Floating rate securities

Transcription

1 Caps and Swaps

2 Floang rae secures Coupon paymens are rese perodcally accordng o some reference rae. reference rae + ndex spread e.g. -monh LIBOR + 00 bass pons (posve ndex spread 5-year Treasury yeld 90 bass pons (negave ndex yeld Reference rae can be some fnancal ndex e.g. reurn on he S & 500 or non-fnancal ndex e.g. prce of a commody or nflaon ndex (n 997, US governmen begn ssung such bonds

3 Caps Resrcon on he maxmum coupon rae-cap. The bondholder effecvely sold an opon o he bond ssuer; coupon rae aken o be mn (r floa, r cap. Floors Mnmum coupon rae specfed for a floang rae secury-floor. The bond ssuer sold an opon o he bond holder; coupon rae aken o be max (r floa, r floor. Cap and floor provsons are embedded opons n fxed ncome secures.

4 Range noes Coupon rae s equal o he reference rae as long as he reference rae s whn a ceran range a he rese dae. If he reference rae s ousde of he range, he coupon rae s zero for ha perod. Inverse floaers Coupon raes are rese perodcally accordng o K L reference rae. To preven he coupon rae o fall below zero, a floor value of zero s usually mposed. In general, an nverse floaer s creaed from a fxed rae secury called collaeral. Acually, from he collaeral, wo bonds are creaed: a floaer and an nverse floaer.

5 Consder a 0-year 7.5% coupon sem-annual pay bond. $00 mllon of he bond s used as a collaeral o creae a floaer wh a par value of $50 mllon and an nverse floaer wh a par value of $50 mllon. Floaer coupon rae: reference rae + % Inverse floaer coupon rae: 4% reference rae The weghed average of he coupon rae of he combnaon of he wo bonds s 0.5(reference rae + % + 0.5(4% reference rae 7.5%. If a floor s mposed on he nverse, hen correspondngly a cap s mposed on he floaer: nverse s prce collaeral s prce floaer s prce

6 lan vanlla neres rae swap I s an agreemen whereby wo pares underake o exchange, a known daes n he fuure, a fxed for a floang se of paymens. 0 + R Le R be he -perod spo rae prevalng a me (e.g. 3-monh or 6-monh LIBOR rae for a quarerly or sem-annual swap, respecvely; X be he fxed rae conraced a he ouse pad by he fxed-rae payer; N be he noonal prncpal of he swap ousandng a me be he frequency or enor of he swap + n years e.g. /4 for sem-annual swap.

7 Fxed leg s made up by paymens B pad a me + B N X Floang leg consss of paymen A a me + where A Snce he realzaon a me of he spo rae s no known a me 0, N R < V ( A E( NR + where (, T s he prce a me of a dscoun bond maurng a me T. Le F denoe he forward rae beween [, +] agreed a me 0. By he compoundng rule of dscounng + + F or + F.

8 Consder he porfolo consruced a me 0 whch holds one un of dscoun bond maurng a me and shors one un of dscoun bond maurng a me +. Value of he porfolo a me s V ( R + R + R. Consder he paymen of amoun R a me +, s presen value R a me s, whch s he same as he presen value a + R me of he above porfolo of wo bonds.

9 Hence, a me 0, he commmen o pay R a me + and he sraegy of holdng a bond and shorng a bond + mus have he same value, ha s, ( 0, + R + or R +. Noe ha R s he same as he projeced forward rae F. To avod arbrage, he unknown -perod spo rae mus be se equal o he projeced forward rae F.

10 resen value a me 0 of floang leg paymens V A N F. + ( resen value a me 0 of fxed leg paymens V ( B N X +. The equlbrum swap rae s defned o be he fxed rae X such ha he above wo presen values are he same: X N X N + +. Ths s he weghed average of he projeced forward raes. By seng N X + we have X w F. w N +,

11 For he payer of he fxed rae, he presen value of he swap a me s + + +, (, ( ( n swap N F X N NV where F are now he forward raes calculaed from he dscoun curve a me. The second erm can be wren as,where X s he equlbrum swap rae prevalng a me. +, ( X N +. (, ( ( ( 0 0 swap B X X N X X NV Some smplfcaon Take N, we oban n n n n F

12 Use of a currency swap o enhance yeld Drec Synhec US Treasury noes Invesor 8.4% (US$ Yeld pckup 8.5% 8.4% 0.37% German gov bonds 8.45% (DM Invesor 8.45% (DM Swap house 8.4% (US$

13 Insead of buyng 0-year US Treasury noes yeldng 8.4%, he nvesor purchased 0-year German governmen bonds yeldng 8.45% (denomnaed and payable n deushemarks, and smulaneously enered no a currency swap. Under he swap, he nvesor agreed o exchange s DM cashflows over he lfe of he swap for US dollars. Rsks (besdes he defaul rsk of he German governmen. Defaul rsk of he swap counerpary; 2. Over he 0-year lfe, he nvesor mgh have desred o lqudae he nvesmen early and sell he German bonds pror o he maury of he swap (lef wh a swap for whch had no obvous use as a hedgng nsrumen.

14 Combnaon of swaps Combnaon of wo plan vanlla commody swaps, a plan vanlla currency swap, and a plan vanlla neres rae swap. Goal To enable an ol-producng naon o oban a fxed long-erm supply of rce n exchange for long-erm quany of ol. Whou he swap The ol-producng naon was smply o sell ol on he spo marke for US dollars, hen conver hose dollars no Japanese yen and purchase rce n Japan on he spo marke.

15 Srucure of he swaps. A commody swap was enered no under whch he ol producer locked n long-erm fxed dollar prce for sellng fuure specfed ol producon. 2. The US dollars were ndrecly convered no fxed yen usng a combnaon of (a fxed-for-floang US dollar denomnaed neres rae swap, hen followed by (b floang-rae dollar for fxed rae yen currency swap. 3. The fxed-rae yen were convered hrough a commody swap no he yen needed o buy a fxed quany of rce on he spo marke. Counerpary rsks of he four swaps!