CDIAC provides information, education and technical assistance on public debt and investments to local public agencies and other public finance professionals. 1
The California Debt and Investment Advisory Commission 0 Technical Webinar Series Bond Math 2 The Economics of Bonds Housekeeping •Feedback Button •Questions and Answers •Polling Questions 2
The California Debt and Investment Advisory Commission 0 Technical Webinar Series Bond Math 2 The Economics of Bonds Piecing Together Bond Finances •Introduction of Speakers Robert G. Friar, Jr. Managing Director, The PFM Group Kenneth D. Fullerton Managing Director, The PFM Group 3
ad~ice ·O~er O~er ad~isor pro~ided The California Debt and Investment Advisory Commission 0 Technical Webinar Series Robert G. Friar, Jr. Managing Director, The PFM Group 27 years of experience in Municipal Finance ·Has been in~ol~ed in all aspects of the business across the country, as both an underwriter and financial •Currently assists clients in the structuring and financing of complex airport projects Kenneth D. Fullerton Managing Director, The PFM Group • 30 years of experience in Municipal finance • Has financial on o~er 100 financings totaling o~er $15 billion for airport clients. •Current airport clients include Chicago, New York, Washington, Tampa, San Jose, Oakland, Salt lake, Reno, Columbus, Pro~idence, Ft. Myers, Pittsburgh, Memphis and many others 4
Pie c ing T oge the r Bond F inanc e Pr e se nte d by Ke nne th D. F ulle r ton & Robe r t G. F r iar , Jr .
T opic s T he Yie ld Curve 1 Wha t it is a nd why it ma tte rs zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Bo nd Pric ing 2 Pa r, pre mium a nd disc o unt b o nds Othe r T ype s o f Bo nds 3 Ca pita l a ppre c ia tio n a nd ze ro c o upo n b o nds Bo nd Re de mptio ns a nd Ac c rue d I nte re st 4 Ho w b o nds a re re de e me d Spre a dshe e t F o rmula s 5 Built in func tio ns fo r do ing b o nd c a lc ula tio ns Co nc lusio n 6 6
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. T he Yie ld Cur ve Definition: A curve on a graph in which the yield of fixed-interest securities is plotted against the length of time they have to run to maturity. • Unde r no rma l c o nditio ns, inte re st ra te s o n b o nds with sho rte r ma turitie s a re lo we r tha n b o nds with lo ng e r ma turitie s. Normal Yield Curve (Upwardly Sloping) 4.000% 3.500% 3.000% 2.500% 2.000% 1.500% 1.000% 0.500% 0.000% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Years to Maturity 7
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA T he Yie ld Cur ve (c o ntinue d) T he re a re a numb e r o f the o rie s tha t a tte mpt to e xpla in why ra te s te nd to b e hig he r o n lo ng e r ma turitie s tha n o n sho rte r o ne s (a n “upwa rdly slo ping ” yie ld c urve ). T wo o f the se a re : - L iq uidity Pre mium: All thing s b e ing e q ua l, inve sto rs fa c e g re a te r unc e rta inty ho lding lo ng e r te rm b o nds tha n sho rte r te rm b o nds. Ma ny mo re unpre dic ta b le thing s a re like ly to ha ppe n in the ne xt te n ye a rs tha n in the ne xt two a nd inve sto rs de ma nd hig he r ra te s to c o mpe nsa te the m fo r this risk. - Ma rke t E xpe c ta tio ns: T his the o ry sa ys tha t inve sto rs, in g e ne ra l, e xpe c t inte re st ra te s in the future will b e hig he r tha n the y a re to da y. T he y the re fo re de ma nd a n inte re st ra te o n lo ng e r ma turitie s tha t wo uld g ive the m the sa me e xpe c te d to ta l re turn ha d the y a lte rna tive ly inve ste d in a sho rte r ma turity a nd the n re inve ste d a t the hig he r future ra te tha t the y a re e xpe c ting . 8
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA T he Yie ld Cur ve (c o ntinue d) • T he yie ld c urve c a n, a nd do e s, c ha ng e o ve r time a s e c o no mic c o nditio ns c ha ng e . I t c a n fla tte n so tha t sho rt te rm ra te s a nd lo ng te rm ra te s a re the sa me . Flat Yield Curve 6.000% 5.000% 4.000% 3.000% 2.000% 1.000% 0.000% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Years to Maturity 9
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA T he Yie ld Cur ve (c o ntinue d) T he yie ld c urve c a n e ve n b e c o me inve rte d whe re lo ng te rm ra te s a re lo we r tha n sho rt te rm ra te s. An inve rte d yie ld c urve is c o nside re d to b e a ne g a tive e c o no mic indic a to r. I nve rsio n indic a te s tha t inve sto rs b e lie ve inte re st ra te s will b e lo we r in the future a nd tha t o fte n me a ns tha t e c o no mic a c tivity is a t le a st like ly to slo w a nd ma y e ve n me a n tha t a re c e ssio n is c o ming . A tig hte ning o f sho rt te rm inte re st ra te s b y the F e de ra l Re se rve in o rde r to slo w the e c o no my o r to re ig n in infla tio n c a n le a d to a n inve rte d yie ld c urve . Inverted Yield Curve 6.000% 5.000% 4.000% 3.000% 2.000% 1.000% 0.000% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Years to Maturity 10
T he Yie ld Cur ve (c o ntinue d) • So fa r in 2011 the US T re a sury yie ld c urve ha s fla tte ne d c o nside ra b ly: 2011 Treasury Yield Curve 6.000% January October 5.000% 4.000% Treasury Yields 3.000% 2.000% 1.000% 0.000% zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Years to Maturity 11
2. Bond Pr ic ing Pa r, Disc o unt a nd Pre mium Bo nds • T he yie ld o n a b o nd is a me a sure o f the re turn, o r e a rning s, re a lize d b y ho lding the b o nd. T he yie ld is de te rmine d b y the ma rke t, the o ve ra ll supply a nd de ma nd fo r the b o nd. As we sa w in the pre vio us se c tio n the yie ld will usua lly va ry de pe nding o n the fina l ma turity zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA o f the b o nd. • T he pr ic e to b e pa id fo r a b o nd a lso va rie s b a se d o n the c oupon tha t is a tta c he d to the b o nd. T he c o upo n is the a c tua l ra te o f inte re st tha t is pa id to the b o nd inve sto r. A 5% c o upo n o n a $100 b o nd pa ys $5/ ye a r. • Par Bond • A par bond is a b o nd tha t c a n b e purc ha se d a t 100% o f its unde rlying va lue . A b o nd tha t ha s a princ ipa l a mo unt o f $100 a t ma turity will se ll fo r $100 rig ht no w if its c o upo n is the sa me a s the c urre nt ma rke t yie ld. Of c o urse , ma rke t yie lds c ha ng e a ll the time so a b o nd tha t is tra ding a t pa r to da y ma y no t b e tra ding a t pa r to mo rro w. 12
Bond Pr ic ing Pa r, Disc o unt a nd Pre mium Bo nds • One o f the mo re c o nfusing a spe c ts o f b o nds is the re la tio nship b e twe e n pric e a nd yie ld: • I f yo u o wn a b o nd a nd the mar ise s the pr ic e of the bond falls . ke t yie ld r • I f yo u o wn a b o nd a nd the mar ke t yie ld falls the pr ise s . ic e of the bond r Years to Market Maturity Coupon Yield Price T his is a table • P 5 5.00% 4.00% 104.491 R that shows E 5 5.00% 4.25% 103.347 M what happe ns 5 5.00% 4.50% 102.217 I U to the pr ic e of a M 5 5.00% 4.75% 101.101 bond with a 5% 5 5.00% 5.00% 100.000 PAR D c oupon as mar ke t 5 5.00% 5.25% 98.913 I S yie lds c hange 5 5.00% 5.50% 97.840 C zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA O 5 5.00% 5.75% 96.781 U N 5 5.00% 6.00% 95.735 T 13
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Bond Pr ic ing (c o ntinue d) Disc ount Bond I f ma rke t yie lds rise to 6%, the b o nd with a 5% c o upo n is no w pa ying a ra te tha t is le ss va lua b le in the ma rke t. T he pric e o f this le ss va lua b le b o nd will the re fo re fa ll a nd it will tra de a t a disc ount to pa r, sa y 95% o f its o rig ina l pa r va lue if it is five ye a rs until the b o nd ma ture s. By tra ding a t a disc o unt this b o nd will ha ve a n o ve ra ll yie ld o f 6% (the ra te de ma nde d b y the ma rke t): 5% fro m the c o upo n a nd a n a dditio na l 1%/ ye a r fro m the disc o unt a s the pric e o f the b o nd will slo wly a ppro a c h 100% o f its pa r va lue a t ma turity. One re a so n a n inve sto r mig ht pre fe r a disc o unt b o nd: Ca ll pro te c tio n. I n a ma rke t e nviro nme nt whe re inte re st ra te s a re fa lling it will ta ke lo ng e r fo r a b o nd with a lo we r c o upo n to b e pro fita b ly c a lle d b y the issue r o f the b o nd whe n c o mpa re d to a hig he r c o upo n b o nd. 14
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