected future spot rates that may differ from the actual spot rates that occur in the future. Spot rates can be used to compute the forward rate (or expected future spot rate) for any time in the future for any investment horizon. 12. You are a financial consultant. At various times you have heard comments on interest rates from one of your clients. How would you respond to each comment? (a) Respond to: “The yield curve is upward-sloping today. This suggests that the market consensus is that interest rates are expected to increase in the future.” This is not necessarily true because investors demand a greater return as the maturity increases. The maturity premium results from the fact that more uncertainty exists for longer term maturity. Other factors causing the yield curve to be upward-sloping include liquidity considerations and supply and demand concerns. For example, if investors wanted fewer longer term bonds than were currently being supplied, then this would drive up the yield on longer term bonds. (b) Respond to: “I can’t make any sense out of today’s term structure. For short-term yields (up to three years) the spot rates increase with maturity; for maturities greater than three years but less than eight years, the spot rates decline with maturity; and for maturities greater than eight years the spot rates are virtually the same for each maturity. There is simply no theory that explains a term structure with this shape.” There are various theories that can account for any slope that the yield curve might take. First, there is the pure expectations theory where the forward rates exclusively represent the expected future rates. Since these rates can either increase or decrease for any time period, the yield curve can be sloped upward or downward for that time period. Second, there is the liquidity preference theory which asserts that investors do not like uncertainty and so much be offered a higher rate of return for longer term maturities. Thus, the forward rate will not only reflect expectations about future interest rates but also a “liquidity” premium that will be higher for longer term securities. Ceteris paribus, an increasing liquidity premium implies that the yield curve will be upward sloping. The preferred habitat theory also adopts the view that the term structure reflects the expectation of the future path of interest rates as well as a risk premium. However, the preferred habitat theory rejects the assertion that the risk premium must rise uniformly with maturity. The preferred habitat theory asserts that to the extent that the demand and supply of funds in a given maturity range do not match, some lenders and borrowers will be induced to shift to maturities showing the opposite imbalances. However, they will need to be compensated by an appropriate risk premium whose magnitude will reflect the extent of aversion to either price or reinvestment risk. Thus this theory proposes that the shape of the yield curve is determined by both expectations of future interest rates and a risk premium, positive or negative, to induce market participants to shift out of their preferred habitat. Thus, according to this theory, yield curves sloping up, down, flat, or humped are all possible. The market segmentation theory also recognizes that investors have preferred habitats dictated by the nature of their liabilities. This theory also proposes that the major reason for the shape of the yield curve lies in asset-liability management constraints (either regulatory or self-imposed) and/or creditors (borrowers) restricting their lending (financing) to specific maturity sectors. However, the market segmentation theory differs from the preferred habitat theory in that it assumes that neither investors nor borrowers are willing to shift from one maturity sector to another to take advantage of opportunities arising from differences between expectations and forward rates. Thus for the segmentation theory, the shape of the yield curve is determined by supply of and demand for securities within each maturity sector. (c) Respond to: “When I want to determine the market’s consensus of future interest rates, I calculate the forward rates.” A future (expected) interest rate that can be computed from either the spot rates or the yield curve is called a forward rate. From the yield curve we can extrapolate the theoretical spot rates. In addition, we can extrapolate what some market participants refer to as the market's consensus of future interest rates. The market prices its expectations of future interest rates into the rates offered on investments with different maturities. A natural question about forward rates is how well they do at predicting future interest rates. Studies have demonstrated that forward rates do not do a good job in predicting future interest rates. However, from an investor’s point of view, forward rates indicate how their expectations must differ from the market's consensus in order to make the correct decision. For this reason, some market participants prefer not to talk about forward rates as being market consensus rates. Instead, they refer to forward rates as being hedge-able rates. 13. You observe the yields of the following Treasury securities (all yields are shown on a bond-equivalent basis): Year (Period) Yield to Maturity (%) Spot Rate (%) Year (Period) Yield to Maturity (%) Spot Rate (%) 0.5 (1) 5.25 5.25 5.5 (11) 7.75 7.97 1.0 (2) 5.50 5.50 6.0 (12) 8.00 8.27 1.5 (3) 5.75 5.76 6.5 (13) 8.25 8.59 2.0 (4) 6.00 ? 7.0 (14) 8.50 8.92 2.5 (5) 6.25 ? 7.5 (15) 8.75 9.25 3.0 (6) 6.50 ? 8.0 (16) 9.00 9.61 3.5 (7) 6.75 ? 8.5 (17) 9.25 9.97 4.0 (8) 7.00 ? 9.0 (18) 9.50 10.36 4.5 (9) 7.25 ? 9.5 (19) 9.75 10.77 5.0 (10) 7.50 ? 10.00 (20) 10.00 11.20 All the securities maturing from 1.5 years on are selling at par. The 0.5 and 1.0-year securities are zero-coupon instruments. Answer the below questions. (a) Calculate the missing spot rates. First, we compute the spot rate for year 2 by following the seven step procedure given below. Step One. Take the semiannual yield to maturity (coupon rate) for year two times $100 to get the cash flow for periods one through three. We have: (0.0600 / 2)$100 = $3.00 for t = 1, 2, and 3. Step Two. Get the appropriate semiannual discount rate that will be used to get the present value of each cash flow in Step One. These rates are the spot rates given spot rate column divided by two. We get: 0.0525 / 2 = 0.02625 for t = 1, 0.0550 / 2 = 0.02750 for t = 2, and 0.05759 / 2 = 0.028798 for t = 3. Step Three. Compute the sum of the present values of all of the cash flows in Step One using the appropriate discount rates from Step Two. We get cash flows of $2.92326 + $2.84156 + $2.75506 = $8.51989. Step Four. Subtract the sum of the present values of the cash flows in Step Three from $100. We get: $100.00 – $8.51989 = $91.48011. Step Five. Compute the cash flow in period 4 which is the $3.00 coupon payment plus the par value of $100 and divide this by the cash flow computed in Step Four. We get $103.00 / $91.48011 = 1.125928. Step Six. Take the value in Step Five to the one-fourth power and subtract one. The power is determined by dividing one by the period for which we are computing the spot rate which is period four. We get: 0.030096. Step Seven. Convert the value in Step Six to the bond-equivalent rate by multiplying by two and then converting to percentage form (by multiplying by 100). We get: 0.030096(2)(100) = 6.01917% or about 6.02%, which is the theoretical two-year spot rate. We now compute the spot rate for year 2.5 in a like manner noting that we are now working with one more period and using the spot rate just computed when discounting cash flows for period four. In Step One, we compute the cash flows for periods one through four using the semiannual coupon rate of 6.25% / 2 = 3.125% or 0.03125 for year 2.5. We get $3.125 for each cash flow. In Step Two, we gather all appropriate discount rates for each period (also incorporating the spot rate just computed for year two that will be used when discounting the cash flow for period four). For Step Three, we get: $11.6504 for the sum of the present values of all cash flows. In Step Four, we get $88.3496. In Step Five, we get 1.1672. In Step Six, we get 0.031411. In Step Seven, we get 6.2822% or about 6.28% which is the 2.5-year spot rate. We now compute the spot rate for period 3.0. In Step One, we get $3.25 for each cash flow. The values for Steps Three through Step Seven are: $14.9008, $85.0992, 1.2133, 0.03275, and 6.5495% or about 6.55% which is the 3.0-year spot rate. Similarly, we can compute the theoretical spot rates for the remaining four periods which are years 3.5, 4.0 , 4.5, and 5.0. Rounded off, we get the respective theoretical spot rates of 6.8213% for year 3.5, 7.0985% for year 4.0, 7.3815% for year 4.5, and 7.6712% for year 5.0. Below we fill in the missing spot rates in bold-face print (rounded-off to the nearest 0.01%). We have: Year (Period) Yield to Maturity (%) Spot Rate (%) Year (Period) Yield to Maturity (%) Spot Rate (%) 0.5 (1) 5.25 5.25 5.5 (11) 7.75 7.97 1.0 (2) 5.50 5.50 6.0 (12) 8.00 8.27 1.5 (3) 5.75 5.76 6.5 (13) 8.25 8.59 2.0 (4) 6.00 6.02 7.0 (14) 8.50 8.92 2.5 (5) 6.25 6.28 7.5 (15) 8.75 9.25 3.0 (6) 6.50 6.55 8.0 (16) 9.00 9.61 3.5 (7) 6.75 6.82 8.5 (17) 9.25 9.97 4.0 (8) 7.00 7.10 9.0 (18) 9.50 10.36 4.5 (9) 7.25 7.38 9.5 (19) 9.75 10.77 5.0 (10) 7.50 7.67 10.00 (20) 10.00 11.20 (b) What should the price of a 6% six-year Treasury security be? Following the process in part (a), we get respective spot rates for years 5.5 and 6.0 of 7.9684% and 8.2740%. These are more accurate than those given and can be used when computing the price of a 6% six-year Treasury security because we have to discount the cash flows for periods eleven and twelve by the appropriate discount rate (which are the theoretical spot rates for those two periods). With the twelve spot rates known, we can proceed to compute the price of the 6% six-year Treasury security. The price of this security is the present value of its cash flows. Per $100 par value, the semiannual coupon payment is $100(0.06 / 2) = $3.00. There will be twelve payments of $3.00 plus the payment of the par value of $100 received at the end of period twelve. As noted above, the appropriate discount rate for each of the twelve cash flows are the twelve spot rates that correspond to each of the twelve periods when cash flows are received. The present value of the twelve respective cash flows is: $2.9233, $2.8412, $2.7550, $2.6645, $2.5702, $2.4726, $2.3723, $2.2696, $2.1650, $2.0590, $1.9520, and $1.844. These total $28.8894. The present value of the $100 par value discounted at the theoretical spot rate of 4.1370% is $61.4808. Thus, the price of a 6% six-year Treasury security should be $90.3702 or about $90.37. [NOTE. The price of a zero-coupon Treasury security is the present value of its maturity value discounted using the theoretical semiannual spot rate for year six (period twelve). As seen above, the semiannual spot rate for a six-year Treasury security is 8.2740% / 2 = 4.1370%. Thus, per $100 of par value, we get: $100 / (1.041370)12 = $100(0.614808) = $61.48.] (c) What is the six-month forward rate starting in the sixth year? The six-month forward rate for period twelve can be computed by knowing the spot rates for periods twelve and thirteen. The 6-year spot rate at the beginning of year six (or period twelve) is 8.27%. The semiannual rate is 4.135%. The 6.5-year (or period-13) spot rate is 8.59% with a semiannual rate of 4.295%. The six-month forward rate at the start of the sixth year or twelfth period (f12) is the rate that will satisfy the following equation: f12 = . Inserting in our values, we get: f12 = = = 1.0623428 – 1 = 0.0623428 or about 6.2343%. The bond equivalent yield is 2(0.0623428) = 0.1246856 or about 12.4686%. [NOTE. We can check this out by considering two equal investment plans for a $100. The first plan is to invest $10,000 at the semiannual 6-year spot rate for 12 semiannual periods and then reinvest this amount at the six-month forward rate starting in year six. We get: $10,000(1.04135)12(1.062343%) = $17,275.29. The second plan is to invest $10,000 for 6.5 years at the 6.5-year semiannual spot rate, which is $10,000(1.04295)13 = $10,000(1.727529) = $17,275.29.] 14. You observe the following Treasury yields (all yields are shown on a bond equivalent basis): Year (Period) Yield to Maturity (%) Spot Rate (%) 0.5 (1) 10.00 10.00 1.0 (2) 9.75 9.75 1.5 (3) 9.50 9.48 2.0 (4) 9.25 9.22 2.5 (5) 9.00 8.95 3.0 (6) 8.75 8.68 3.5 (7) 8.50 8.41 4.0 (8) 8.25 8.14 4.5 (9) 8.00 7.86 5.0 (10) 7.75 7.58 5.5 (11) 7.50 7.30 6.0 (12) 7.25 7.02 6.5 (13) 7.00 6.74 7.0 (14) 6.75 6.46 7.5 (15) 6.50 6.18 8.0 (16) 6.25 5.90 8.5 (17) 6.00 5.62 9.0 (18) 5.75 5.35 9.5 (19) 5.50 ? 10.0 (20) 5.25 ? All the securities maturing from 1.5 years on are selling at par. The 0.5 and 1.0-year securities are zero-coupon instruments. Answer the below questions. (a) Calculate the missing spot rates. We use the seven step procedure described in Problem 13, part (a) to compute the theoretical 9.5-year spot rate. Step One. Take the semiannual yield to maturity (coupon rate) for year 9.5 times $100 to get the cash flow for periods one through eighteen. We have: (0.0550 / 2)$100 = $2.75 for t = 1 through 18. Step Two. Get the appropriate semiannual discount rate that will be used to get the present value of each cash flow in Step One. These rates are the annual spot rates given above divided by two. Step Three. Compute the sum of the present values of all of the cash flows in Step One using the appropriate discount rates from Step Two. We get $36.1660. Step Four. Subtract the sum of the present values of the cash flows in Step Three from $100. We get: $100.00 – $36.1660 = $63.8340. Step Five. Compute the cash flow in period 19 which is the $2.75 coupon payment plus the par value of $100 and divide this by the cash flow computed in Step Four. We get $102.75 / $63.8340 = 1.6096. Step Six. Take the value in Step Five to the one-nineteenth power and subtract one. The one-nineteenth power is determined by dividing one by the period for which we are computing the spot rate which is period nineteen. We get: 0.02537. Step Seven. Convert the value in Step Six to the bond-equivalent rate by multiplying by two and then converting to percentage form (by multiplying by 100). We get: 0.02537(2)(100) = 5.0740% or about 5.07%, which is the theoretical 6.5-year spot rate. Using the seven step procedure, we get the following values when computing the theoretical 10-year spot rate. For Step One, we get the coupon semiannual coupon payment of $2.625 for each period. The values for Steps Three through Seven are: $36.1529, $63.8471, 1.6074, 0.0240, and 4.8027%. Thus, the theoretical 10-year spot rate is about 4.80%. (b) What should the price of a 5% four-year Treasury security be? The price of a 5% four-year Treasure security is the present value of its cash flows. Per $100 par value, each cash flow is the semiannual coupon payment of $100(0.05 / 2) = $2.50. There will be eight payments of $2.50 plus the payment of the par value of $100 received at the end of period eight. The appropriate discount rates for each of the eight cash flows are the eight spot rates that correspond with each of the eight periods when cash flows are received. The present values of the eight respective cash flows are: $2.3810, $2.2730, $2.1757, $2.0876, $2.0085, $1.9375, $1.9738, and $1.8169. The sum of these cash flows is $16.5540. The present value of the $100 par value discounted at the theoretical spot rate of 4.07% is $72.6768. Thus, the price of a 5% four-year Treasury security should be $16.5540 + $72.6768 = $89.2308 or about $89.23. 15. What Treasury issues can be used to construct the theoretical spot rate curve? A default-free theoretical spot rate curve can be constructed from the yield on Treasury securities. The Treasury issues that are candidates for inclusion are (i) on-the-run Treasury issues, (ii) on-the-run Treasury issues and selected off-the-run Treasury issues, (iii) all Treasury coupon securities, and bills, and (iv) Treasury coupon strips. After the securities that are to be included in the construction of the theoretical spot rate curve are selected, the methodology for constructing the curve must be determined. If Treasury coupon strips are used, the procedure is simple, because the observed yields are the spot rates. If the on-the-run Treasury issues with or without selected off-the-run Treasury issues are used, a methodology called bootstrapping is used. 16. What are the problems with using only on-the-run Treasury issues to construct the theoretical spot rate curve? There are two problems with using just the on-the-run issues. First, there is a large gap between some of the maturities points, which may result in misleading yields for those maturity points when estimated using the linear interpolation method. Second, the yields for the on-the-run issues may be misleading because most offer the favorable financing opportunity in the repo market. 17. When all Treasury issues are used to construct the theoretical spot rate curve, what methodology is used to construct the curve? The extrapolation method can be used to form the on-the-run or par coupon curve from on-the-run observed Treasury yields (for each on-the-run coupon issue, the estimated yield necessary to make the issue trade at par is used). This method extrapolates the missing yields from the surrounding maturity points on the par yield curve. The simplest extrapolation method, and the one most commonly used, is linear extrapolation. Specifically, given the yield on the par coupon curve at two maturity points, the following is calculated: . Then, the yield for all intermediate semiannual maturity points is found by adding to the yield at the lower maturity the amount computed here. We run into problems if we use only on-the-run Treasury issues to construct the theoretical spot rate curve. For example, there is a large gap between some of the maturities points, and the yields for the on-the-run issues may be misleading because most offer the favorable financing opportunity in the repo market. To overcome these problems, we convert the par yield curve into the theoretical spot rate curve using bootstrapping. To explain the process of estimating the theoretical spot rate curve from observed yields on Treasury securities, consider a six-month Treasury bill where its annualized yield is the six-month spot rate and a one-year Treasury where its annualized yield is the one year spot rate. Given these two spot rates, the price of a theoretical 1.5-year zero-coupon Treasury should equal the present value of three cash flows from an actual 1.5-year coupon Treasury, where the yield used for discounting is the spot rate corresponding to the cash flow. Doubling the computed yield, we obtain the bond-equivalent yield, which is the theoretical 1.5-year spot rate. That rate is the rate that the market would apply to a 1.5-year zero-coupon Treasury security if, in fact, such a security existed. Given the theoretical 1.5-year spot rate, we can obtain the theoretical 2-year spot rate and so forth until we derive theoretical spot rates for the remaining 15 half-yearly rates. The spot rates using this process represent the term structure of interest rates. 18. Answer the below questions. (a) What are the limitations of using Treasury strips to construct the theoretical spot rate curve? There are three problems with using the observed rates on strips. First, the liquidity of the strips market is not as great as that of the Treasury coupon market. Thus, the observed rates on strips reflect a premium for liquidity. Second, the tax treatment of strips is different from that of Treasury coupon securities. Specifically, the accrued interest on strips is taxed even though no cash is received by the investor. Finally, there are maturity sectors in which non-U.S. investors find it advantageous to trade off yield for tax advantages associated with a strip. (b) When Treasury strips are used to construct the curve, why are only coupon strips used? By using only coupon strips, the biases would be consistent in terms of liquidity, tax treatment, and international demand factors. Also, simply using observed Treasury coupon strips is easier than going through tedious computation procedures to get spot rates. This simple procedure avoids using methodologies such as bootstrapping, which use on-the-run Treasury issues with or without selected off-the-run Treasury issues to construct a theoretical spot rate. There can be significant divergence between the coupon strips and the rates generated from bootstrapping after the six-year maturity point. When the on-the-run issues are supplemented with the 20-year and 25-year off-the-run issues, the theoretical spot rate curve comes closer to the coupon strips curve. We can come even closer to the coupon strips curve by using an exponential spline methodology. For this approach, the spot rates are closer to the coupon strips, particularly after the six-year maturity point. 19. What actions force a Treasury’s bond price to be valued in the market at the present value of the cash flows discounted at the Treasury spot rates? The price of a Treasury security should be equal to the present value of its cash flow where each cash flow is discounted at the theoretical spot rates. If this does not occur then an arbitrage situation develops where a large profit can be made with no risk involved. Thus, arbitrage forces a Treasury to be priced based on spot rates and not the yield curve. The ability of dealers to purchase securities and create value by stripping forces Treasury securities to be priced based on the theoretical spot rates. 20. Explain the role that forward rates play in making investment decisions. Although a forward rate may never be realized in practice, it is still important for investors because it tells them about their expectations relative to what the market consensus expects. This allows them to make decisions based upon the market expects. For example, forward rates indicate how an investor’s expectations must differ from the market’s consensus in order to make the correct decision. Some investors may not speak about forward rates as being market consensus rates. Instead, they refer to forward rates as being hedge-able rates. For example, by buying the one-year security, the investor can hedge the six-month rate six months from now. 21. “Forward rates are poor predictors of the actual future rates that are realized. Consequently, they are of little value to an investor.” Explain why you agree or disagree with this statement. To see the importance of knowing the market’s consensus for future interest rates, consider the following two investment alternatives for an investor who has a one-year investment horizon. Alternative 1 is to buy a one-year instrument. Alternative 2 is to buy a six-month instrument and then reinvest its value by purchasing another six-month instrument. With alternative 1, the investor will realize the one-year spot rate and that rate is known with certainty. In contrast, with alternative 2, the investor will realize the six-month spot rate, but the six-month rate six months from now is unknown. Therefore, for alternative 2, the rate that will be earned over one year is not known with certainty. The forward rate is the rate that will make the two alternatives equal. This rate is referred to as the market’s expected future six-month spot rate six months from now. By knowing this rate, an investor can make a decision as to what (s)he thinks about future spot rates. For example, suppose the investor expects that six months from now, the six-month rate will be lower than the forward rate. If so, then the investor will choose alternative 1. Thus, knowing the forward rate does have practical value for an investor even if the forward rate is hindsight is not accurate. 22. Bart Simpson is considering two alternative investments. The first alternative is to invest in an instrument that matures in two years. The second alternative is to invest in an instrument that matures in one year and at the end of one year, reinvest the proceeds in a one-year instrument. He believes that one-year interest rates one year from now will be higher than they are today and therefore is leaning in favor of the second alternative. What would you recommend to Bart Simpson? Bart has two choices. Choice 1 is to buy a two-year instrument. Choice 2 is to buy a one-year instrument and then reinvest its value by purchasing another one-year instrument. With choice 1, the Bart will realize the two-year spot rate and that rate is known with certainty. In contrast, with choice 2, the Bart will realize the one-year spot rate, but the one-year rate one year from now is unknown. Therefore, for choice 2, the rate that will be earned over two years is not known with certainty. The one-year forward rate is the rate that will make the two choices equal. This rate is referred to as the market’s expected future one-year spot rate one year from now. By knowing this rate, Bart can make a decision as to what he thinks about future spot rates. For example, suppose the Bart expects that one year from now, the one year spot rate will be higher than the forward rate. If so, then the Bart will choose choice 2. However, this rate must be higher than the forward rate and not just higher than the rate Bart may have in mind. Thus, Bart should be careful. It is just not enough to believe rates will be higher. There is a certain threshold (the forward rate) that must be met before anyone considers a rollover strategy connected with alternative 2. 23. Answer the below questions. (a) What is the common hypothesis about the behavior of short-term forward rates shared by the various forms of the expectations theory? There are several forms of the expectations theory: pure expectations theory, liquidity theory, and preferred habitat theory. Expectations theories share a hypothesis about the behavior of short-term forward rates are related to expected future short-term rates. These theories also assume that the forward rates in current long-term bonds are closely related to the market’s expectations about future short-term rates. These three theories differ, however, as to whether other factors also affect forward rates, and how. The pure expectations theory postulates that no systematic factors other than expected future short-term rates affect forward rates; the liquidity theory and the preferred habitat theory assert that there are other factors. Accordingly, the last two forms of the expectations theory are sometimes referred to as biased expectations theories. (b) What is price risk and reinvestment risk and how do these two risks affect the pure expectations theory? There are two risks that cause uncertainty about the return over some investment horizon: price risk and reinvestment risk. Let’s begin by describe price risk. Price risk is the uncertainty about the price of the bond at the end of the investment horizon. For example, an investor who plans to invest for four years might consider the following three investment alternatives: (i) invest in a four-year bond and hold it for four years, (ii) invest in an 8-year bond and sell it at the end of four years, and (iii) invest in a 16-year bond and sell it at the end of four years. The return that will be realized for the second and third alternatives is not known because the price of each long-term bond at the end of four years is not known. In the case of the 8-year bond, the price will depend on the yield on four-year debt securities four years from now; and the price of the 16-year bond will depend on the yield on 12-year bonds four years from now. Because forward rates implied in the current term structure for a future 8-year bond and a future 16-year bond are not perfect predictors of the actual future rates, there is uncertainty about the price for both bonds five years from now. Thus there is price risk, that is, the risk that the price of the bond will be lower than currently expected at the end of the investment horizon. An important feature of price risk is that it is greater the longer the maturity of the bond. The second risk has to do with the uncertainty about the rate at which the proceeds from a bond can be reinvested until the expected maturity date: that is, reinvestment risk. For example, an investor who plans to invest for four years might consider the following three alternative investments: (i) invest in a four-year bond and hold it for four years, (ii) invest in a six-month instrument and when it matures, reinvest the proceeds in six-month instruments over the entire four-year investment horizon, and (iii) invest in a two-year bond and when it matures, reinvest the proceeds in a two-year bond. The risk in the second and third alternatives is that the return over the four-year investment horizon is unknown because rates at which the proceeds can be reinvested until maturity are unknown. (c) Give three interpretations of the pure expectations theory. There are several interpretations of the pure expectations theory that have been put forth by economists. These interpretations are not exact equivalents nor are they consistent with each other, in large part because they offer different treatments of price risk and reinvestment associated with realizing a return. The broadest interpretation of the pure expectations theory suggests that investors expect the return for any investment horizon to be the same, regardless of the maturity strategy selected. For example, consider an investor who has a five-year investment horizon. According to this theory, it makes no difference if a five-year, 12-year, or 30-year bond is purchased and held for five years because the investor expects the return from all three bonds to be the same over five years. A major criticism of this very broad interpretation of the theory is that, because of price risk associated with investing in bonds with a maturity greater than the investment horizon, the expected returns from these three very different bond investments could differ in significant ways. A second interpretation, referred to as the local expectations theory, a form of pure expectations theory, suggests that the returns on bonds of different maturities will be the same over a short-term investment horizon. For example, if an investor has a six-month investment horizon, buying a 5-year, 10-year, or 20-year bond will produce the same six-month return. It has been demonstrated that the local expectations formulation, which is narrow in scope, is the only one of the interpretations of the pure expectations theory that can be sustained in equilibrium. A third interpretation of the pure expectations theory suggests that the return that an investor will realize by rolling over short-term bonds to some investment horizon will be the same as holding a zero-coupon bond with a maturity that is the same as that investment horizon. (Because a zero-coupon bond has no reinvestment risk, future interest rates over the investment horizon do not affect the return.) This variant is called the return-to-maturity expectations interpretation. For example, let’s assume that an investor has a five-year investment horizon. By buying a five-year zero-coupon bond and holding it to maturity, the investor’s return is the difference between the maturity value and the price of the bond, all divided by the price of the bond. According to return-to-maturity expectations, the same return will be realized by buying a six-month instrument and rolling it over for five years. Most people have grave problems with the validity of this theory simply due to the unknown nature of future interest rates when assets are rolled over. 24. Answer the below questions. (a) What are the two biased expectations theories about the term structure of interest rates? The two biased expectations theories are the liquidity theory and the preferred habitat theory. They are considered “biased” because they argue that factors, other than the market’s expectations about future rates, affect forward rates. (b) What are the underlying hypotheses of these two theories? The liquidity theory states that investors will hold longer-term maturities if they are offered a long-term rate higher than the average of expected future rates by a risk premium that is positively related to the term to maturity. Put differently, the forward rates should reflect both interest-rate expectations and a “liquidity” premium (really a risk premium), and the premium should be higher for longer maturities. The preferred habitat theory also adopts the view that the term structure reflects the expectation of the future path of interest rates as well as a risk premium. However, the preferred habitat theory rejects the assertion that the risk premium must rise uniformly with maturity. The market segmentation theory also recognizes that investors have preferred habitats dictated by the nature of their liabilities. However, the market segmentation theory differs from the preferred habitat theory in that it assumes that neither investors nor borrowers are willing to shift from one maturity sector to another to take advantage of opportunities arising from differences between expectations and forward rates. 25. Answer the below questions. (a) “Empirical evidence suggests that with respect to bond risk premiums that influence the shape of the Treasury yield curve, there is a linear relationship between Treasury average returns and duration.” Explain whether you agree or disagree with this statement. If you disagree, explain the type of relationship that has been observed. Based on empirical evidence, one would disagree with the statement because it has been shown that there is a nonlinear relation between Treasury average returns (as represented by bond risk premium) and duration (which is a measure of the price sensitivity of a bond to changes in interest rates). More details are supplied below including the observed linear relation between duration and the theoretical expected return curve. Ilmanen investigated the effect of the behavior of the bond risk premium using historical average returns on U.S. Treasury securities. Exhibit 5-12 shows the empirical average return curve as a function of average duration (not maturity) for the period 1972 to 2001. Exhibit 5-12 is the theoretical expected return curve based on expectations only (the first influence listed above). Notice that this curve is linear (i.e., it increases linearly with duration). In contrast, notice that the empirical evidence suggests that the bond risk premiums are not linear in duration. Instead, the empirical evidence suggests that at the front-end of the yield curve (i.e., up to a duration of 3), bond risk premiums increase steeply with duration. However, after a duration of 3, the bond risk premiums increase slowly. Ilmanen suggests that the shape shown in Exhibit 5-12 “may reflect the demand for long-term bonds from pension funds and other long-duration liability holders.” (b) What is meant by the “convexity bias” influence on the shape of the Treasury yield curve? Empirical evidence suggests that the three main influences on the shape of the Treasury yield curve are (1) the market’s expectations of future rate changes, (2) bond risk premiums, and (3) convexity bias. The convexity bias influence, according to Ilmanen, is the least well known of the three influences. Recall that convexity implies that when interest rates change by a large number of basis points, a Treasury security’s price change will not be the same for an increase and decrease in interest rates. More specifically, the price appreciation when interest rates fall will be greater than the price decline when interest rates rise by the same number of basis points. For example, if interest rates decline by 100 basis points, the price of a Treasury security might appreciate by 20%, but if interest rates increase by 100 basis points, the price of the same Treasury security might decline by only 15%. This attractive property of a bond is due to the shape of the relationship between price and yield and is referred to the bond’s convexity. The longer the maturity, the more convexity the security has. That is, longer-term Treasury securities have a more attractive feature due to convexity than shorter-term Treasury securities. As a result, investors are willing to pay more for longer-term Treasury securities and therefore accept lower returns. This influence on the shape of the Treasury yield curve is what is referred to as the convexity bias. 26. Answer the below questions. a. What is meant by the swap rate? The fixed interest rate that is paid by the fixed rate counterparty is called the swap rate. Dealers in the swap market quote swap rates for different maturities. b. What is meant by the swap curve? The relationship between the swap rate and maturity of a swap is called the swap rate yield curve or, more commonly, the swap curve. Because the reference rate is typically LIBOR, the swap curve is also called the LIBOR curve. c. Explain whether you agree or disagree with the following statement: “A country’s swap curve is a default-free yield curve.” The swap rate yield curve, or simply swap curve or LIBOR curve, provides information about interest rates in a country and is used as an interest rate benchmark. This swap curve is not a default-free yield curve because it reflects inter-bank credit risk. Unlike a country’s government bond yield curve, the swap curve reflects the credit risk of the counterparty to an interest rate swap. Since the counterparty to an interest rate swap is typically a bank-related entity, the swap curve reflects the average credit risk of representative banks that provide interest rate swaps. 27. Why do market participants in some countries prefer to use the swap curve rather than the government bond yield curve? In many countries, market participants use the country’s swap curve as the benchmark interest rates rather than the country’s government bond yield curve. In recent years the liquidity of the interest rate swap has increased to the point where it is now a more liquid market than the market for some government bonds. One would expect that if a country has a government bond market, the yields in that market would be the best benchmark. That is not necessarily the case. Below we give three advantages of using a swap curve over a country’s government securities yield curve. First, there may be technical reasons why within a government bond market some of the interest rates may not be representative of the true interest rate but instead be biased by some technical or regulatory factor unique to that market. Second, to create a representative government bond yield curve, a large number of maturities must be available. Finally, the ability to compare government yields across countries is difficult because there are differences in the credit risk for every country. 28. A client observes that a corporate bond that he is interested in purchasing with a triple A rating has a benchmark spread that is positive when the benchmark is U.S. Treasuries but negative when the benchmark is the LIBOR curve. The client asks you why. Provide an explanation. The LIBOR or swap curve reflects more risk than the U.S. Treasuries benchmark curve which is a default-free yield curve. In brief, the LIBOR curve reflects inter-bank credit risk. Unlike a country’s government bond yield curve, the swap curve reflects the credit risk of the counterparty to an interest rate swap. Thus, this creates the possibility of a large enough credit risk that can explain why the client observes that a corporate bond with a triple A rating has a negative benchmark spread when the benchmark is the LIBOR curve. CHAPTER 6 TREASURY AND FEDERAL AGENCY SECURITIES CHAPTER SUMMARY The second largest sector of the bond market (after the mortgage market) is the market for U.S. Treasury securities. One of the smallest sector is the U.S. government agency securities market. We discuss these two sectors together in this chapter. As explained in Chapter 11, a majority of the securities backed by a pool of mortgages are guaranteed by a federally sponsored agency of the U.S. government. These securities are classified as part of the mortgage-backed securities market rather than as U.S. government agency securities. TREASURY SECURITIES Two factors account for the prominent role of U.S. Treasury securities: volume (in terms of dollars outstanding) and liquidity. The Department of the Treasury is the largest single issuer of debt in the world. The large volume of total debt and the large size of any single issue have contributed to making the Treasury market the most active and hence the most liquid market in the world. The dealer spread between bid and ask price is considerably narrower than in other sectors of the bond market. All Treasury securities are noncallable. Therefore, investors in Treasury securities are not subject to call risk. Types of Treasury Securities The Treasury issues marketable and nonmarketable securities. Our focus here is on marketable securities. Marketable Treasury securities are categorized as fixed-principal securities or inflation-indexed securities. Fixed-income principal securities include Treasury bills, Treasury notes, and Treasury bonds. Treasury bills are issued at a discount to par value, have no coupon rate, and mature at par value. The current practice of the Treasury is to issue all securities with a maturity of one year or less as discount securities. As discount securities, Treasury bills do not pay coupon interest. Instead, Treasury bills are issued at a discount from their maturity value; the return to the investor is the difference between the maturity value and the purchase price. All securities with initial maturities of two years or more are issued as coupon securities. Coupon securities are issued at approximately par and, in the case of fixed-principal securities, mature at par value. Treasury coupon securities issued with original maturities of more than one year and no more than 10 years are called Treasury notes. Treasury coupon securities with original maturities greater than 10 years are called Treasury bonds. Callable bonds have not been issued since 1984. The U.S. Department of the Treasury issues Treasury securities that adjust for inflation. These securities are popularly referred to as Treasury inflation protection securities, or TIPS. The principal that the Treasury Department will base both the dollar amount of the coupon payment and the maturity value on is adjusted semiannually. This is called the inflation-adjusted principal. The Treasury Auction Process Treasury securities are sold in the primary market through sealed-bid auctions. Each auction is announced several days in advance by means of a Treasury Department press release or press conference. The announcement provides details of the offering, including the offering amount and the term and type of security being offered, and describes some of the auction rules and procedures. Treasury auctions are open to all entities. The auction for Treasury securities is conducted on a competitive bid basis. There are actually two types of bids that may be submitted by a bidder: noncompetitive bids and competitive bids. A noncompetitive bid is submitted by an entity that is willing to purchase the auctioned security at the yield that is determined by the auction process. When a noncompetitive bid is submitted, the bidder only specifies the quantity sought. The quantity in a noncompetitive bid may not exceed $5 million. A competitive bid specifies both the quantity sought and the yield at which the bidder is willing to purchase the auctioned security. The competitive bids are then arranged from the lowest yield bid to the highest yield bid submitted. The highest yield accepted by the Treasury is referred to as the stop-out yield (or high yield). Bidders whose bid is higher than the stop-out yield are not distributed any of the new issue (i.e., they are unsuccessful bidders). Bidders whose bid was the stop-out yield (i.e., the highest yield accepted by the Treasury) are awarded a proportionate amount for which they bid. Secondary Market The secondary market for Treasury securities is an over-the-counter market where a group of U.S. government securities dealers offer continuous bid and ask prices on outstanding Treasuries. There is virtual 24-hour trading of Treasury securities. The three primary trading locations are New York, London, and Tokyo. The normal settlement period for Treasury securities is the business day after the transaction day (“next day” settlement). The most recently auctioned issue is referred to as the on-the-run issue or the current issue. Securities that are replaced by the on-the-run issue are called off-the-run issues. At a given point in time there may be more than one off-the-run issue with approximately the same remaining maturity as the on-the-run issue. Treasury securities are traded prior to the time they are issued by the Treasury. This component of the Treasury secondary market is called the when-issued market, or wi market. When-issued trading for both bills and coupon securities extends from the day the auction is announced until the issue day. Government dealers trade with the investing public and with other dealer firms. When they trade with each other, it is through intermediaries known as interdealer brokers. Dealers leave firm bids and offers with interdealer brokers who display the highest bid and lowest offer in a computer network tied to each trading desk and displayed on a monitor. Dealers use interdealer brokers because of the speed and efficiency with which trades can be accomplished. Price Quotes for Treasury Bills The convention for quoting bids and offers is different for Treasury bills and Treasury coupon securities. Bids and offers on Treasury bills are quoted in a special way. Unlike bonds that pay coupon interest, Treasury bill values are quoted on a bank discount basis, not on a price basis. The quoted yield on a bank discount basis is not a meaningful measure of the return from holding a Treasury bill. There are two reasons for this. First, the measure is based on a face-value investment rather than on the actual dollar amount invested. Second, the yield is annualized according to a 360-day rather than a 365-day year, making it difficult to compare Treasury bill yields with Treasury notes and bonds, which pay interest on a 365-day basis. The measure that seeks to make the Treasury bill quote comparable to Treasury notes and bonds is called the bond equivalent yield. The CD equivalent yield (also called the money market equivalent yield) makes the quoted yield on a Treasury bill more comparable to yield quotations on other money market instruments that pay interest on a 360-day basis. It does this by taking into consideration the price of the Treasury bill rather than its face value. Quotes on Treasury Coupon Securities Treasury coupon securities are quoted in a different manner than Treasury bills—on a price basis in points where one point equals 1% of par. The points are split into units of 32nds, so that a price of 96–14, for example, refers to a price of 96 and 14 32nds, or 96.4375 per 100 of par value. The 32nds are themselves often split by the addition of a plus sign or a number. In addition to price, the yield to maturity is typically reported alongside the price. When an investor purchases a bond between coupon payments, if the issuer is not in default, the investor must compensate the seller of the bond for the coupon interest earned from the time of the last coupon payment to the settlement date of the bond. This amount is called accrued interest. When calculating accrued interest, three pieces of information are needed: (i) the number of days in the accrued interest period, (ii) the number of days in the coupon period, and (iii) the dollar amount of the coupon payment. The number of days in the accrued interest period represents the number of days over which the investor has earned interest. The calculation of the number of days in the accrued interest period and the number of days in the coupon period begins with the determination of three key dates: the trade date, settlement date, and date of previous coupon payment. The trade date is the date on which the transaction is executed. The settlement date is the date a transaction is completed. For Treasury securities, settlement is the next business day after the trade date. Interest accrues on a Treasury coupon security from and including the date of the previous coupon payment up to but excluding the settlement date. The number of days in the accrued interest period and the number of days in the coupon period may not be simply the actual number of calendar days between two dates. For Treasury coupon securities, the day count convention used is to determine the actual number of days between two dates. This is referred to as the actual/actual day count convention. STRIPPED TREASURY SECURITIES The Treasury does not issue zero-coupon notes or bonds. However, because of the demand for zero-coupon instruments with no credit risk, the private sector has created such securities. In August 1982, both Merrill Lynch and Salomon Brothers created synthetic zero-coupon Treasury receipts. Merrill Lynch marketed its Treasury receipts as Treasury Income Growth Receipts (TIGRs), and Salomon Brothers marketed its receipts as Certificates of Accrual on Treasury Securities (CATS). The procedure was to purchase Treasury bonds and deposit them in a bank custody account. The firms then issued receipts representing an ownership interest in each coupon payment on the underlying Treasury bond in the account and a receipt for ownership of the underlying Treasury bond’s maturity value. This process of separating each coupon payment, as well as the principal (called the corpus), and selling securities against them is referred to as coupon stripping. Other investment banking firms followed suit by creating their own receipts. They all are referred to as trademark zero-coupon Treasury securities because they are associated with particular firms. In February 1985, the Treasury announced its Separate Trading of Registered Interest and Principal of Securities (STRIPS) program to facilitate the stripping of designated Treasury securities. Today, all Treasury notes and bonds (fixed-principal and inflation indexed) are eligible for stripping. The zero-coupon Treasury securities created under the STRIPS program are direct obligations of the U.S. government. Moreover, the securities clear through the Federal Reserve’s book-entry system. Creation of the STRIPS program ended the origination of trademarks and generic receipts. On dealer quote sheets and vendor screens STRIPS are identified by whether the cash flow is created from the coupon (denoted ci), principal from a Treasury bond (denoted bp), or principal from a Treasury note (denoted np). Strips created from the coupon are called coupon strips and strips created from the principal are called principal strips. The reason why a distinction is made between coupon strips and principal strips has to do with the tax treatment by non-U.S. entities, as discussed in the next section. Tax Treatment A disadvantage of a taxable entity investing in stripped Treasury securities is that accrued interest is taxed each year even though interest is not paid. Thus these instruments are negative cash flow instruments until the maturity date. They have negative cash flow because tax payments on interest earned but not received in cash must be made. Reconstituting a Bond Reconstitution is the process of coupon stripping and reconstituting that will prevent the actual spot rate curve observed on zero-coupon Treasuries from departing significantly from the theoretical spot rate curve. As more stripping and reconstituting occurs, forces of demand and supply will cause rates to return to their theoretical spot rate levels. FEDERAL AGENCY SECURITIES Federal agency securities are securities issued by government-chartered entities. These entities are either federally related institutions or government-sponsored enterprises. Federally related institutions are agencies of the federal government. Government-sponsored enterprises (GSEs) are privately owned, publicly chartered entities. They are instrumentalities (not agencies) of the U.S. government that like federally related institutions provide them privileges that granted to private sector corporations. Despite this difference, we refer to GSEs in this chapter as agencies. An important issue associated with federal agency securities is their credit quality. A commonly shared view is that although any agency issue may not carry the explicit guarantee of the U.S. government, there is an implicit guarantee due to their ability to borrow from the U.S. Treasury. Because of the credit risk, federal agency securities trade at a higher yield in the market than U.S. Treasury securities. As with Treasury securities, these securities trade in a multiple-dealer over-the-counter secondary market but with trading volume significantly less than that in the Treasury market. There are two types of securities that can be issued. The first are the typical bond used by other issuers in the bond market. This type of debt obligation is referred to as a debenture. The other type, and the one that is probably the best known by bond market participants, is a security backed by a pool of residential mortgage loans. This type of debt obligation is called a mortgage-backed security. Fannie Mae and Freddie Mac Fannie Mae and Freddie Mac are the two major suppliers of funds to the residential mortgage market. They issue similar debt instruments and currently face the same legal constraint. Due to the major downturn in the housing and credit markets beginning in 2007, in September 2008 the entity that regulates Fannie Mae and Freddie Mac, the Federal Housing Finance Agency (FHFA), placed these two GSEs in conservatorship. This meant that the FHFA had complete control over the operations and assets of these two GSEs. Federal Farm Credit Bank System The Federal Farm Credit Bank System (FFCBS) was established by Congress is to facilitate the supply of credit the agricultural sector of the economy. The Farm Credit System consists of three entities: the Federal Land Banks, Federal Intermediate Credit Banks, and Banks for Cooperatives. The FFCBFC or simply Farm Credit issues debt with a broad range of structures and maturities. Farm Credit Discount Notes are similar to U.S. Treasury bills with maturities from one day to 365 days. Farm Credit Designated Bonds can have a non-callable or callable structure that generally has 2- to 10-year maturities at issuance. The callable Designated Bonds have a one-time only redemption feature. Farm Credit Bonds can be customized for institutional investors as structured notes. Farm Credit Master Notes are debt obligations whose coupon rate is indexed to some reference rate. Federal Agricultural Mortgage Corporation The purpose of the Federal Agricultural Mortgage Corporation (Farmer Mac) is to provide a secondary market for first mortgage agricultural real estate loans. Farmer Mac raises funds by selling debentures and mortgage-backed securities backed by the loans purchased. The latter securities are called agricultural mortgage-backed securities (AMBSs). Federal Home Loan Bank System The Federal Home Loan Bank System (FHL Banks) consists of the 12 district Federal Home Loan Banks and their member banks. Each member bank issues consolidated debt obligations, which are joint and several obligations of the 12 member banks. Tennessee Valley Authority The Tennessee Valley Authority (TVA) was established by Congress in 1933 primarily to provide flood control, navigation, and agricultural and industrial development. Created to promote the use of electric power in the Tennessee Valley region, the TVA is the largest public power system in the United States. The debt obligations issues bonds with a wide range of maturities and targeting individual (retail) and institutional investors. The TVA Discount Notes have a maturity of one year or less. They are offered to on continuing basis to investors via investment dealers and dealer banks. The bonds issued, referred to as TVA Power Bonds can have a final maturity of up to 50 years and have a variety of bond structures issued in two programs. KEY POINTS • The U.S. Treasury market is closely watched by all participants in the financial markets because interest rates on Treasury securities are the benchmark interest rates throughout the world. • The Treasury issues three types of securities: bills, notes, and bonds. Treasury bills have a maturity of one year or less, are sold at a discount from par, and do not make periodic interest payments. Treasury notes and bonds are coupon securities. • The Treasury issues coupon securities with a fixed principal and an inflation-protected principal. The coupon payment for the latter is tied to the Consumer Price Index and the securities are popularly referred to as Treasury Inflation Protection Securities (TIPS). • Treasury securities are issued on a competitive bid auction basis, according to a regular auction cycle. The secondary market for Treasury securities is an over-the-counter market, where dealers trade with the general investing public and with other dealers. • In the secondary market, Treasury bills are quoted on a bank discount basis; Treasury coupon securities are quoted on a price basis. • Although the Treasury does not issue zero-coupon Treasury securities, government dealers have created these instruments synthetically by a process called coupon stripping. Zero-coupon Treasury securities are created via the STRIPS program. • The federal agency securities market is the market for the debt instruments issued by federally related institutions and government-sponsored enterprises. Unless otherwise specified, the securities issued by these entities are not explicitly or implicitly guaranteed by the full faith and credit of the U.S. government. ANSWERS TO QUESTIONS FOR CHAPTER 6 (Questions are in bold print followed by answers.) 1. What are the differences among a Treasury bill, Treasury note, and Treasury bond? Fixed-Principal Treasury Securities are fixed-income principal securities that include Treasury bills, Treasury notes, and Treasury bonds. As discussed below the main differences involve maturity and how earnings are received over time. Treasury bills are issued at a discount to par value, have no coupon rate, and mature at par value. The current practice of the Treasury is to issue all securities with a maturity of one year or less as discount securities. As discount securities, Treasury bills do not pay coupon interest. Instead, Treasury bills are issued at a discount from their maturity value; the dollar return to investors is the difference between the maturity value and the purchase price. All securities with initial maturities of two years or more are issued as coupon securities. Coupon securities are issued at approximately par and, in the case of fixed-principal securities, mature at par value. Treasury coupon securities issued with original maturities of more than one year and no more than 10 years are called Treasury notes. Treasury coupon securities with original maturities greater than 10 years are called Treasury bonds. (On quote sheets, an “n” is used to denote a Treasury note. No notation typically follows an issue to identify it as a bond.) 2. The following questions are about Treasury Inflation Protected Securities (TIPS). (a) What is meant by the “real rate”? In terms of TIPS, the real rate is the coupon rate. This is discussed below. The U.S. Department of the Treasury issues Treasury securities that adjust for inflation. These securities are popularly referred to as Treasury inflation protection securities, or TIPS. TIPS work as follows. The coupon rate on an issue is set at a fixed rate. That rate is determined via the auction process. The coupon rate is called the “real rate” since it is the rate that the investor ultimately earns above the inflation rate. The inflation index that the government has decided to use for the inflation adjustment is the non-seasonally adjusted U.S. City Average All Items Consumer Price Index for All Urban Consumers (CPI-U) (b) What is meant by the “inflation-adjusted principal”? For TIPS, the inflation-adjusted principal is the principal that the Treasury Department will base both the dollar amount of the coupon payment and the maturity value on. It is adjusted semiannually. Part of the adjustment for inflation comes in the coupon payment since it is based on the inflation-adjusted principal. However, the U.S. government has decided to tax the adjustment each year. This feature reduces the attractiveness of TIPS as investments in accounts of tax-paying entities. Because of the possibility of disinflation (i.e., price declines), the inflation-adjusted principal at maturity may turn out to be less than the initial par value. However, the Treasury has structured TIPS so that they are redeemed at the greater of the inflation adjusted principal and the initial par value. An inflation-adjusted principal must be calculated for a settlement date. The inflation-adjusted principal is defined in terms of an index ratio, which is the ratio of the reference CPI for the settlement date to the reference CPI for the issue date. The reference CPI is calculated with a three-month lag. For example, the reference CPI for May 1 is the CPI-U reported in February. The U.S. Department of the Treasury publishes and makes available on its website (www.publicdebt.treas.gov) a daily index ratio for an issue. (c) Suppose that the coupon rate for a TIPS is 3%. Suppose further that an investor purchases $10,000 of par value (initial principal) of this issue today and that the semiannual inflation rate is 1%. Answer the below questions. (1) What is the dollar coupon interest that will be paid in cash at the end of the first six months? In our example, the coupon rate for a TIPS is 3%, the annual inflation rate is 2%, and an investor purchases today $10,000 par value (principal) of this issue. The semiannual inflation rate is 1% (2% divided by 2). The inflation-adjusted principal at the end of the first six-month period is found by multiplying the original par value by one plus the semiannual inflation rate. In our example, the inflation adjusted principal at the end of the first six-month period is (1.01)$10,000 = $10,100. It is this inflation adjusted principal that is the basis for computing the coupon interest for the first six-month period. The coupon payment is then 1.5% (one-half the real rate of 3%) multiplied by the inflation-adjusted principal at the coupon payment date ($10,100). The coupon payment is therefore 0.015($10,100) = $151.50. (2) What is the inflation-adjusted principal at the end of six months? As seen in part (1) when computing the coupon payment, we find that the inflation adjusted principal at the end of the first six-month period is (1.01)$10,000 = $10,100. Given the semiannual inflation rate for the next six months we could compute the inflation-adjusted principal at year’s end. Assuming the semiannual inflation rate remains at 1%, then we would get: (1.01)$10,100 = $10,201. The coupon payment would be 0.015($10,201) = $153.015. (d) Suppose that an investor buys a five-year TIP and there is deflation for the entire period. What is the principal that will be paid by the Department of the Treasury at the maturity date? With deflation, the inflation-adjusted principal would fall. However, the Treasury has structured TIPS so that they are redeemed at the greater of the inflation adjusted principal and the initial par value. Thus, the investor who buys a five-year TIP is promised the original principle amount at the maturity date. (e) What is the purpose of the daily index ratio? The purpose of the daily index ratio is to help compute an inflation-adjusted principal for a settlement date. The inflation-adjusted principal is defined in terms of an index ratio, which is the ratio of the reference CPI for the settlement date to the reference CPI for the issue date. The reference CPI is calculated with a three-month lag. For example, the reference CPI for May 1 is the CPI-U reported in February. The U.S. Department of the Treasury publishes and makes available on its Web site (www.publicdebt.treas.gov) a daily index ratio for an issue. (f) How is interest income on TIPS treated at the federal income tax level? For TIPS, the coupon payment is based on the inflation-adjusted principal. The U.S. government taxes the adjustment each year. This feature reduces the attractiveness of TIPS as investments in accounts of tax-paying entities. 3. What is the when-issued market? Treasury securities are traded prior to the time they are issued by the Treasury. This component of the Treasury secondary market is called the when-issued market, or wi market. When-issued trading for both bills and coupon securities extends from the day the auction is announced until the issue day. 4. Why do government dealers use government brokers? When government dealers trade with each other, it is through intermediaries known as interdealer brokers. They use interdealer brokers because of the speed and efficiency with which trades can be accomplished. Also, interdealer brokers keep the names of the dealers involved in trades confidential. The quotes provided on the government dealer screens represent prices in the “inside” or “interdealer” market. 5. Suppose that the price of a Treasury bill with 90 days to maturity and a $1 million face value is $980,000. What is the yield on a bank discount basis? The convention for quoting bids and offers is different for Treasury bills and Treasury coupon securities. Bids and offers on Treasury bills are quoted in a special way. Unlike bonds that pay coupon interest, Treasury bill values are quoted on a bank discount basis, not on a price basis. The yield on a bank discount basis is computed as follows: where Yd = annualized yield on a bank discount basis (expressed as a decimal), D = dollar discount, which is equal to the difference between the face value and the price, F = face value and t = number of days remaining to maturity. For our problem, a Treasury bill with 90 days to maturity, a face value of $1,000,000, and selling for $980,000 would be selling with a dollar discount of D = F – P = $1,000,000 – $980,000 = $20,000. Given D = $20,000, F = $1,000,000 and t = 90, the Treasury bill would be quoted at the following yield: Yd = = 0.02(4) = 0.0800 or 8.00%. 6. The bid and ask yields for a Treasury bill were quoted by a dealer as 5.91% and 5.89%, respectively. Shouldn’t the bid yield be less than the ask yield, because the bid yield indicates how much the dealer is willing to pay and the ask yield is what the dealer is willing to sell the Treasury bill for? The higher bid means a lower price. So the dealer is willing to pay less than would be paid for the lower ask price. We illustrate this below. Given the yield on a bank discount basis (Yd), the price of a Treasury bill is found by first solving the formula for the dollar discount (D), as follows: D = Yd (F) . The price is then price = F – D. For the 100-day Treasury bill with a face value (F) of $100,000, if the yield on a bank discount basis (Yd) is quoted as 5.91%, D is equal to: D = Yd (F) = 0.0591($100,000) = $1,641.67. Therefore, price = $100,000 – $1,641.67 = $98,358.33. For the 100-day Treasury bill with a face value (F) of $100,000, if the yield on a bank discount basis (Yd) is quoted as 5.89%, D is equal to: D = Yd (F) = 0.0589($100,000 = $1,636.11. Therefore, price is: P = F – D = $100,000 – $1,636.11 = $98,363.89. Thus, the higher bid quote of 5.91% (compared to lower ask quote 5.89%) gives a lower selling price of $98,358.33 (compared to $98,363.89). The 0.02% higher yield translates into a selling price that is $5.56 lower. In general, the quoted yield on a bank discount basis is not a meaningful measure of the return from holding a Treasury bill, for two reasons. First, the measure is based on a face-value investment rather than on the actual dollar amount invested. Second, the yield is annualized according to a 360-day rather than a 365-day year, making it difficult to compare Treasury bill yields with Treasury notes and bonds, which pay interest on a 365-day basis. The use of 360 days for a year is a money market convention for some money market instruments, however. Despite its shortcomings as a measure of return, this is the method that dealers have adopted to quote Treasury bills. Many dealer quote sheets, and some reporting services, provide two other yield measures that attempt to make the quoted yield comparable to that for a coupon bond and other money market instruments. 7. Assuming a $100,000 par value, calculate the dollar price for the following Treasury coupon securities given the quoted price. (a) The quoted price for a $100,000 par value Treasury coupon security is 84.14. What is the dollar price? Treasury coupon securities are quoted in a different manner than Treasury bills—on a price basis in points where one point equals 1% of par. (Notes and bonds are quoted in yield terms in when-issued trading because coupon rates for new notes and bonds are not set until after these securities are auctioned.) The points are split into units of 32nds, so that a price of 96–14, for example, refers to a price of 96 and 14 32nds, or 96.4375 per 100 of par value (96 + 14/32 = 96 + 0.4375 = 96.4375). The 32nds are themselves often split by the addition of a plus sign or a number. A plus sign indicates that half a 32nd (or a 64th) is added to the price, and a number indicates how many eighths of 32nds (or 256ths) are added to the price. A price of 96–14+, therefore, refers to a price of 96 plus 14 32nds plus 1 64th, or 96.453125 (e.g., 96 + 14/32 + 1/64 = 96 + 0.4375 + 0.0625 = 96.453125), and a price of 96–142 refers to a price of 96 plus 14 32nds plus 2 256ths, or 96.4453125 (96 + 14/32 + 2/256 = 96 + 0.4375 + 0.0078125 = 96.4453125). Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 84–14, the dollar price is: 84 + 14/32 = 84 + 0.4375 = 84.4375 per 100 of par value. The dollar price is: 84.4375 ($100,000 / 100) = $84,437.50. (b) The quoted price for a $100,000 par value Treasury coupon security is 84.14+. What is the dollar price? Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 84–14+, the dollar price is: 84 + 14/32 + 1/64 = 84 + 0.4375 + 0.015625 = 84.453125 per 100 of par value. The dollar price is: 84.453125 ($100,000 / 100) = $84,453.13. (c) The quoted price for a $100,000 par value Treasury coupon security is 103.284. What is the dollar price? Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 103–284 the dollar price is: 103 + 28/32 + 4/256 = 103 + 0.875 + 0.015625 = 103.89063 per 100 of par value. The dollar price is: 103.89063 ($100,000 / 100) = $103,890.63. (d) The quoted price for a $100,000 par value Treasury coupon security is 105.059. What is the dollar price? Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 105–059 the dollar price is: 103 + 5/32 + 9/256 = 103 + 0.15625 + 0.0351562 = 103.19141 per 100 of par value. The dollar price is: 103.19141($100,000 / 100) = $103,191.41. 8. Answer the below questions for a treasury auction. (a) For a Treasury auction what is meant by a noncompetitive bidder? A noncompetitive bidder is a bidder is who is willing to purchase the auctioned security at the yield that is determined by the auction process. More details are supplied below. The auction for Treasury securities is said to be conducted on a competitive bid basis. However, there are actually two types of bids that may be submitted by a bidder: noncompetitive bid and competitive bid. A noncompetitive bid is submitted by an entity that is willing to purchase the auctioned security at the yield that is determined by the auction process. When a noncompetitive bid is submitted, the bidder only specifies the quantity sought. The quantity in a noncompetitive bid may not exceed $1 million for Treasury bills and $5 million for Treasury coupon securities. A competitive bid specifies both the quantity sought and the yield at which the bidder is willing to purchase the auctioned security. (b) For a Treasury auction what is meant by the high yield? In a Treasury auction, the results are determined by first deducting the total noncompetitive tenders and nonpublic purchases (such as purchases by the Federal Reserve) from the total securities being auctioned. The remainder is the amount to be awarded to the competitive bidders. The competitive bids are then arranged from the lowest yield bid to the highest yield bid submitted. (This is equivalent to arranging the bids from the highest price to the lowest price that bidders are willing to pay.) Starting from the lowest yield bid (or highest price bid), all competitive bids are accepted until the amount to be distributed to the competitive bidders is completely allocated. The highest yield accepted by the Treasury is referred to as the high yield (or stop-out yield). Bidders whose bid is higher than the high yield are not distributed any of the new issue (i.e., they are unsuccessful bidders). Bidders whose bid was the high yield (i.e., the highest yield accepted by the Treasury) are awarded a proportionate amount for which they bid. For example, suppose that $4 billion was tendered for at the high yield but only $3 billion remains to be allocated after allocating to all bidders who bid lower than the high yield. Then each bidder who bid the high yield will receive $3 billion / $4 billion = 0.75 = 75% of the amount for which they tendered. So, if an entity tendered for $5 million, then that entity would be awarded only 0.75($5 million) = $3.75 million. 9. In a Treasury auction, how is the price that a competitive bidder must pay determined in a single-price auction format? The competitive bidder pays the price associated with the high yield. However, the price can differ slightly from par to reflect adjustments to make the yield equal to the high yield. More details are supplied below. All bidders that bid less than the high yield are awarded the amount that they bid. The Treasury will report what percentage someone will receive if their bid is equal to the high yield. For example, the Treasury might report: “Tenders at the high yield were allotted 50%.” This means that if an entity bid for $10 million at the high yield that entity was awarded $5 million. Now that the winning bidders are determined along with their allotment, the price can be set following the conventions of a single-price auction (because all U.S. Treasury auctions are single-price auctions). In a single-price auction, all bidders are awarded securities at the highest yield of accepted competitive tenders (i.e., the high yield). This type of auction is called a “Dutch auction.” Thus, all bidders (competitive and noncompetitive) are awarded securities at the high yield. The Treasury does not actually offer securities with a coupon rate equal to the high yield because it adjusts the coupon rate and the price so that the yield offered on the security is equal to the high yield. This makes the yield a more common number (e.g., 3.025 becomes 3.000 and price can differ slightly from par. 10. In a Treasury auction, how is the price that a noncompetitive bidder must pay determined in a single-price auction format? A noncompetitive bidder is a bidder is who is willing to purchase the auctioned security at the yield that is determined by the auction process. This yield is the high yield. However, the price can differ slightly from par to reflect adjustments to make the yield equal to the high yield. More details are supplied below. Once the winning bidders are determined along with their allotment, the price can be set following the conventions of a single-price auction (because all U.S. Treasury auctions are single-price auctions). In a single-price auction, all bidders are awarded securities at the highest yield of accepted competitive tenders (i.e., the high yield). This type of auction is called a “Dutch auction.” Thus, all bidders (competitive and noncompetitive) are awarded securities at the high yield. The Treasury does not actually offer securities with a coupon rate equal to the high yield because it adjusts the coupon rate and the price so that the yield offered on the security is equal to the high yield. This makes the yield a more common number (e.g., 3.025 becomes 3.000 and price can differ slightly from par. 11. Suppose that a Treasury coupon security is purchased on April 8 and that the last coupon payment was on February 15. Assume that the year in which this security is purchased is not a leap year. Answer the below questions. (a) How many days are in the accrued interest period? The calculation of the number of days in the accrued interest period and the number of days in the coupon period begins with the determination of three key dates: the trade date, settlement date, and date of previous coupon payment. The trade date is the date on which the transaction is executed. The settlement date is the date a transaction is completed. For Treasury securities, settlement is the next business day after the trade date. Interest accrues on a Treasury coupon security from and including the date of the previous coupon payment up to but excluding the settlement date. In our problem, the settlement day of February 15th will be excluded when determining the accrued interest period. The number of days in the accrued interest period and the number of days in the coupon period may not be simply the actual number of calendar days between two dates. The reason is that there is a market convention for each type of security that specifies how to determine the number of days between two dates. These conventions are called day count conventions. There are different day count conventions for Treasury securities than for government agency securities, municipal bonds, and corporate bonds. The day count convention used for Treasury coupon securities involves determining the actual number of days between two dates. This is referred to as the actual/actual day count convention. In our problem, we consider a Treasury coupon security whose previous coupon payment was February 15. The next coupon payment would be on August 15. The Treasury security is purchased with a settlement date of April 8. In the Figure below, we show the actual number of days between February 15 (the previous coupon date) and April 8 (the settlement date): February 15 to February 28 (count Feb. 15) 14 days March (31 days in March) 31 days April 1 to April 8 (don’t count April 8) 7 days Actual number of days 52 days The number of days in the accrued interest period represents the number of days over which the investor has earned interest. For February, we have 14 remaining days (e.g., the 13 days from February 15 up to February 28 and the additional day of February 15th (since by convention we count the day that the day on which the last coupon was paid). We have 31 days for March. For April, we have 7 days up to April 7 (by convention we do not count April 8th as a day since that is the settlement day). Thus, the accrued interest period is 14 + 31 + 7 = 52 days. [NOTE. The number of days in the coupon period is the actual number of days between February 15 and August 15, which is 182 days. The number of days between the settlement date (April 8) and the next coupon date (August 15) is therefore 182 days – 52 days = 130 days. Notice that in computing the number of days from February 15 to February 28, February 15 is counted in determining the number of days in the accrued interest period; however, the settlement date (April 8) is not included.] (b) If the coupon rate for this Treasury security is 7% and the par value of the issue purchased is $1 million, what is the accrued interest? When an investor purchases a bond between coupon payments, if the issuer is not in default, the investor must compensate the seller of the bond for the coupon interest earned from the time of the last coupon payment to the settlement date of the bond. This amount is called accrued interest. When calculating accrued interest, three pieces of information are needed: (i) the number of days in the accrued interest period, (ii) the number of days in the coupon period, and (iii) the dollar amount of the coupon payment. The number of days in the accrued interest period represents the number of days over which the investor has earned interest. Given these values, the accrued interest (AI) assuming semiannual payment is calculated as follows: AI = . In our problem, we have 52 days in the accrued interest period, 182 days in a coupon period from February 15 through August 15, and the annual dollar coupon per $100 of par value is $7. The accrued interest is: AI = = = $1.00. 12. Answer the below questions. (a) What is meant by coupon stripping in the Treasury market? Coupon stripping, in general, refers to detaching the coupons from a bond and trading the principal repayment and the coupon amounts separately, thereby creating zero coupon bonds. The Treasury does not issue zero-coupon notes or bonds. However, because of the demand for zero-coupon instruments with no credit risk, the private sector has created such securities. The profit potential for a government dealer who strips a Treasury security lies in arbitrage resulting from the mispricing of the security. More details are given below. (b) What is created as a result of coupon stripping in the Treasury market? As discussed below, a zero-coupon Treasury security results from the coupon stripping in the Treasury market. To illustrate the process of coupon stripping and what is created, suppose that $500 million of a 10-year fixed-principal Treasury note with a coupon rate of 5% is purchased by a dealer firm to create zero-coupon Treasury securities. The cash flow from this Treasury note is 20 semiannual payments of $12.5 million each ($500 million times 0.05 divided by 2) and the repayment of principal (also called the corpus) of $500 million 10 years from now. As there are 11 different payments to be made by the Treasury, a security representing a single payment claim on each payment is issued, which is effectively a zero-coupon Treasury security. The amount of the maturity value for a security backed by a particular payment, whether coupon or corpus, depends on the amount of the payment to be made by the Treasury on the underlying Treasury note. In our example, 20 zero-coupon Treasury securities each have a maturity value of $12.5 million, and one zero-coupon Treasury security, backed by the corpus, has a maturity value of $500 million. The maturity dates for the zero-coupon Treasury securities coincide with the corresponding payment dates by the Treasury. 13. Why is a stripped Treasury security identified by whether it is created from the coupon or the principal? On dealer quote sheets and vendor screens STRIPS are identified by whether the cash flow is created from the coupon (denoted ci), principal from a Treasury bond (denoted bp), or principal from a Treasury note (denoted np). Strips created from the coupon are called coupon strips and strips created from the principal are called principal strips. The reason why a distinction is made between coupon strips and principal strips has to do with the tax treatment by non-U.S. entities where some foreign buyers have a preference for principal strips. This preference is due to the tax treatment of the interest in their home country. The tax laws of some countries treat the interest as a capital gain, which receives a preferential tax treatment (i.e., lower tax rate) compared with ordinary interest income if the stripped security was created from the principal. 14. What is the federal income tax treatment of accrued interest income on stripped Treasury securities? Interest income from Treasury securities is subject to federal income taxes but is exempt from state and local income taxes. A disadvantage of a taxable entity investing in stripped Treasury securities is that accrued interest is taxed each year even though interest is not paid. Thus these instruments are negative cash flow instruments until the maturity date. In brief, they have negative cash flow because tax payments on interest earned but not received in cash must be made. 15. What is a government-sponsored enterprise? A government-sponsored enterprise (GSE) is a one of several types of government-chartered entities. GSEs are divided into two types. The first is a publicly owned shareholder corporation. There are three such GSEs: the Federal National Mortgage Association (“Fannie Mae”), the Federal Home Loan Mortgage Corporation (“Freddie Mac”), and the Federal Agricultural Mortgage Corporation (“Farmer Mac”). The other type of GSE is a funding entity of a federally chartered bank lending system. These GSEs include the Federal Home Loan Banks and the Federal Farm Credit Banks. The GSEs issue two types of securities: debentures and mortgage-backed securities. Because of credit risk and liquidity, GSEs trade in the market at a yield premium to (i.e., yield greater than) comparable-maturity Treasury securities. 16. Explain why you agree or disagree with the following statement: “The debt of government-owned corporations is guaranteed by the full faith and credit of the U.S. government, but that is not the case for the debt of government-sponsored enterprises.” One would not agree with this statement because both government-owned corporations and also government-sponsored enterprises are not backed by the full faith and credit of the U.S. government. A government-owned corporation (GOC) is one of several types of government-chartered entities. Two examples of a government-owned corporation are the Tennessee Valley Authority (TVA) and the U.S. Postal Service. However, the only government-owned corporation that is a frequent issuer of debt in the market is the TVA. TVA debt obligations are not guaranteed by the U.S. government. However, the securities are rated triple A by Moody’s and Standard and Poor’s. The rating is based on the TVA’s status as a wholly owned corporate agency of the U.S. government and the view of the rating agencies of the TVA’s financial strengths. Another type of government-chartered entity is a government-sponsored enterprise (GSE). Like GOCs, GSEs are not backed by the U.S. government. GSEs are divided into two types. The first is a publicly owned shareholder corporation. There are three such GSEs: the Federal National Mortgage Association (“Fannie Mae”), the Federal Home Loan Mortgage Corporation (“Freddie Mac”), and the Federal Agricultural Mortgage Corporation (“Farmer Mac”). The other type of GSE is a funding entity of a federally chartered bank lending system. These GSEs include the Federal Home Loan Banks and the Federal Farm Credit Banks. 17. In the fall of 2010, the author of this book received an offering sheet for very short-term Treasury bills from a broker. The offering price for a few of the issues exceeded the maturity value of the Treasury bill. When the author inquired if this was an error, the broker stated that it was not and that there were institutional investors who were buying very short-term Treasury bills above the maturity value. What does that mean in terms of the yield such investors were willing to receive at that time? As show in our illustration below, paying above the maturity value means that investors are ceteris paribus willing to earn a negative rate of return. To begin with, T-bills are sold at a discount, and prices are quoted as a percentage of the maturity value. The discount is the difference between the face value and the purchase price, and represents the interest earned on the investment. Unlike Treasuries with longer maturities, T-bills don't pay periodic interest payments; the full value of the interest is factored into the discount and earned if the bill is held to maturity. The discount rate, also called the discount yield, on T-bills is established by the competitively determined purchase price and may be calculated on a bank discount basis as: where Yd = annualized yield on a bank discount basis (expressed as a decimal), D = dollar discount, which is equal to the difference between the face value and the price, F = face value and t = number of days remaining to maturity. For our problem, let us assume a Treasury bill with 90 days to maturity, a face value of $1,000,000, and selling for $1,001,000 (which in this case “selling” means what some institutional buyers are willing to pay). The dollar “discount” (which is not really a discount) when investors will pay more than face value is: D = F – P = $1,000,000 – $1,001,000 = $1,000. Given D = $1,000, F = $1,000,000 and t = 90, the Treasury bill would, by its traditional formula, be quoted at the following yield: Yd = = –0.0010(4) = –0.0040 or –0.40%. Even if Yd was its normal positive quoted yield on a bank discount basis, it is not a meaningful measure of the return from holding a Treasury bill for two reasons. First, the measure is based on a face value investment rather than on the actual dollar amount invested. Second, the yield is annualized according to a 360-day rather than a 365-day year, making it difficult to compare Treasury bill yields with Treasury notes and bonds, which pay interest on a 365-day basis. The measure that seeks to make the Treasury bill quote comparable to Treasury notes and bonds is called the bond equivalent yield. The CD equivalent yield (also called the money market equivalent yield ) makes the quoted yield on a Treasury bill more comparable to yield quotations on other money market instruments that pay interest on a 360-day basis. It does this by taking into consideration the price of the Treasury bill rather than its face value. The formula for the CD equivalent yield is Considering out hypothetical 90-day Treasury bill with a face value of $1,000,000, selling for $1,000,100, and offering a yield on a bank discount basis of 0.40%, we get: = 0.0036 or about 0.36%. Solution Manual for Bond Markets, Analysis and Strategies Frank J. Fabozzi 9780132743549, 9780133796773