...MEASURES OF CREDIT SPREAD: YIELD SPREAD: Yield Spread is the difference between the yield-to-maturity of a risky bond and the yield-to-maturity of an on-the-run treasury benchmark bond with similar but not necessarily identical maturity. YTM is the constant discount rate which, when applied to the bond’s cash flows, re-prices the bond. Assumptions: * An investor who buys a bond can achieve a return equal to the YTM if the bond is held to maturity and if all coupons can be reinvested at the same rate as the YTM. In practice, this is difficult if not impossible to achieve since changes in the credit quality of the issuer may cause yields to change through time. As many investors may re-invest coupons at rates closer to LIBOR, at least temporarily, the realized return will usually be lower than the YTM. * The YTM assumes that the yield curve is flat which is not generally true. In practice, there are different reinvestment rates for different maturities. The YTM assumes that these reinvestment rates are the same for all maturities. Weaknesses: * It shares all of the weaknesses of the YTM measure in terms of constant reinvestment rate and hold to maturity. * It is not a measure of return of a long-defaultable bond, short treasury position. * As a relative value measure, it can only be used with confidence to compare different bonds with the same maturity which may have different coupons. * The benchmark security’s maturity may not match that...
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... rates of bonds ¤ Why bonds with the same maturity have different yields/ interest rates? => Risk structure of interest rates ¤ Why bonds with iden3fied characteris3cs have different yields/ interest rates? => Term structure of interest rates FIGURE 1 Long-‐Term Bond Yields, 1919– 2008 Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Sta4s4cs, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15/data.htm. Risk Structure of Interest Rates ¤ Bonds with the same maturity have different interest rates due to they have different characteris3cs of: ¤ Default risk ¤ Liquidity ¤ Tax considera3ons/ tax status ¤ Special provisions Default risk ¤ Default (credit) risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value ¤ Securi3es with a higher degree of risk have to offer higher yields to be chosen...
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... Var for Interest Rate Derivatives Interest rate risk and Bond portfolio management Profile of Interest Rate Markets, Instruments & Institutions Bond Price P 1 y C1 1 1 y C2 2 1 y Ct C3 3 1 y n Cn price Sum of the present values of each cashflows p P n t 1 1 y t M 1 y n yield price < par (discount bond) price = par (par bond) price > par (premium bond) Concept of Accrued Interest p When you buy a bond between coupon dates, you pay the seller: Clean Price plus the Accrued Interest – pro-rated share of the fi coupon: i d h f h first interest d does not compound b d between coupon payment dates. LD Days Accrued Interest Total T from last Coupon between Coupon Date Dates Days ND (Coupon) Dirty Price Clean price Accrued Interest Accrued Interest Face * C T LD * 2 ND LD Bond Valuation Value of a bond is the present value of future cashflows, so the pricing equation of the bond is: tP 1 y n C1 v 1 y Ct C2 1 v 1 y C3 2v M 1 y n1v Cn tP t 1 1 y 1 y v t 1 1 y v 1 y n1 When v= 1, what happens? This gives the dirty price (also known as the full price) The dirty price is the fair value or market value of the bond You...
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...Why Bonds With Different Maturities Have Different Interest Rates In this paper, I will discuss why bonds with different maturities can have different interest rates. I will do so by explaining the importance of understanding the term structure, as well as the three theories that support the term structure; the expectations theory, the segmented markets theory, and the liquidity premium theory. Term Structure According to Hubbard and O’Brien, the term structure “is the relationship among the interest rates on bonds that are otherwise similar but have different maturities.” Term structure is most commonly analyzed by looking at the Treasury yield curve, which is the relationship of interest rates on Treasury bonds with different maturities on a particular day. Yields generally tend to move in line with maturity, producing an upward sloping yield curve or a “normal yield curve.” Rarely, however, the yields on the long-term treasuries fall below the yields of short-term treasuries. This creates an inverted yield curve. According to a class lecture, six times when the yield curve became inverted, there was an economic recession. Wheelock and Wohar believe that term structure plays an important role in an economy because it “has been found useful for forecasting such variables as output growth, inflation, industrial production, consumption, and recessions.” The Expectations Theory According to Hubbard and O’Brien, the expectations theory “holds that the interest rate on a...
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... a) Bond – is a long term contract under which the borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond. Treasury bonds – sometimes referred to as government bonds, are issued by the U.S. federal government. These bonds have not default risk. However, these bonds decline when interest rates rise, so they are not free of all risk Corporate bonds – issued by corporate; exposed to default risk – if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments. Different corporate bonds have different levels of default risk, depending on the issuing company’s characteristics and the terms of the specific bond. Default risk often referred to as “credit risk” and the larger the default or credit risk, the higher the interest rate the issuer must pay. Municipal bond – or “munis “ are issued by state and local governments. Like corporate bonds, munis have default risk. Munis offer one major advantage over all the other bonds is exempt from federal taxes and also from state taxes if the holder is a resident of the issuing state. Munis bonds carry interest rates that are considerably lower than those on corporate bonds with the same default risk Foreign bond – are issued by foreign governments or foreign corporations. Foreign corporate bonds are of course exposed to default risk, and so are some foreign government bonds. An additional risk exists if the bonds are denominated...
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...1. What is the Treasury yield curve and what does it represent? The yield curve is one way to look at interest rates. It shows the relationship between the rates or yields being offered by bonds of different maturities. It is usually based on U.S. Treasury Bonds. It is mainly used as a benchmark for other debt in the market, such as mortgage rates and bank lending rates. Investors also use the yield curve as a reference point for forecasting interest rates, pricing bonds and creating strategies for boosting total returns. It is also a reliable leading indicator of economic activity. 2. Explain the difference between current yield and yield-to-maturity (YTM). Current Yield: it is the annual return earned on the price paid for a bond. It is calculated by dividing the bond’s annual coupon interest payment by its purchase price. Yield-to-maturity: it is the total return an investor will receive if the bond or the security is held until the maturity date. It reflects the total return to the bond holder of holding the bond until maturity which includes which includes all the interest payments from the time of purchase until maturity including interest on interest, it also includes any appreciation or depreciation in the price of the bond. 3. Explain the difference between the coupon rate and the YTM. Coupon rate: it is the amount of interest paid every year on a bond. It is expressed as a percentage of the face value of the bond. It determines the income that will...
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...of bonds: namely, the 1-year zero coupon bond. However, there are many types of bonds: bonds with different maturity, bonds issued by different parties (i.e. government vs. corporate), etc. As a result, there is a different interest rate for each type of bond. We will look at the behavior of interest rates of two groups of bonds: (1) Bonds with the same features but are issued by different agency. In other words, we want to look at the risk structure of interest rates. (2) Bonds issued by the same agency but have different term to maturity (i.e. life of the bond). In other words, we want to look at the term structure of interest rates. 1. Risk structure of interest rate As we have discussed in the previous section, the (relative) risk level of an asset affects its demands according to the theory of asset demand. The higher the relative risk level, the lower the demand of that asset. According to the theory of asset demand, this leads to an increase in interest rate. In other words, investors need to be compensated with a higher return (in the form of higher interest rate) in order to induce them to hold the assets. There are a number of factors that affect the risk level of a bond. In this section, we will focus on only 3 of them: default risk, liquidity, and tax consideration. (i) Default risk Default risk represents the probability (or chance) that the issuer of the bonds will not be able to pay the coupon payments on time and the principal on the maturity date. The bond issuer...
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...institutions (2) Loanable funds theory (3) In‡ ation, nominal interest, and real interest rate (4) Bond valuation (5) Yield (6) Yield curve Corresponding book chapters: Chapter 1 and 2. 1 1.1 Main function performed by …nancial institutions There are many types of …nancial institutions: commercial banks, investment banks, pension funds, mutual funds, hedge funds, credit rating agencies, etc. Financial institutions facilitate funds transfer from suppliers to users. In some transactions, there is no need for a …nancial institution. In the following example, a small company borrows directly from the owner’ friends. s 2 In other transactions, a …nancial institution is useful or even necessary. In the following example, the credit rating agency (Moody’ indirectly participates in funds transfer. s) 3 In the following example, the bank directly participates in funds transfer. Several questions naturally arise: (1) How do banks make money? (2) Why don’ companies borrow directly from households? t (3) What risks do banks face? (4) How do banks manage these risks? These are the main questions that we will study in this course. 4 1.2 Loanable funds theory Interest rate is the cost of borrowing or the price paid for the rental of funds. There are many interest rates in the economy, such as interest rates on mortgages, auto loans, corporate bonds, and government bonds. Because di¤erent interest rates have a tendency to move in tandem, people often talk about...
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...Return and Yield to Maturity Please do all calculations in Excel and put your answers in the blue cells. Please do not move or reformat the blue cells. Names: Question 1 On November 14, 1995, a customer could have purchased a 1-year STRIP at a zero rate of 5.45%, or a 1.5-year STRIP at a zero rate of 5.47%. Using the information from the table below, calculate the realized rate of return (semi-annually compounded) on each security over the subsequent year. STRIPS pricing on November 14, 1996: Maturity Ask Rate Ask Price Bid Price in Bid Price in Bid Rate 0.5 5.29% in 97.4232 32nds 97:13 Decimal 97.4063 5.33% 1 5.44% 94.7742 94:24 94.7500 5.47% 1.5 5.58% 92.0762 92:01 92.0313 5.61% 1-year STRIP 5.45% 1.5-year STRIP 5.54% Reference Cells 1-year STRIP 1.5-year STRIP Rate 5.45% 5.47% 1-year STRIP: cost = 1/(1+0.0545/2)2 = 0.947649 payoff = 1 growth factor (payoff/cost) = 1/0.947649 = 1.055243 semi-annually compounded rate of return = 2x[(1.055243)0.5 - 1] = 5.45% 1.5-year STRIP: cost = 1/(1+0.0547/2)3 = 0.922242 payoff = 0.974063 (from bid price of 0.5-year STRIP on November 14, 1996) growth factor (payoff/cost) = 0.974063/0.922242 = 1.05619 semi-annually compounded rate of return = 2x[(1.05619)0.5 - 1] = 5.54% Question 2 Suppose that at time 0 you buy a 6%-coupon 30-year bond priced at par, and at time 0.5 you sell this bond at a price of 90% of par value. a) What is your time 0.5 payoff per $1 of initial investment? $0.93 Two approaches, giving same answer: #1) Sell bond immediately...
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...corporate stocks. The New York Stock Exchange is an example of a capital market. b. Primary markets are the markets in which newly issued securities are sold for the first time. Secondary markets are where securities are resold after initial issue in the primary market. The New York Stock Exchange is a secondary market. c. In private markets, transactions are worked out directly between two parties and structured in any manner that appeals to them. Bank loans and private placements of debt with insurance companies are examples of private market transactions. In public markets, standardized contracts are traded on organized exchanges. Securities that are issued in public markets, such as common stock and corporate bonds, are ultimately held by a large number of individuals. Private market securities are more tailor-made but less liquid, whereas public market securities are more liquid but subject to greater standardization. d. Derivatives are claims whose value depends on what happens to the value of some other asset. Futures and options are two important types of derivatives, and their values depend on what happens to the prices of other assets, say IBM stock, Japanese yen, or pork bellies. Therefore, the value of a derivative security is derived from the value of an underlying real asset. e. An investment banker is a middleman between businesses and savers. Investment banking houses assist in the design of corporate securities and...
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...Financial Modelling – Session VII Email: jcadete@clsbe.lisboa.ucp.pt Financial Modelling Joaquim Joaquim Cadete Cadete 1 How your work is going to be scored? Svensson Model: IR Swaps: CIR Model: Modeling Formalization (6) Functions Efficiency Gains (3) Functions Efficiency Gains (3) Further Improvements (5) Efficiency Gains (3) User’s Perspective Your Grade Financial Modelling Joaquim Cadete 2 Risk Management: the main concern… Counterparty risk Credit risk Interest rate risk Capital risk and solvency Funding risk Risk Management Reputational risk Foreign exchange risk Off-balance sheet risk Operational risk Financial Modelling Market or trading risk Sovereign risk Regulatory risk Joaquim Cadete 3 Risk and Return Theories Diversification Standard deviation of portfolio return σ Unsystematic or diversifiable risk Systematic or Total risk market-related risk Number of holdings Financial Modelling Joaquim Cadete 4 Interest rate risk: the first layer of volatility… Operational Risk: Betas. Operational risk Systematic risk or nondiversifiable risk Unsystematic or diversifiable risk A Total Risk Shareholders’ risk A E E A E A= E Financial Modelling Joaquim Cadete 5 Interest rate risk: the first layer of volatility… Operational Risk: Betas. If A = E, then RA =...
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...Interest rate is a significant tool for investors of bonds but also for policy makers, in terms of having an overview of whether to invest in short or longer term securities. This essay will go on to explain the term structure of interest rate how it is used by investors, the different theories and hypothesis behind it but also how the creation of long term rates effects its relation to risk. The term structure of interest rates also called the yield curve shows the relationship between interest rate and time to maturity of bonds, it is a common method of bond valuation. A graph is used to represent this relationship in relation to long term interest rates and short term interest rates where the maturity of an investment (x axis ) is compared to the interest rate (y axis) showing the yield (rate return) on bonds with the different maturity length. Term structure of interest usually refers to zero coupon bonds which are bonds without coupons (weekly interest rate payments on the bond) which are sold at its face value requiring as a result a fixed interest rate. The yield curve usually indicates that holding long term bonds generates a higher yield in comparison to holding short term assets which are highly liquid e.g. money short term bonds such as bills etc. This previous statement is demonstrated by the typical yield curve (fig1) which slopes upward but flattens out eventually showing the usual pattern of long term bonds which generate...
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...3. In February 1995, Copiers, Inc. Issued one-year zero-coupon bonds with a face value of $1000. The bonds sold for $910 a piece and were rated AA by Standard & Poors. Buyers of the bonds were promised a single $1000 payment at the end of one year. At the time the bonds were issued, one-year Treasury securities were yielding 6.6%. Assume that the market risk premium was 7.2%. A. What was the yield-to-maturity at the time if issuance of the Copiers, Inc, bond? One-Year Zero Coupon Rate, with an AA rating. Face Value = $ 1,000.00 Bond Issued at = $ 910.00 Years to Maturity = 1 year Treasury Securities Interest Rate = 6.6 % Market Risk Premium = 7.20 % If Present Value = Future Value / ( 1 + r )t | t = (Future Value / Present Value ) 1/ t – 1 | t = (1000 / 910 )1 - 1 | t = 1.0989 – 1 | t = 9.89 % Yield to Maturity | | B. Using the table below, calculate the expected return on the Copiers, Inc. Bond when it was issued. Rating | AAA | | AA | | A | | BBB | Beta | 0.19 | | 0.20 | | 0.21 | | 0.22 | Source: Fama, Gene and Ken French, 1993, "Common Risk Factors in the Returns on Bonds and Stocks", on Bonds and Stocks, “Journal of Financial Economics, 33, 3-56, Table 4 | Expected Return Rate = (Risk Free Return) + (Beta) * (Expected Market Return – Risk Free Return) Risk Free Return: Treasury Interest Rate = 6.6 % Expected Market Return: Return of market as a whole Considering that: Market Risk Premium = Expected Market Return – Risk Free...
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...default risk premium, RP, is assumed to be zero since the security is backed by the U.S. government; this security is commonly considered the risk-free asset. 2. The term structure of interest rates is the relationship of the rate of return to the time to maturity for any class of similar-risk securities. The graphic presentation of this relationship is the yield curve. 3. For a given class of securities, the slope of the curve reflects an expectation about the movement of interest rates over time. The most commonly used class of securities is U.S. Treasury securities. a. Downward sloping: Long-term borrowing costs are lower than short-term borrowing costs. b. Upward sloping: Short-term borrowing costs are lower than long-term borrowing costs. c. Flat: Borrowing costs are relatively similar for short- and long-term loans. The upward-sloping yield curve has been the most prevalent historically. 4. a. According to the expectations theory, the yield curve reflects investor expectations about future interest rates, with the differences based on inflation expectations. The curve can take any of the three forms. An upward-sloping curve is the result of increasing inflationary expectations, and vice versa. b. The liquidity preference...
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...default risk premium, RP, is assumed to be zero since the security is backed by the U.S. government; this security is commonly considered the risk-free asset. 2. The term structure of interest rates is the relationship of the rate of return to the time to maturity for any class of similar-risk securities. The graphic presentation of this relationship is the yield curve. 3. For a given class of securities, the slope of the curve reflects an expectation about the movement of interest rates over time. The most commonly used class of securities is U.S. Treasury securities. a. Downward sloping: Long-term borrowing costs are lower than short-term borrowing costs. b. Upward sloping: Short-term borrowing costs are lower than long-term borrowing costs. c. Flat: Borrowing costs are relatively similar for short- and long-term loans. The upward-sloping yield curve has been the most prevalent historically. 4. a. According to the expectations theory, the yield curve reflects investor expectations about future interest rates, with the differences based on inflation expectations. The curve can take any of the three forms. An upward-sloping curve is the result of increasing inflationary expectations, and vice versa. b. The liquidity preference...
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