Unformatted text preview: Chapter 10 Bond Prices and Yields 10.1 Bond Characteris6cs U.S. Credit Market Instruments O/S 2008 Q3 U.S. Equity Market (Common) U.S. Credit Market Debt $19,648 B illion $51,796 Debt by Selected Major Borrowers (Not ExhausBve List): U.S. Government SecuriBes $13,850 (27%) (Includes Agency & GSE) %s are percent of Total U.S. Credit Market Debt, source is Federal Reserve Flow of Funds U.S. Credit Market Instruments O/S 2008 Q3 By Selected Major Borrowers (Not ExhausBve List) Corporate & Foreign Bonds $11,262 Billion (22%) Municipal Bonds G.O., Revenue, Notes $2,669 Billion (5%) Mortgages $14,720 Billion (28%) Bond CharacterisBcs • Face or par value: payment to the bondholder at the maturity of the bond. • Coupon rate: interest payment per year, as a percentage of par value. – Special case: Zero coupon bond • Compounding and payments – Accrued Interest • Bond indenture: contract se_ng forth the terms of a bond issue, obligaBons of issuer, etc Treasury Notes and Bonds T Note maturiBes range up to 10 years T bond maturiBes range from 10 to 30 years Typically semiannual coupon payment. Bid and ask price – Quoted in dollars and 32nds as a percent of par – Typical par = $1,000 • Accrued interest – Quoted price does not include interest accrued – Invoice price = Quoted price + accrued interest • • • •
ȹ Annual Coupon Payment ȹȹ Days since last coupon payment ȹ Accrued interest = ȹ ȹȹ ȹ ȹ Ⱥȹ Days separating coupon payments Ⱥ 2 Figure 10.1 Prices and Yields of U.S. Treasuries Corporate Bonds & Debt • Most bonds are traded over the counter • Par = $1,000 • Call provisions • ConverBble provision – Allow the issuer to repurchase the bond at a speciﬁed call price before maturity – Allow bondholder to exchange the bond for a speciﬁed # of shares of common stock in the ﬁrm. – Allow bondholder to exchange for par at some date or extend the bond for a given number of years • Put provision (pugable bonds) • FloaBng rate bonds: coupon resets periodically to a speciﬁed market rate. Problem 1 Suppose that Verizon issues two bonds with idenBcal coupon rates and maturity dates. • One bond is callable, however, while the other is not. Which bond will sell at a higher price? • One bond is converBble, while the other is not. Which bond will sell at a higher price? Figure 10.2 LisBng of Corporate Bonds Other DomesBc Issuers • • • • • • Federal Home Loan Bank Board Farm Credit Agencies Ginnie Mae Fannie Mae Freddie Mac MunicipaliBes InternaBonal Bonds • Foreign bonds – Issued by a borrower from a country other than the one in which the bond is sold. – Bonds are denominated in the currency of the country in which it is sold. • Yankee bonds, Samurai bonds, Bulldog bonds • E.g. Yankee bonds are registered with the SEC. since they are marketed and sold in US. • Eurobonds – Bonds issued in the currency of one country but sold in other naBonal markets. • Eurodollar bonds: dollar
denominated bonds sold outside US • Euroyen bonds: Yen
denominated bonds sold outside Japan InnovaBons in the Bond Market • Inverse ﬂoaters – Coupon rate falls when interest rates rise & vice versa • Asset
backed bonds – Income from speciﬁed assets is used to service the bond • Pay
in
kind bonds – Bond issuer may choose to pay interest either in cash or in addiBonal bonds. • Catastrophe bonds – In the event of a speciﬁed ‘disaster’ the bond issuer’s required payments are reduced or eliminated. InnovaBons in the Bond Market • Indexed bonds – Payments are Bed to a price index or the price of a commodity. • TIPS (Treasury InﬂaBon Protected SecuriBes) With TIPS the par value of the bond increases with the Consumer Price Index. HypotheBcal Principal and Interest Payments on a TIPS Assume a coupon rate of 4%, and par value of $1000. ȹ Interest + Price appreciation ȹ ȹ 40.80 + 20 ȹ Nominal return at the end of year 1 = ȹ ȹ = 6.08% ȹ = ȹ Initial price ȹ Ⱥ ȹ 1000 Ⱥ ȹ1 + Nominal return ȹ 1.0608 Real return at the end of year 1 = ȹ − 1 = 4% ȹ − 1 = ȹ 1 + Inflation rate Ⱥ 1.02 € 10.2 BOND PRICING Bond Price • Bond price depends on the following factors – Coupon payment and frequency – Maturity – Market interest rate – Call risk (for callable bond) – Tax agributes – Liquidity – Reinvestment rate risk – etc Bond Prices & Yields a) Bond value for a corporate bond: Par = $1,000, Coupon rate=10%, interest rate = r = 12%, Maturity = T = 10 years, P = price, What is the bond’s price using semiannual compounding? Ans: Coupon payment C=1000(10%)/2=$50 Ⱥ 2T Ⱥ 20 $50 Ⱥ $C Ⱥ Par $1, 000 P = Ⱥ∑ = Ⱥ∑ Ⱥ + Ⱥ + t 2T t 20 Ⱥ t =1 (1 + r/2) Ⱥ (1 + r/2) Ⱥ t =1 (1.06) Ⱥ (1 + .06) = $573.50 + $311.80 = $885.30 Bond Pricing Between Coupon Dates • The ﬂat price or quoted price assumes the bond is purchased on a coupon payment date. • If the bond buyer purchases a bond between payment dates the buyer’s invoice price = ﬂat price + accrued interest. Bond Pricing Between Coupon Dates Annual Coupon$ Days since last coupon payment Accrued Interest = x 2 Days between coupon payments € • A bond has a ﬂat price of $925.30 and an annual coupon of $42.50. 160 days have passed since the last coupon payment and there are 182 days separaBng the coupon payments. What is the bond’s invoice price? $42.50 160 Accrued Interest = x = $18.68 2 182 € Invoice price = Flat price + Accrued Interest = 925.3+ 18.68=943.98 Bond ValuaBon in Excel 10.3 BOND YIELDS Bond Prices and Yields • Prices and Yields (required rates of return) have an inverse relaBonship (convexity) • When yields get very high the value of the bond will be very low • When yields approach zero, the value of the bond approaches the sum of the cash ﬂows Promised Yield to Maturity (YTM) • YTM is the discount rate that makes the present value of a bond’s payments equal to its price • Find the YTM for a 8% coupon, 30
year bond selling at $1,276.76 Ⱥ 2T $C Ⱥ Par P = Ⱥ∑ Ⱥ + t 2T Ⱥ t =1 (1 + r) Ⱥ (1 + r) Ⱥ 60 $40 Ⱥ $1, 000 $1, 276.76 = Ⱥ∑ Ⱥ + t 60 Ⱥ t =1 (1 + r) Ⱥ (1 + r) € Thus, r=3% • AssumpBon of this calculaBon? €
– This is a trial and error solution unless you have a financial calculator. – The assumption of this calculation is that each $40 coupon is reinvested at 3% (the promised ytm). Figure 10.3 The Inverse RelaBonship Between Bond Prices and Yields Table 10.2 Bond prices at diﬀerent market interest rates (8% coupon bond, coupons paid semiannually) A bond will sell at par value when its coupon rate equals the market interest rate. Compute yield to maturity in Excel AlternaBve Measures of Yield • Current Yield – Annual dollar coupon divided by the price – premium bonds: bonds selling above par value • Coupon rate > current yield > yield to maturity – discount bonds: bonds selling below par value • Coupon rate < current yield < yield to maturity • Yield to Call – Call price replaces par – Call date replaces maturity • Holding Period Yield – Considers actual reinvestment rate on coupons – Considers any change in price if the bond is sold prior to maturity Figure 10.4 Bond Prices (8% coupon rate and 30
year maturity): Callable and Straight Debt Call price is 110% of par Problem 2 Suppose the 8% coupon, 30
year maturity bond sells for $1150 and is callable in 10 years at a call price of $1100. What is the yield to maturity and yield to call? ANS: C=$40, number of semiannual periods= 20 or 60, Final payment= 1100 or 1000, and Market price of the bond = $1150. Figure 10.5 Growth of $1000 invested in a 2 year bond (10% coupon, annual) realized compound return: $1000(1+r)2 = $1210 r=10% realized compound return: $1000(1+r)2 = $1208 r=9.91% Tradeoﬀ in price risk and reinvestment rate risk • Market interest rate increases, – Bond price falls, resulBng in lower value in bond porvolio – Reinvested coupon income compounds more rapidly at higher rate • Market interest rate fallss, – Bond price rises, resulBng in higher value in bond porvolio – Reinvested coupon income compounds at lower rate 10.4 BOND PRICES OVER TIME Premium and Discount Bonds • Premium Bond – Coupon rate exceeds yield to maturity – Bond price will decline to par over its maturity • Discount Bond – Yield to maturity exceeds coupon rate – Bond price will increase to par over its maturity • Can you explain why these price change will occur? Figure 10.6 Premium and Discount Bonds over Time Figure 10.7 The Price of a Zero Coupon Bond over Time How does one earn a rate of return on a zero coupon bond? Par (1 + r) N P= What are STRIPS? € How is the price appreciaBon taxed? 10.5 DEFAULT RISK AND BOND PRICING Default Risk and RaBngs • Main RaBngs Companies – Moody’s Investor Service – Standard & Poor’s – Fitch • Main RaBng Categories – Investment grade – SpeculaBve grade ( junk bonds) Figure 10.8 DeﬁniBons of Bond RaBng Classes Factors Used by RaBng Companies • Coverage raBos – TIE and Fixed Charges Coverage raBo • Leverage raBos – Debt to equity or Debt to assets • Liquidity raBos – Current and quick raBo • Proﬁtability raBos – Return on assets and return on equity • Cash ﬂow to debt – Cash ﬂow to debt Financial Ra6os and Default Risk ProtecBon Against Default • Sinking funds – Issuer may repurchase a given fracBon of the outstanding bonds each year, or – Issuer may either repurchase at the lower of open market price or at a pre
speciﬁed price, usually par; bonds are chosen randomly • Serial bonds – Staggered maturity dates • SubordinaBon of future debt – Senior debt holders must be paid in full before junior debt holders. ProtecBon Against Default • Dividend restricBons – Limit on liquidaBng dividends • Collateral – A speciﬁc asset pledged against possible default on a bond. – What is a bond called that has no speciﬁc collateral? Figure 10.9 Callable Bond Issued by Mobil Example 10.10 YTM and Default Credit Default Swaps A credit default swap (CDS) is an insurance policy on the default risk of a bond or loan. • The seller of the swap collects an annual premium (and someBmes an upfront fee) from the swap buyer. • The buyer of the swap collects nothing unless the bond issuer or loan borrower defaults, in which case the seller of the swap essenBally pays the drop in value from par to the swap buyer. Credit Default Swaps • CDSs can be used to speculate on ﬁnancial health of ﬁrms. – Swap buyer need not hold the underlying bond or loan. – At their peak there were reportedly $63 trillion worth of CDS; US GDP is about $14 trillion. – What is the implicaBon of the size of this market if the economy experiences greater than expected defaults? – Did this contribute to the Financial Crisis of 2008? Credit Default Swaps Credit Default Swaps • New regulaBons on CDS will be implemented – CDS contracts will be required to be traded on an exchange with collateral requirements to limit risk. – Exchange trading will also increase transparency of posiBons of insBtuBons. 10.6 THE YIELD CURVE Term Structure of Interest Rates • RelaBonship between yields to maturity and maturity • Yield curve: a graph of the yields on bonds relaBve to the number of years to maturity – Have to be similar risk or other factors would be inﬂuencing yields Figure 10.10 Yields Spreads on 10 year bonds Figure 10.11 Treasury Yield Curves Theories of the Term Structure • Expecta6ons – Long term rates are a funcBon of expected future short term rates – Upward slope means that the market is expecBng higher future short term rates – Downward slope means that the market is expecBng lower future short term rates • Liquidity Preference – Upward bias over expectaBons – The observed long
term rate includes a risk premium Figure 10.13 Returns to Two 2
year Investment Strategies Forward Rates Implied in the Yield Curve (1 + y n ) = (1 + y n −1 ) (1 + f n ) 2 1 (1 + 0.12) = (1 + 0.11) (1 + 0.1301)
n n −1 • For example, using 1
yr and 2
yr rates € • Longer term rate, yn = 12% • Shorter term rate, yn
1 = 11% • Forward rate, a one
year rate in one year = 13.01% Figure 10.14 Illustra6ve Yield Curves Figure 10.15 Term Spread ...
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