A CMO Primer: the Law of Conservation of Structured Securities Risk by Craig Mccann, Ph.D., CFA1
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3. VALUATION of BONDS and STOCK Investors Corporation
3. VALUATION OF BONDS AND STOCK Objectives: After reading this chapter, you should be able to: 1. Understand the role of stocks and bonds in the financial markets. 2. Calculate value of a bond and a share of stock using proper formulas. 3.1 Acquisition of Capital Corporations, big and small, need capital to do their business. The investors provide the capital to a corporation. A company may need a new factory to manufacture its products, or an airline a few more planes to expand into new territory. The firm acquires the money needed to build the factory or to buy the new planes from investors. The investors, of course, want a return on their investment. Therefore, we may visualize the relationship between the corporation and the investors as follows: Capital Investors Corporation Return on investment Fig. 3.1: The relationship between the investors and a corporation. Capital comes in two forms: debt capital and equity capital. To raise debt capital the companies sell bonds to the public, and to raise equity capital the corporation sells the stock of the company. Both stock and bonds are financial instruments and they have a certain intrinsic value. Instead of selling directly to the public, a corporation usually sells its stock and bonds through an intermediary. An investment bank acts as an agent between the corporation and the public. Also known as underwriters, they raise the capital for a firm and charge a fee for their services. The underwriters may sell $100 million worth of bonds to the public, but deliver only $95 million to the issuing corporation. -
Understanding the Z-Spread Moorad Choudhry*
Learning Curve September 2005 Understanding the Z-Spread Moorad Choudhry* © YieldCurve.com 2005 A key measure of relative value of a corporate bond is its swap spread. This is the basis point spread over the interest-rate swap curve, and is a measure of the credit risk of the bond. In its simplest form, the swap spread can be measured as the difference between the yield-to-maturity of the bond and the interest rate given by a straight-line interpolation of the swap curve. In practice traders use the asset-swap spread and the Z- spread as the main measures of relative value. The government bond spread is also considered. We consider the two main spread measures in this paper. Asset-swap spread An asset swap is a package that combines an interest-rate swap with a cash bond, the effect of the combined package being to transform the interest-rate basis of the bond. Typically, a fixed-rate bond will be combined with an interest-rate swap in which the bond holder pays fixed coupon and received floating coupon. The floating-coupon will be a spread over Libor (see Choudhry et al 2001). This spread is the asset-swap spread and is a function of the credit risk of the bond over and above interbank credit risk.1 Asset swaps may be transacted at par or at the bond’s market price, usually par. This means that the asset swap value is made up of the difference between the bond’s market price and par, as well as the difference between the bond coupon and the swap fixed rate. -
Introduction to the Measurement of Interest Rate Risk
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute®. This topic is also covered in: INTRODUCTION TO THE MEASUREMENT O F INTEREST RATE RISK Study Session 16 EXAM FOCUS This topic review is about the relation of yield changes and bond price changes, primarily based on the concepts of duration and convexity. There is really nothing in this study session that can be safely ignored; the calculation of duration, the use of duration, and the limitations of duration as a measure of bond price risk are all important. You should work to understand what convexity is and its relation to the interest rate risk of fixed- income securities. There are two important formulas: the formula for effective duration and the formula for estimating the price effect of a yield change based on both duration and convexity. Finally, you should get comfortable with how and why the convexity of a bond is affected by the presence of embedded options. LOS 67.a: Distinguish between the full valuation approach (the scenario analysis approach) and the duration/convexity approach for measuring interest rate risk, and explain the advantage of using the full valuation approach. The full valuation or scenario analysis approach to measuring interest rate risk is based on applying the valuation techniques we have learned for a given change in the yield curve (i.e., for a given interest rate scenario). For a single option-free bond, this could be simply, “if the YTM increases by 50 bp or 100 bp, what is the impact on the value of the bond?” More complicated scenarios can be used as well, such as the effect on the bond value of a steepening of the yield curve (long-term rates increase more than short-term rates). -
VALUATION of CALLABLE BONDS: the SALOMON BROTHERS APPROACH Fernando Daniel Rubio Fernández
VALUATION OF CALLABLE BONDS: THE SALOMON BROTHERS APPROACH Fernando Daniel Rubio Fernández VALUATION OF CALLABLE BONDS: THE SALOMON BROTHERS APPROACH FERNANDO RUBIO1 Director FERNCAPITAL S.A. and Invited Professor at the Graduated Business School Universidad de Valparaíso, Chile. Pasaje La Paz 1302, Viña del Mar, Chile. Phone (56) (32) 507507 EXTRACT This paper explain, analyze and apply in an example the original paper developed by Kopprasch, Boyce, Koenigsberg, Tatevossian, and Yampol (1987) from The Salomon Brothers Inc. Bond Portfolio Analysis Group. Please, be aware. This paper is for educational issues only. There is a Spanish version in EconWPA. JEL Classification: G10, G15, G21, G32. Keywords: Salomon Brothers, bond portfolio, duration and convexity, effective duration, valuation, callable and non callable bond. Originally developed January, 1999 Originally published October, 2004 This update July, 2005 1 This paper was made while I was assisting to the Doctoral Programme in Financial Economics, Universidad Autónoma de Madrid, Spain. Comments and suggestions will be appreciated. Please, send them by e-mail to [email protected] [email protected] 1 VALUATION OF CALLABLE BONDS: THE SALOMON BROTHERS APPROACH Fernando Daniel Rubio Fernández VALUATION OF CALLABLE BONDS: THE SALOMON BROTHERS APPROACH By Professor Dr. © Fernando Rubio 1 DURATION AND CONVEXITY FOR NORMAL (NO CALLABLE) BONDS Bonds are fixed income investments that have a fixed interest rate or coupon, payable on the principal amount. All fixed income investments are evidence of indebtedness which represent a loan or debt between the issuer and the owner or holder of the security. The value of any bond is the present value of its expected cash flows. -
Default & Returns on High Yield Corporate Bonds
Soluzioni Innovative: (Private) & Public Debt Crediamo nella supremazia della Conoscenza. Dr. Edward Altman Crediamo nelle forza delle Idee. Co-Founder & Senior Advisor Classis Capital Sim SpA Crediamo nell’Ispirazione. 1 Turin, April 12, 2017 Agenda . Current Conditions and Outlook in Global Credit Markets . Assessing the Credit Health of the Italian SME Sector . Minibond Issuers 2 Major Agencies Bond Rating Categories Moody's S&P/Fitch Aaa AAA Aa1 AA+ Aa2 AA Aa3 AA- A1 A+ A2 A A3 A- Baa1 BBB+ Baa2 Investment BBB Baa3 Grade BBB- Ba1 High Yield BB+ Ba2 ("Junk") BB Ba3 BB- B1 B+ B2 B B3 B- High Yield Caa1 CCC+ Market Caa CCC Caa3 CCC- Ca CC C C D 3 Size Of High-Yield Bond Market 1978 – 2017 (Mid-year US$ billions) $1.800 $1,624 $1.600 Source: NYU $1.400 Salomon Center $1.200 estimates US Market using Credit $1.000 Suisse, S&P $800 and Citi data $ (Billions)$ $600 $400 $200 $- 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 1994 – 2016 (Mid-year € billions)* 500 468€ 471 Western Europe Market 418 400 370 ) 300 283 Source: Credit 200 194 Suisse Billions ( 154 € 108 100 81 61 70 89 84 81 79 80 77 0 2 5 9 14 27 45 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 *Includes non-investment grade straight corporate debt of issuers with assets located in or revenues derived from Western Europe, or the bond is denominated in a Western European currency. -
Managing Interest Rate Risk by Managing Duration
VANDERBILT AVENUE ASSET MANAGEMENT Managing Interest Rate Risk by Managing Duration In a perfect world, interest rates would not fluctuate and the value of the bonds in your portfolio would not change over time. Unfortunately, we live in a world where interest rates move up and down…sometimes dramatically…over the course of a bond’s term. This movement can have a meaningful impact on your portfolio, if not taken into account in the day-to-day management of your fixed income assets. One of the ways we help to insulate your portfolio from negative interest rate moves and to take advantage of those that are positive, is to carefully monitor its duration. In what follows, we will examine the concept of duration and its applicability as an interest rate risk management tool. Duration as a risk measure: There is an inverse relationship between the price of a bond and its yield. The yield on a bond is the discount rate that makes the present value of the bond’s cash flows equal to its price. Thus, as the bond’s price declines, its yield increases, a direct reflection of the discount between the bond’s par value and the price investors are willing to pay for it. In a rising interest rate environment investors demand greater yields, which can only be provided by lowering the asking price for the bond. Conversely, in a decreasing interest rate environment, the bond’s fixed rate of return may make it very attractive to investors, causing its price to rise (a reflection of increased demand) and its yield to decline. -
1 Bond Valuation
Structure of fixed income securities • A Fixed Income Security promises to pay fixed coupon payments at a prespecified dates and a fixed principal amount Bond Valuation (the face value) at the maturity date. • When there are no coupon payments then the bond is called a •The Structure of fixed income securities zero coupon bond or a pure discount bond. •Price & yield to maturity (ytm) •Term structure of interest rates Payments of a “N” year bond with annual coupon C and face value F •Treasury STRIPS •No-arbitrage pricing of coupon bonds payments: C C …………… C C+F Time: 0 1 2 ………….. N-1 N Coupon Bonds The U.S. government issues bonds • The coupon payments on coupon bonds are typically stated as a Default free bonds issued by the government: percentage of the principal (or face value) paid per year. Treasury bills have an initial maturity less than one year and are all • If coupon payments are made n times per year, then the coupon discount bonds amount is (c x F)/n, where c is the coupon rate and F is the face Treasure notes have initial maturities between one and ten years and value. pay coupons Treasury bonds have initial maturities longer than ten years and pay Understanding the terms: U.S. Treasury Notes and Bonds are coupons typically issued with face value of $10,000, and pay semi-annual coupons. Assume a 30 year coupon rate of 7.5%. What payments Default free bonds issued by government sponsored agencies do you receive from buying this bond? Fannie Mae: Federal National Mortgage Association Ginnie Mae: Government National Mortgage Association You receive a coupon payment of (0.075 x $10,000)/2 = $375 twice a Freddie Mac: Federal Home Loan Mortgage Corporation year and on the maturity date you will receive the coupon of $375 Federal Home Loan Bank plus the principal of $10,000. -
Chapter 10 Bond Prices and Yields Questions and Problems
CHAPTER 10 Bond Prices and Yields Interest rates go up and bond prices go down. But which bonds go up the most and which go up the least? Interest rates go down and bond prices go up. But which bonds go down the most and which go down the least? For bond portfolio managers, these are very important questions about interest rate risk. An understanding of interest rate risk rests on an understanding of the relationship between bond prices and yields In the preceding chapter on interest rates, we introduced the subject of bond yields. As we promised there, we now return to this subject and discuss bond prices and yields in some detail. We first describe how bond yields are determined and how they are interpreted. We then go on to examine what happens to bond prices as yields change. Finally, once we have a good understanding of the relation between bond prices and yields, we examine some of the fundamental tools of bond risk analysis used by fixed-income portfolio managers. 10.1 Bond Basics A bond essentially is a security that offers the investor a series of fixed interest payments during its life, along with a fixed payment of principal when it matures. So long as the bond issuer does not default, the schedule of payments does not change. When originally issued, bonds normally have maturities ranging from 2 years to 30 years, but bonds with maturities of 50 or 100 years also exist. Bonds issued with maturities of less than 10 years are usually called notes. -
Glossary of Bond Terms
Glossary of Bond Terms Accreted value- The current value of your zero-coupon municipal bond, taking into account interest that has been accumulating and automatically reinvested in the bond. Accrual bond- Often the last tranche in a CMO, the accrual bond or Z-tranche receives no cash payments for an extended period of time until the previous tranches are retired. While the other tranches are outstanding, the Z-tranche receives credit for periodic interest payments that increase its face value but are not paid out. When the other tranches are retired, the Z-tranche begins to receive cash payments that include both principal and continuing interest. Accrued interest- (1) The dollar amount of interest accrued on an issue, based on the stated interest rate on that issue, from its date to the date of delivery to the original purchaser. This is usually paid by the original purchaser to the issuer as part of the purchase price of the issue; (2) Interest deemed to be earned on a security but not yet paid to the investor. Active tranche- A CMO tranche that is currently paying principal payments to investors. Adjustable-rate mortgage (ARM)- A mortgage loan on which interest rates are adjusted at regular intervals according to predetermined criteria. An ARM's interest rate is tied to an objective, published interest rate index. Amortization- Liquidation of a debt through installment payments. Arbitrage- In the municipal market, the difference in interest earned on funds borrowed at a lower tax-exempt rate and interest on funds that are invested at a higher-yielding taxable rate. -
Bonds and Yield to Maturity
Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time. Specify (i) maturity date when the principal is repaid; (ii) coupon payments over the life of the bond. P stream of coupon payments maturity date Cash flows in bonds 1. Coupon rate offered by the bond issuer represents the cost of raising capital (reflection of the creditworthiness of the bond issuer). 2. Assume the bond issuer does not default or redeem the bond prior to maturity date, an investor holding this bond until maturity is assured of a known cash flow pattern. Other features in bond indenture 1. Floating rate bond – coupon rates are reset periodically according to some predetermined financial benchmark. 2. Amortization feature – principal repaid over the life of the bond. 3. Callable feature (callable bonds) The issuer has the right to buy back the bond at a specified price. Usually this call price falls with time, and often there is an initial call protection period wherein the bond cannot be called. 4. Put provision – grants the bondholder the right to sell back to the issuer at par value on designated dates. 5. Convertible bond – giving the bondholder the right to exchange the bond for a specified number of shares. * Bondholder can take advantage of the future growth of the issuer’s company. * Issuer can raise capital at a lower cost. 6. Exchangeable bond – allows bondholder to exchange the issue for a specified number of common stocks of another corporation. -
SESSION 7: VALUING a CONTRACTUAL CLAIM (BONDS) the Nature of Contractual Claims
SESSION 7: VALUING A CONTRACTUAL CLAIM (BONDS) The nature of contractual claims ¨ A contractual claim cash flow is set at the time a contract or transaction is initiated, with the promisor committing to deliver that cash flow at the specified time. ¨ The cash flow that is contracted can be a constant cash flow or it can be tied to an observable and specific index or value. ¤ An example of the first would be a conventional fixed rate coupon bond ¤ An example of the second would be a floating rate bond. 2 The Effect of Default ¨ Even though a claim is contractually set, there is the possibility that the promisor may default. ¨ If the promisor has no default risk, the claim is said to be a risk free claim. ¤ The only entities that can conceivable by default free are governments that control the printing of currency. ¤ Not all governments are default free. ¨ If there is default risk, you have to adjust for the likelihood of default, when valuing the claim. 3 A fixed rate, risk free bond ¨ To value a fixed rate, risk free bond (issued by a government that is default free), you will discount the coupons (which are annuity) and the face value of the bond at the risk free rate. ¨ Thus, if you view the US government as default free, the value of 3% coupon rate, US treasury bond with ten years to maturity, if the US$ risk free rate today for a 10-year bond is 2% can be written as follows: Price of the Bond = 30* PV(A,10,2%) + 1000/1.0210 =$1089.83 ¨ This bond is trading at above par (with the face value of $1000 defined as par) because the market interest rate is lower than the coupon rate. -
Recent Interest Rate Changes, Effective Duration and Effect on Your Portfolio
CMTA Conference Track 2 April 15th, 2015 Recent Interest Rate Changes, Effective Duration and Effect on Your Portfolio Presented by: Jessica Burruss, Director, BondEdge Sales BondEdge is a leading provider of fixed income portfolio analytics to institutional investors with over 30 years expertise working with a client base that includes more than 400 investment managers, banks, insurance companies, state and local government agencies, brokerage firms, depository institutions, and pension funds 1 Agenda Review of recent interest rate movements Specific examples of analytic measures that matter Forward looking simulations -BondEdge best practices 2 6/16/2015 3 6/16/2015 Are shifts parallel ….? Recent Shifts in the US Yield Curve Page 4 CONFIDENTIAL Dynamic Risk Measures - Dynamic risk measures were developed to overcome the limitations inherent in static risk measures - Dynamic risk measures include, but are not limited to: ‣ Option-adjusted spread (OAS) ‣ Option-adjusted duration (OAD) ‣ Option-adjusted convexity (OAC) ‣ Key rate durations (KRD) ‣ Spread Duration - Dynamic risk measures are a “probabilistic” combination of static outcomes March 7-9, 2012 5 Dynamic Risk Measures – Price Sensitivity Effective Duration ‣ Option-adjusted measure of a bond‘s sensitivity to changes in interest rates. Calculated as the average percentage change in a bond's value (price plus accrued interest) under parallel shifts of the Treasury curve. ‣ Incorporates the effect of embedded options for corporate bonds and changes in prepayments for mortgage-backed securities (including pass-throughs, CMOs and ARMs) . For Municipal Variable Rate Demand Notes (VRDNs), Effective Duration is calculated based on cash flows to the next reset date. ‣ BondEdge uses +/- 100 bps, then derives two new spot curves from the shifted par curves.