Chapter 9 Bond Prices and Yield

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1 Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value or principal paymen, e.g. $1000 Mauriy, e.g. 3 monh, 1 year, 30 year, ec. Bond can be classified according o is aribues Paymen ype, e.g. semi-annual coupon Issuer, e.g. governmen, agency, corporae, ec. Mauriy, e.g. shor, medium, long, ec. Securiy, e.g. secured, unsecured, ec. 2/1/2006 FIN Invesmens - Professor Rui Yao 2 1

2 Deb Classes: Paymen ype Pure discoun bond or zero-coupon bond No coupon paymens prior o mauriy Bond s face value paid a mauriy Coupon bond A saed coupon paid periodically prior o mauriy. Bond s face value paid a mauriy Perpeual (Consol) bond A saed coupon paid a periodic inervals forever Self-amorizing bond Cerain amoun of principal paid a each period No balloon paymen a mauriy 2/1/2006 FIN Invesmens - Professor Rui Yao 3 Deb Classes: Issuers End of Q2:2003 2/1/2006 FIN Invesmens - Professor Rui Yao 4 2

3 Deb Classes: Corporae Bonds Credi Raing Moody S&P Qualiy of Issue Aaa AAA Highes qualiy. Very small risk of defaul. Aa AA High qualiy. Small risk of defaul. A A High-Medium qualiy. Srong aribues, bu poenially vulnerable. Baa BBB Medium qualiy. Currenly adequae, bu poenially unreliable. Ba BB Some speculaive elemen. Long-run prospecs quesionable. B B Able o pay currenly, bu a risk of defaul in he fuure. Caa CCC Poor qualiy. Clear danger of defaul. Ca CC High specullaive qualiy. May be in defaul. C C Lowes raed. Poor prospecs of repaymen. D - In defaul. 2/1/2006 FIN Invesmens - Professor Rui Yao 5 Source of Risks for Bond Holders Ineres rae risk (Marke risk) he major facor affecing bond prices he price of bond changes in he opposie direcion of ineres rae change All bonds are exposed o ineres rae risk Inflaion risk Inflaion reduces purchasing power Parially capured by marke ineres rae All bonds are exposed o inflaion risk, hough floaing-rae and inflaion-indexed ones are o a lesser degree 2/1/2006 FIN Invesmens - Professor Rui Yao 6 3

4 Source of Risks Credi risk Inabiliy of issuer o pay coupon and/or principal Corporae Emerging marke High-yield bonds Liquidiy risk Inabiliy o unload posiion wihou subsanial coss Municipal, corporae, and emerging marke bond 2/1/2006 FIN Invesmens - Professor Rui Yao 7 Bond Pricing Discouned cash flow approach Idenify cash flows in coupon and principal paymen Apply one discoun rae (marke ineres rae / yieldo-mauriy) o discoun all fuure cash flows Quoing convenions for bond coupon raes APR (annual percenage raes) Also called BEY (bond equivalen yields) APR / # of periods per year = rae per-period Conver APR o EAY (effecive annual yield) EAY accouns for compounded ineres 1+EAY=(1+rae per period) n = (1+APR/n) n 2/1/2006 FIN Invesmens - Professor Rui Yao 8 4

5 Bond Pricing Bond Value, P C C C F P = C F C 1 F = + = [1 ] + r = 1 C: Coupon per period in dollars r : Ineres rae (discoun rae) per period Price of a 8% semi-annual coupon 30 year -bond? F = $1,000, C = $40, = 60 When marke ineres rae is 8%, r = 4%, hen P =? When marke ineres rae is 10%, r = 5%, hen P =? 2/1/2006 FIN Invesmens - Professor Rui Yao 9 Bond Pricing Bond price higher if Marke ineres rae is lower Price converges o par as a bond approaches mauriy if marke ineres rae says consan Coupon Rae = 8% F = $1,000 C = $40 Mauriy Marke Ineres Rae (APR) Year 4% 6% 8% 10% 12% 14% Premium Bond P > par value Par Bond P=par value Discoun Bond P < par value 2/1/2006 FIN Invesmens - Professor Rui Yao 10 5

6 Bond Yield-o-Mauriy Yield o Mauriy (YM) he ineres rae (or discoun rae) ha makes he PV of bond cash flow equal o is price YM is he average reurn of holding a bond o mauriy oal reurn from holding he bond for one period if he marke ineres rae says consan YM is differen from curren yield Curren Yield = Annual coupon Bond marke price Curren yield ignores he capial gain (loss) componen of oal holding period reurn (HPR) 2/1/2006 FIN Invesmens - Professor Rui Yao 11 Bond Yield-o-Mauriy Q: wha is he relaionship beween coupon rae, curren yield and ym? A: I depends on he ype of bond 1. premium bond Coupon rae > curren yield > ym 2. par bond Coupon rae = curren yield = ym 3. discoun bond Coupon rae < curren yield < ym 2/1/2006 FIN Invesmens - Professor Rui Yao 12 6

7 YM vs. Curren Yield An Example Example: Wha s YM of a bond wih F = $1,000, C = $40, = 60, P = $1,276.76? 60 C F 40 P = + 1, = = 1 r = 3%, r BEY = 2 r = 6%, = We refer r BEY as commonly used YM r EAY 1, = 6.09% Noice he differences/similariies among coupon rae, marke ineres rae (YM/APR/r BEY ), per-period discoun rae r,r EAY, and curren yield = /1/2006 FIN Invesmens - Professor Rui Yao 13 Bond Yield-o-Call A callable bond gives he issuer he righ o buy back a bond from he invesor a a specified price afer he proecion period Q: When will a firm call is bond? Puable bond; converible bond Yield-o-Call he discoun rae which makes he PV of cash flow up o call dae equal o he curren price Cash flow includes coupon paymen and call price Ofen used for premium bond 2/1/2006 FIN Invesmens - Professor Rui Yao 14 7

8 An Example of Yield-o-Call Example: Yield-o-call for a bond wih 20 year mauriy, 5 year call a $1,050, 9% coupon, priced a P = $1, ,000 P = + 40 ( ) ( Implied YM = 8% = 1 ) Yield o call: r = 3.72%, r BEY = 7.44% ,050 1, = + 10 = 1 Q: Which yield measure is more relevan o he bond invesor? 2/1/2006 FIN Invesmens - Professor Rui Yao 15 Bond Defaul Risk Corporae bond may defaul Lower expeced cash flow / yield han promised Saed YM = maximum possible yield Saed YM vs expeced YM 10yr, 9% coupon, $750 price, and 70% par recovery Saed YM: r = 6.825%, r BEY = 13.65% = 45 1, = 1 Expeced YM: r = 5.815%, r BEY = 11.63% = + 20 (1 + r + = 1 ) 2/1/2006 FIN Invesmens - Professor Rui Yao 16 8

9 Municipal Bond Issued by sae or local governmen Exemp from federal (and local) income ax rm rm = ( 1 τ ) r or r = 1 τ Example: r m : yield on ax-free municipal r: equivalen axable yield τ: ax-rae your marginal ax rae is 30%, -bond offers 10% yield, wha yield does a muni bond need o offer o ge you ineresed? 2/1/2006 FIN Invesmens - Professor Rui Yao 17 Yield Curve Definiion A graph of YM as a funcion of mauriy Also called erm srucure of ineres raes Bloomberg: hp:// Expecaion heory: YM deermined by expecaion of fuure rae Liquidiy preference heory: Invesor demands a risk premium for long-erm bond Explains upward-rending yield curve on average Marke segmenaion heory: Separaion of long-mauriy and shor-mauriy bond markes, wih each a is own equilibrium Explains all forms of yield curve 2/1/2006 FIN Invesmens - Professor Rui Yao 18 9

10 Recap How o value a bond based on DCF approach? Wha s he meaning of yield? Wha are he differences beween curren yield, YM and yield-o-call? How does call and defaul opions affec bond yield? How o find he equivalen axable yield of a municipal bond? 2/1/2006 FIN Invesmens - Professor Rui Yao 19 Wha are he hree heories of yield 10

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