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Bond Prices and Yield: Investment Essentials
Chapter 10 Bond Prices and Yield Bodie, Kane, and Marcus Essentials of Investments Tenth Edition 10.1 Bond Characteristics • Bond • Security that obligates issuer to make payments to holder over time • Face Value, Par Value • Payment to bondholder at maturity of bond • Coupon Rate • Bond’s annual interest payment per dollar of par value • Zero-Coupon Bond • Pays no coupons, sells at discount, provides only payment of par value at maturity Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2 Figure 10.1 Prices/Yields of U.S. Treasury Bonds U.S. Treasury Quotes: Treasury note and bond data are representative over-the-counter quotations as of 3pm Eastern time. Maturity Coupon Bid Asked Change Asked Yield 10/15/2015 0.250 100.0938 100.1094 -0.0078 0.155 10/15/2016 0.625 100.1563 100.1953 0.0000 0.534 11/15/2018 9.000 131.8984 131.9297 0.0313 1.247 11/30/2018 1.375 99.8984 99.9297 0.0703 1.392 8/15/2023 6.250 132.9453 132.9922 0.4531 2.188 8/15/2026 6.750 144.3828 144.4609 0.6953 2.449 11/15/2027 6.125 139.7188 139.7969 0.7969 2.562 2/15/2031 5.375 134.5625 134.6406 0.9766 2.748 2/15/2036 4.500 125.0781 125.1563 1.1250 2.916 5/15/2044 3.375 104.7500 104.8125 1.2500 3.125 Source: Wall Street Journal Online, August 15, 2014. Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3 10.1 Bond Characteristics • Treasury Bonds and Notes • Accrued interest and quoted bond prices • Quoted prices do not include interest accruing between payment dates • Accrued interest = π¨πππππ ππππππ πππππππ π × π«πππ πππππ ππππ ππππππ πππππππ π«πππ ππππππππππ ππππππ ππππππππ Example: Consider a bond with the following characteristics: Semi-annual payments, coupon rate of 6%, $1,000 par value. If 45 days have passed since the last coupon payment, what is the accrued interest? 45 A.I . ο½ ο΄ $30 ο½ $7.42 182 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4 Figure 10.2 Listing of Corporate Bonds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5 10.1 Bond Characteristics • Corporate Bonds • Call provisions on corporate bonds • Callable bonds: May be repurchased by issuer at specified call price during call period • Convertible bonds • Allow bondholder to exchange bond for specified number of common stock shares Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6 10.1 Bond Characteristics • Corporate Bonds • Puttable bonds • Holder may choose to exchange for par value or to extend for given number of years • Floating-rate bonds • Coupon rates periodically reset according to specified market date Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7 10.1 Bond Characteristics • Preferred Stock • Commonly pays fixed dividend • Floating-rate preferred stock becoming more popular • Dividends not normally tax-deductible • Corporations that purchase other corporations’ preferred stock are taxed on only 30% of dividends received Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8 10.1 Bond Characteristics • Other Domestic Issuers • State, local governments (municipal bonds) • Federal Home Loan Bank Board • Farm Credit agencies • Ginnie Mae, Fannie Mae, Freddie Mac Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9 10.1 Bond Characteristics • International Bonds • Foreign bonds • Issued by borrower in different country than where bond sold, denominated in currency of market country • Eurobonds • Denominated in currency (usually that of issuing country) different than that of market Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10 10.1 Bond Characteristics • Innovation in the Bond Market • Inverse floaters • Coupon rate falls when interest rates rise • Asset-backed bonds • Income from specified assets used to service debt • Pay-in-kind bonds • Issuers can pay interest in cash or additional bonds • Catastrophe bonds • Higher coupon rates to investors for taking on risk Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11 10.1 Bond Characteristics • Innovation in the Bond Market • Indexed bonds • Payments tied to general price index/price of particular commodity • Treasury Inflation Protected Securities (TIPS): Par value of bond increases with consumer price index • Nominal return = • Real return = πΌππ‘ππππ π‘+πππππ πππππππππ‘πππ πΌπππ‘πππ πππππ 1+πππππππ πππ‘π’ππ 1+πΌπππππ‘πππ −1 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 12 Table 10.1 Principal and Interest Payments Principal and interest payments for a Treasury Inflation Protected Security Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 13 10.2 Bond Pricing • Bond value = Present value of coupons + Present par value • Bond value = π πΆππ’πππ π‘=1 (1+π)π‘ + πππ π£πππ’π (1+π)π • T = Maturity date • r = discount rate • Bond price = πΆππ’πππ × = πΆππ’πππ 1 π 1− 1 1+π π + πππ π£πππ’π × 1 (1+π)π × π΄πππ’ππ‘π¦ ππππ‘ππ π, π + πππ π£πππ’π × ππ ππππ‘ππ (π, π) Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 14 10.2 Bond Pricing: Example • What is the price of the following two bonds: Bond A Bond B Maturity (T) 4 Years 30 Years Coupon Rate (C) 5% 5% Discount Rate (r) 8% 8% Par Value (FV) $1,000 $1,000 Bond A Bond B 1 ο ο¨1 ο« r ο© 1 ο ο¨1 ο« r ο© οT οT PV ο½ C ο΄ ο« FV ο΄ ο¨1 ο« r ο© PV ο½ C ο΄ ο« FV ο΄ ο¨1 ο« r ο© r r 1 ο (1.08) ο4 1 ο (1.08) ο30 ο4 ο½ $50 ο΄ ο« $1, 000 ο΄ (1.08) ο½ $50 ο΄ ο« $1, 000 ο΄ (1.08) ο30 .08 .08 ο½ $165.61 ο« $735.03 ο½ $900.64 ο½ $562.89 ο« $99.38=$662.27 οT Present Value of Coupons οT Present Par Value Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 15 10.2 Bond Pricing • Prices fall as market interest rate rises • Interest rate fluctuations are primary source of bond market risk • Bonds with longer maturities more sensitive to fluctuations in interest rate Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 16 Figure 10.3 Inverse Relationship between Bond Prices and Yields Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 17 Table 10.2 Bond Prices at Different Interest Rates Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 18 10.2 Bond Pricing • Bond Pricing between Coupon Dates • Invoice price = Flat price + Accrued interest • Bond Pricing in Excel • =PRICE (settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of par value, number of coupon payments per year) Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 19 Spreadsheet 10.1 Valuing Bonds Coupon Rate: 6.25% Matures: August 15, 2023 Formula in column B Coupon Rate: 4.375% Matures: Nov 15, 2039 Coupon Rate: 8% Matures: Aug. 15, 2041 Settlement date 8/15/2011 =DATE(2011,8,15) 8/15/2011 8/15/2011 Maturity date 8/15/2023 =DATE(2023,8,15) 11/15/2039 8/15/2041 0.0625 0.04375 0.08 0.02598 0.03697 0.1 100 100 100 2 2 2 111.819 81.071 92 0 184 182 1.094 0 112.913 81.071 Annual coupon rate Yield to maturity Redemption value (% of FV) Coupon payments per year Flat price (% of par) Days since last coupon Days in coupon period Accrued interest Invoice price 137.444 =PRICE(B4,B5,B6,B7,B8,B9) 0 =COUPDAYBS(B4,B5,2,1) 184 =COUPDAYS(B4,B5,2,1) 0 =(B13/B14)*B6*100/2 137.444 =B12+B15 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 20 10.3 Bond Yields • Yield to Maturity • Discount rate that makes present value of bond’s payments equal to price. • Current Yield • Annual coupon divided by bond price • Premium Bonds • Bonds selling above par value • Discount Bonds • Bonds selling below par value Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 21 Spreadsheet 10.2 Finding Yield to Maturity Semiannual coupons Settlement date Maturity date Annual coupon rate Bond price (flat) Redemption value (% of face value) Coupon payments per year Yield to maturity (decimal) Annual coupons 1/1/2000 1/1/2030 0.08 127.676 100 2 1/2/2000 1/2/2030 0.08 127.676 100 1 0.0600 0.0599 The formula entered here is =YIELD(B3,B4,B5,B6,B7,B8) Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 22 10.3 Bond Yields • Yield to Call • Calculated like yield to maturity • Time until call replaces time until maturity; call price replaces par value • Premium bonds more likely to be called than discount bonds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 23 Figure 10.4 Bond Prices: Callable and Straight Debt Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 24 10.3 Bond Yields • Realized Compound Returns versus Yield to Maturity • Realized compound return • Compound rate of return on bond with all coupons reinvested until maturity • Horizon analysis • Analysis of bond returns over multiyear horizon, based on forecasts of bond’s yield to maturity and investment options • Reinvestment rate risk • Uncertainty surrounding cumulative future value of reinvested coupon payments Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 25 Figure 10.5 Growth of Invested Funds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 26 10.4 Bond Prices Over Time • Yield to Maturity versus Holding Period Return (HPR) • Yield to maturity measures average RoR if investment held until bond matures • HPR is RoR over particular investment period; depends on market price at end of period Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 27 Figure 10.6 Price Paths of Coupon Bonds in Case of Constant Market Interest Rates Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 28 10.4 Bond Prices Over Time • Zero-Coupon Bonds and Treasury STRIPS • Zero-coupon bond: Carries no coupons, provides all return in form of price appreciation • Separate Trading of Registered Interest and Principal of Securities (STRIPS): Oversees creation of zero-coupon bonds from couponbearing notes and bonds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 29 Figure 10.7 Price of 30-Year Zero-Coupon Bond over Time at Yield to Maturity of 10% Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 30 10.4 Bond Prices Over Time • After-Tax Returns • Built-in price appreciation on original-issue discount bonds constitutes implicit interest payment to holder • IRS calculates price appreciation schedule to determine taxable interest income for built-in appreciation Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 31 10.5 Default Risk and Bond Pricing • Investment grade bond • Rated BBB and above by S&P or Baa and above by Moody’s • Speculative grade or junk bond • Rated BB or lower by S&P, Ba or lower by Moody’s, or unrated Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 32 Figure 10.8 Bond Rating Classes Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 33 10.5 Default Risk and Bond Pricing • Determinants of Bond Safety • Coverage ratios: Company earnings to fixed costs • Leverage ratio: Debt to equity • Liquidity ratios • Current: Current assets to current liabilities • Quick: Assets excluding inventories to liabilities • Profitability ratios: Measures of RoR on assets or equity • Cash flow-to-debt ratio: Total cash flow to outstanding debt Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 34 Table 10.3 Financial Ratios and Default Risk Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 35 10.5 Default Risk and Bond Pricing • Bond Indentures • Indenture • Defines contract between issuer and holder • Sinking fund • Indenture calling for issuer to periodically repurchase some proportion of outstanding bonds before maturity Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 36 10.5 Default Risk and Bond Pricing • Bond Indentures • Subordination clause • Restrictions on additional borrowing stipulating senior bondholders paid first in event of bankruptcy • Collateral • Specific asset pledged against possible default • Debenture • Bond not backed by specific collateral Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 37 10.5 Default Risk and Bond Pricing • Yield to Maturity and Default Risk • Stated yield is maximum possible yield to maturity of bond • Default premium • Increment to promised yield that compensates investor for default risk Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 38 Figure 10.10 Yield Spreads among Corporate Bonds 20 Aaa-rated Baa-rated High yield Yield spread (%) 16 12 8 4 0 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2015 2012 2009 2006 2003 2000 1997 1994 1991 1988 1985 1982 1979 1976 1973 1970 -4 39 10.5 Default Risk and Bond Pricing • Credit Default Swaps (CDS) • Insurance policy on default risk of corporate bond or loan • Designed to allow lenders to buy protection against losses on large loans • Later used to speculate on financial health of companies Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 40 Figure 10.11A Prices of CDSs, U.S. Banks Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 41 Figure 10.11B Prices of CDSs, German Sovereign Debt Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 42 10.6 The Yield Curve • Yield Curve • Graph of yield to maturity as function of term to maturity • Term Structure of Interest Rates • Relationship between yields to maturity and terms to maturity across bonds • Expectations Hypothesis • Yields to maturity determined solely by expectations of future short-term interest rates Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 43 Figure 10.13 Returns to Two 2-Year Investment Strategies Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 44 10.6 The Yield Curve • Forward Rate • Inferred short-term ROI for future period, makes expected total return of long-term bond equal to that of rolling over short-term bonds • (1 + π¦π )π = 1 + π¦π−1 π−1 (1 + ππ ) Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 45 10.6 The Yield Curve • Liquidity Preference Theory • Investors demand risk premium on long-term bonds • Liquidity premium • Extra expected return demanded by investors as compensation for greater risk of long-term bonds • Spread between forward ROI and expected short sale • ππ = πΈ ππ + πΏπππ’ππππ‘π¦ ππππππ’π Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 46 Figure 10.14 Illustrative Yield Curves Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 47 Figure 10.15 Term Spread: Yields on 10-Year v. 90-day Treasuries 16 10-year Treasury 90-day T-bills Difference Interest rate (%) 12 8 4 0 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2015 2012 2009 2006 2003 2000 1997 1994 1991 1988 1985 1982 1979 1976 1973 1970 -4 48
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