Exm FM/ Iere Theory Formul by (/roprcy Th collboro of formul for he ere heory eco of he SO Exm FM / S Exm. Th uy hee free o-copyrghe ocume for ue g Exm FM/. The uhor of h uy hee ug ome oo h uque o h o ego wll repe. Ech ego h oly oe meg hroughou he hee.
Fumel of Iere Theory Tme Vlue of Moey FV V + V FV + ( + ( + ( The mou l eme of grow o by me ( The mou l eme of grow o by me l ( e + l( + e + + δ l( + δ e δ ( + e δ ( ( ( e δ ( u u ( δ e u u ( Effece ere re wh oml re coerble m-hly m + m Effece cou re wh oml re Noml Re Equlece p ( p p ( p coerble p-hly m ( p p δ + + e m p
Effece ul re urg he -h yer ge by: mou ere begg mou ( ( ( ( Noe h he -h yer ge by he me pero [,] Therefore, he ere ere urg he -h yer ge by: ( ( For equle meure of ere we he he followg relohp: ( 3 ( 3 < < < < δ < < < < ue uy Immee pyme re me he e of he pero uy Due pyme re me he begg of he pero uy Immee + + + ( + + ( + ( + + + ( + uy Due + + + ( + + ( + + + ( + ( + ( + Iee for uy Immee uy Due ( + ( + + +
erpeuy 3 lm + + + lm ouou ue V δ δ ( ( + δ δ δ u u δ( u u e p FV e p where p pyme fuco ( Icreg ue yme re,,, ( I ( I ( I ( + ( I ( I ( + ( I ( I ( I ( + ( I ( I lm( I + ( I lm( I Decreg ue yme re, -,,, ( D ( D ( D ( + ( D ( + ( D ( + ( D ( D ( + ( D ree Vlue of he uy wh erm X, X + Y, X + Y,, X + ( Y X + Y ree Vlue of he perpeuy wh erm X, X + Y, X + Y, X Y +
ue wh Term Geomerc rogreo (, +, + q,, + q q 3 ree Vlue V + ( + q + ( + q + + ( + q ( + q q Ueful Iee m + ( + m ( D + ( I ( + + + + ( + ( + + If he ere re re: + + + ( ( + + + If he compoug frequecy of he ere excee he pyme frequecy of yer Ue equle ere re oer yer: j ( + If he pyme frequecy excee he compoug frequecy of he ere ( Ue m-hly uy ( Ue equle ere re effece oer he pyme pero: ( j + m j j j j If he pyme re,,, m m m I If he pyme re,,, m m m, he he pree lue, he he pree lue m m m m I
o Repyme morzo morzo Meho whe pyme me, mu be fr pple o py ere ue he y remg pr of he pyme pple o py prcple Noo mou of he lo umber of pyme pero mou of leel pyme he e of he pero (morze pyme ( lo pyme me effece ere re per pyme pero B blce me, blce fer -h pyme. Noe h B prcple p pyme ( I ere p pyme ( Ueful Equo for eel yme ropece Meho B + Reropece Meho B ( B B + + ( + + + I + I B ( I + Ueful Equo for No-eel yme + + + ( B + + + + B + ( ( + ( I B ( I B B
o Repyme Sg Fu Sg Fu o (SF ccumule moey epre fu by mg pyme, o o he regulr ere pyme, eery pero. Noo j mou of he lo umber of pyme pero effece ere re per pyme pero by he borrower o he leer effece ere re ere by he borrower he g fu D S peroc g fu epo (SFD, ume o be leel S peroc ouly by he borrower ere pyme o leer + SFD S g fu blce fer -h epo e lo blce me Ueful Equo D S j D S j + D + S S j j DS j DS j j S Ne rcpl S S D D D ( j S + j S j S Ne Iere js jd S j Noe o o morze o oer me ere p ecree prcpl p cree SF for ech ouly ere p o leer co Illme o oer me ere p ecree whle he prcpl p co
Bo Bo ere berg ecure; bclly lo from leer perpece llble Bo bo h c be p off (clle before mury Noo F r Fr pr lue coupo re (ere re of bo coupo mou (pyme o leer reempo lue (uully F BV umber of coupo pero o mury mre prce of he bo boo lue of he bo (bo morze blce fer -h pyme yel per pero o eor prce + K ree lue of he reempo lue Fr g mofe coupo re remum If > r he he bo prce premum. >, he mou of he premum. remum ( Fr ( + + + + + ( + + + ( + ( + + Dcou If < r he he bo prce cou. <, he mou of he cou Dcou ( Fr r If r he bo ellg he prce we y h ell pr.
rce remum-dcou Formul Fr + K ( + ( g f Bo morze BV Fr + BV F, he F + ( r m m BVm + Fr Fr I + I BV + + ( Fr + Fr + + If F, he + ( + Wre-Up urg he fr yer (Dcou Wre-Dow urg he fr yer (remum BV BV Wre-Up/Wre-Dow geerl urg me m o me, WD ( Fr + WU ( Fr + Mehm Formul g K + ( K f r F, he K + ( F K > BV BVm Mury o ue rcg llble Bo Type of Bo remum Bo Dcou Bo Te N ug Erle oble Reempo De e oble Reempo De rce Bewee yme De umber of y from l coupo e o eleme e umber of y he bo pero rce lu ccrue + ccrue Iere ( Fr lu ccrue ccrue Iere ( + ( Fr rce
Yel Re of Ieme Ierl Re of Reur (IRR he re of ere whch he pree lue of ll mou ee equl o he pree lue of ll he mou p bc o he eor Ierl Re of Reur (IRR Ge eme ch flow,,,,, he IRR oluo for of he equo + + + or + + + + + ( + ( + ( + Tme Weghe Re of Iere (TWR orbuo me B Fu lue me before he corbuo me j + Effece re oer [, ] B B + j TWR + ( + j ( + j ( + j m Dollr Weghe Re of Iere (DWR B I Il fu blce Fl fu blce Iere ere orbuo or whrwl me (ch flow Ne Ne corbuo Ne B + Ne + I I B Ne DWR I +
Term Srucure of Iere Re Spo Re Deoe by he -yer po re ( The ul ere re o he -yer Treury STRI clle he -yer po re, he ere of po re oer me clle he yel cure. ( To lue bo, e he pree lue of ech pyme he ppropre yel cure re um he pree lue. ( ( + + + + + + + + + + ( + + f f f ( + f (3 Oce we he fou he prce of bo ug he yel cure we c f he yel o mury he co yel o he bo h prce. For exmple urchg bo wh coupo h ch flow ge by, (,,, ( If pyme (,,, ( re o leel Ug he B-II lu. F Worhee Se Fo, (,,, N (. IRR T o Yel o he Bo IRR If pyme (,,, ( re leel Ug he B-II lu. TVM Worhee Se V, N, MT (, FV. I/Y T o Yel o he Bo I/Y Forwr Re Deoe by f he yer forwr re The re gree upo oy for oe-yer lo o be me yer he fuure + f ( + ( + ( + ( + f ( +
Duro Duro meure of ey of fcl e o chge ere re Ieme h Flow,,, Ieme rce + + + Wegh for Mculy Duro Mculy Duro w > ( + + + D w + w + + w M Mofe Duro D ( DM + > > > Duro of eel yme Ieme D ( I Mculy Duro of coupo bo wh fce lue F coupo Fr for pero reempo lue Fr( I + DM Fr + The Duro of Zero-oupo Bo pyble pero Mofe Duro of orfolo wh Ieme D W D + To + WD + WD where X W X X + X + + X oexy pproxmo hge of rce oexy Eme ( ( Δ + ( ( ( Δ + Δ hge rce Δ Δ ( + Δ ( Δ + Δ Δ ( D ( Δ ( Δ D ( Δ + Δ
Immuzo Noo ( ree Vlue of e e mou me ( ree Vlue of ble bly mou me S ( Surplu S ( ( ( oo for Immuzo To chee mmuzo we mu he S, S (, S ( > Immuzo erm of uro coexy we ee o o o ( V Mchg ( o o ( Duro Mchg ( ( (3 Greer oexy for e ( > ( Immuzo erm of he e lbly mou me ( V Mchg ( Duro Mchg (3 Greer oexy for e > > > > > >
Specl e Yel Re Reeme Noo y j ul yel of ol eme (IRR umber of yer umber of pyme effece ere fu X effece ere fu Y Geerl e Suppoe you me l eme of. The yel re y he cul re of reur you re receg o he eme. V he ccumule lue of your eme. + y V Suppoe you re eg pyme o fu X he e of ech pero reeg he ere ccrue ech pero o fu Y ( + + y I y y j V of l eme V of reeme Suppoe you me l eme of o fu X You ree ere ccrue fu X fer ech pero o fu Y rg You ree ere ccrue fu Y fer ech pero o fu Z rg Bo Reeme ( + + + y I X Y X Z Sum of prcpl ere fer pero + y + + I X Y X Th refer o he ce where we he bough bo for prce of Fr + K we ree he coupo pyme Fr o epre ccou he me hey re recee. Noo Z y ul yel of ol eme umber of yer umber of pyme he bo py
Fr + he V of he ccou he prce he l eme. y + + ( y Fr + ( + y m m Fr Fr + + K Of coure we c he more h oe bo ole. If h he ce we ju ee o combe prce coupo pyme ccorgly. Mchg ble Ug Bo We re gog o coer he ce h lbly frequecy mche he coupo frequecy. (e.g. We woul o he lble yer yer wh coupo emully. e F, r eoe he pr lue, coupo re reempo lue, repecely, for he bo wh he loge uro. Deoe F, r for he bo wh he ex loge uro, o o. Sep- urche F r + of he bo. Th percege. Sep- Th ge F r, frcol mou of he coupo he pero before. F r + Sep 3- Deerme he mou lef we ee o mch. Sep 4- urche F r F r + F r + rce of he bo o mch lble : lble me me. Sup Yel ure Suff of he bo. Fr F r F r + Fr + + Fr + Fr +. Th mche ( To lue bo, e he pree lue of ech pyme he ppropre yel cure re um he pree lue. ( ( + + + + + + + + + + ( + + f f f ( + f