Part III : Debt Securities o Bond Prices and Yields o Managing Bond Portfolios
Bond Prices and Yields Chapter 0
Bond Characteristics A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond. Par value face amount of the bond, which is paid at maturity Coupon interest rate stated interest rate (generally fixed) paid by the issuer. (Floating Rate Bond vs. Zero Coupon Bond) Maturity date years until the bond must be repaid. Yield to maturity - rate of return earned on a bond held until maturity (also called the promised yield ).
Different Issuers of Bonds Treasury Bonds and Notes Corporations Municipalities International Bonds Eurobonds Foreign Bonds (Yankee bonds, Samurai bonds, Bulldog bonds, Arirang bonds)
Provisions of Bonds Secured or unsecured Call provision( 수의상환권 ): bonds that may be repurchased by the issuer at a specified call price during the call period. Convertible provision: A bond with an option allowing the bondholder to exchange the bond for a specified number of shares of common stock in the firm. CB, EB, BW Put provision (putable bonds): A bondholder has an option to extend or retire the bond. Floating rate bonds: coupon rates periodically reset according to a specified market rate.
Innovation in the bond markets Inverse floaters Coupon interest when market interest rate Asset-backed bonds Walt Disney, coupon rates tied to the film performance Pay-in-kind bonds Pay interests either in cash or in additional bonds Catastrophe bonds Tokyo Disney land, no payment in case of earthquake, transferring catastrophe risk from insurance co. to capital mkts Indexed bonds Payments tied to a price index or the price of a commodity U.S. Treasury Inflation Protected Securities (TIPS)
Innovation in the bond markets (EX.)U.S. Treasury Inflation Protected Securities (TIPS) A newly issued TIPS bond with a three year maturity, par value of $000, and a coupon rate of 5%. Assume annual coupon payments.
Bond Pricing ㅇ The value of any financial asset is simply the present value of the cash flows the asset is expected to produce. 0 2 n k... Value CF CF 2 CF n Value CF ( k) CF ( 2 k) 2... CF ( n k) n
P B Bond Pricing (cont d) ㅇ채권 (bond) 의수익구조 : 이자 + 액면가 - 일정만기내에규칙적으로발행금리 (coupon rate) 에해당하는이자를지급하고만기시액면가 (face value) 를지급 T t INT t ( k ) t FaceValue T ( k ) INT * PVIFA(k, T) FV * PVIF(k, T) P B = Price of the bond INT t = interest or coupon payments T = number of periods to maturity K = discount rate or yield to maturity (YTM)
What is the opportunity cost of debt capital? The discount rate (k ) is the opportunity cost of debt capital, and is the rate that could be earned on alternative investments of equal risk. k = k* + IP + MRP + DRP + LP
Bond Pricing (cont d) 예상되는현금흐름시점에만기수익률할인율만기액면가액표면이자율채권가격 : ) (, : ), ( : ) ( :, :, : ) ( ) ( ) ( ) ( 0 t 2 0 t CF YTM k maturity n face value F i B k CF k F k F i k F i k F i B t n t t n n n n 2 2 k) ( I... k) ( I k) ( I Bond's value F NT NT NT
Bond Pricing (cont d) Price?: 0-yr, 8% Coupon, FV = $,000 P P Ba Bsa 0 t 20 t 80.06 40 t t 000 (.06) 000.03 (.03) 0 20 int t = i*,000=80 P = 000 T = 0 years r = 6%
Using a Financial Calculator to Value a Bond i=8% k d =6% i=4% k d =3% INPUTS OUTPUT INPUTS OUTPUT 0 6 80 000 N I/YR PV PMT FV -47.20 20 3 40 000 N I/YR PV PMT FV -48.77 P B =80*PVIFA(6%,0)+000*PVIF(6%,0)=80*7.360+000*0.5584 P B =40*PVIFA(3%,20)+000*PVIF(3%,20)=40*4.8775+000*0.5537 Financial Management_Prof. Chung 6-4
Bond Pricing (cont d) ㅇ Bonds with Semiannual Coupons i F /2 B0 k /2 i F /2 ( k /2) 2 i F /2 ( k /2) 2n F ( k /2) 2n 2 n t CF t ( k /2) t ㅇ Bonds paying interests m times/year B 0 i F / m k / m i F / m ( k / m) 2 i F / m ( k / m) F ( k / m) m : number of interest paymentsper year(quarterly, m 4) m n mn m n t CF t ( k / m) t
B 0 ㅇ Bond pricing between coupon dates (cont d) k d ( ) m q T t0 Bond Pricing (cont d) i F / m ( k / m) t F ( k / m) T d : number of days between the trading date and the next interest paymentdate q : number of days between the previous and the next interest paymentdates (ex.) issued on Jan., 2003, maturity of 3 years (maturing on Dec. 3, 2005), FV:,000,000; coupon rate: 5%, quarterly interest payment, as of today (May 0, 2003) current interest rate : 6% B 0 2,500,000,000 0 t 0 t0 ( 0.06 / 4) ( 0.06 / 4) ( 0.06 4 5 ) 9 98,96
Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship. 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. T INT t FaceValue T PB t ( k ) ( k T t )
Figure 0.3 The Inverse Relationship Between Bond Prices and Yields 0-8
Yield to Maturity (YTM) The rate of return earned on a bond if it is held to maturity Interest rate that makes the present value of the bond s payments equal to its price. Solve the bond formula for YTM P B T t Bond Yields INT FaceValue t t ( YTM ) ( YTM T ) T
Bond Yields (cont d) (YTM example) a 0-year, 9% annual coupon bond, sells for $887, a face value of $,000 V B ( INT YTM)... ( INT YTM) N ( M YTM) N $887 ( 90 YTM)... ( 90 YTM) 0 (,000 YTM) 0 YTM 0.9%
Using a Financial Calculator to Solve for the YTM INPUTS 0-887 90 000 N I/YR PV PMT FV OUTPUT 0.9 Financial Management_Prof. Chung 6-2
Bond Yields (cont d) (YTM example) a 30-year, 8% semiannual coupon bond, sells for $,276.76, a face value of $,000 V B INT ( YTM) $,276.76 ( INT... ( YTM) 40 YTM)... ( ( 40 YTM) YTM) ( YTM 3% per half - year,apr : 6%, EAR : ( N 60 M N,000 YTM) 0.03) 2 60 6.09%
Bond Yields (cont d) YTC (Yield to Call): The rate of return on a bond if it is called before its maturity INT INT Call Price VB... N ( YTC) ( YTC) ( YTC) N $887 (YTC example) a 0-year, 9% annual coupon bond, sells for $887, a face value of $,000, callable in 5 years at a call price of $,00 (YTC=3.79%) 90 90,00... 5 5 ( YTC) ( YTC) ( YTC)
(YTC example2) : Bond Yields (cont d) A 20-year maturity 9% coupon bond paying coupons semiannually is callable in five years at a call price of $,050 (face value $,000). The bond currently sells at a yield to maturity of 8%. What is the YTC? V V B B 45 45... ( YTC) ( YTC) 45 ( 0.08 /2)... 45 ( 0.08 /2),098.96 YTC 3.72% per half - year,apr : 7.44%, EAR : ( 0.0372) 0 050 ( YTC) 40 0 000 ( 0.08 /2) 40 2 7.58%
Bond Yields (cont d) CY (Current Yield): The annual interest payment on a bond divided by the bond s current price Find the current yield for a 0-year, 9% annual coupon bond that sells for $887, and has a face value of $,000. Current yield = $90 / $887 = 0.05 = 0.5%
V B The price path of a bond What would happen to the value of this bond if its coupon rate are different at 0%, at 3%, or at 7%? (FV:$,000;Kd=0%;N=5),228 i = 3% (premium bond),000 i = 0%. 772 5 2 9 6 3 0 i = 7% (discount bond) Years to Maturity
Bond values over time At maturity, the value of any bond must equal its par value. If k d remains constant: The value of a premium bond would decrease over time, until it reached $,000. The value of a discount bond would increase over time, until it reached $,000. A value of a par bond stays at $,000.
Default Risk and Ratings Rating companies Moody s Investor Service Standard & Poor s Duff and Phelps Fitch 한신평, 한기평, NICE신용평가 Rating Categories Investment grade (AAA/Aaa BBB/Baa) Speculative grade: Junk bonds (BB/Ba - )
Factors Used by Rating Companies Coverage ratios Times-interest-earned ratio (=EBIT/interest) Leverage ratios Debt-to-equity ratio Liquidity ratios Current ratio (CA/CL); Quick ratio Profitability ratios: firms overall financial health ROA; ROE
Term Structure of Interest Rates Term structure relationship between YTM (yield to maturity) and maturities. The yield curve is a graph of the term structure. Upward-, downwardsloping, humped shape and flat YTM(%)
Theories of Term Structure Expectations Hypothesis Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat
( r r n n E( r ) Expectations Theory Observed long-term rate is a function of today s short-term rate and expected future short-term rates. Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates. n [( E( r ))( E( r : YTM on a bond with maturity of n, n r )(,2 2,3 )) ( E( r n, n n periods observed in the market ) : expected futureshort interest rate between periods (n -) and n ))]
Returns to Two 2-year Investment Strategies
Forward Rates from Observed Rates ( y n ) n ( y ) n ( f n n f n = one-year forward rate for period n y n = YTM for a security with a maturity of n (ex) y 4 = 9.993% y 3 = 9.660% f 4 =? (.0993) 4 = (.0966) 3 (+f 4 ) (.46373) / (.3870) = (+f 4 ) f 4 =.0998 or % )
Liquidity Preference Theory Long-term bonds are riskier. Investors will demand a premium for the risk associated with long-term bonds. The yield curve has an upward bias built into the long-term rates because of the risk premium. Forward rates contain a liquidity premium and are not equal to expected future short-term rates. ( r n ) n ( r )( E( r,2 ) L ) ( E( r n, n ) L n ) L L 2 L n : Liquidity Premium
Liquidity Premiums and Yield Curves Yields Liquidity Premium Liquidity premium Theory Expectation Theory Maturity
Market Segmentation Short- and long-term bonds are traded in distinct markets. Trading in the distinct segments determines the various rates. Observed rates are not directly influenced by expectations. YTM S-T M-T L-T Maturity