Immunisation. Immunisation refers to a hedging strategy in asset-liability management

Transcription

1 Immusato Immusato refers to a hedgg strategy asset-lablty maagemet cosstg offsettg the rsk of some assets or labltes by a opposte posto other assets wth very smlar rsks profle. Immusato s a cocept maly developed for bod portfolos although t ca be exteded to other assets. I the case of partal hedgg of the rsk, oe calls ths strategy partal mmusato. I cotrast, absolute mmusato for bod portfolos refers to the hedgg wth a bod wth same durato ad covexty. The cocept of durato (ad also covexty) plays a fudametal role mmusato theory, hece the other ame for mmusato as durato matchg. I theory, a perfect mmusato s oly attaed f the asset to be hedged ad the uderlyg used are perfect substtute. The usual way of quatfyg terest rsks for a bod portfolo s to use the durato ad covexty. These two cocepts have a log hstory assetlablty maagemet, datg back to Macaulay (938). Durato (see durato) measures the sestvty of a bod portfolo s value to chages yeld. I ts smple form, referred to as the Macaulay durato, t s mathematcally gve by mus the logarthmc dervatve fucto of the bod prce wth respect to ts yeld.

2 Suppose that a bod pays a stream of coupo c at tme t, wth the fal coupo c cludg the otoal of the bod ad y s ts cotuously compouded yeld. The bod prce B, s the gve by the sum of the dscouted cash flows: B = = c e yt (.) The durato s defed as: D = = t c e B yt D = B y (.2), Whch ca be wrtte as a weghted sum of the dfferet paymet tmes: D = = ce t B yt (.3) The term square brackets s the rato of the preset value of the paymet at tme t over the value of the bod, that s the sum of the preset value of the paymets to come. Durato provdes that the rsk of the bod ( terms of chage of the yeld) s gve at frst order by: B y = BD (.3) It reles o the parallel shft of the yeld curve (see durato for a dscusso of more advaced durato cocept). Apart from obvous hedgg purposes, durato also allows to compare vestmets wth dfferet horzos a smple way. Suppose that a fxed coupo bearg bod, wth a maturty of 0 years has a durato of 7 ad a half year. A zero coupo bod maturty 0 years has obvous 0 year durato. Durato explas that the vestmet

3 the zero coupo bod cotas more rsks (to the chage of the yeld) tha the fxed coupo bearg bod. Covexty gves a fer graularty to the terest rate rsk aalyss by examg secod order rsk. Mathematcally, covexty s defed as the secod dervatves of the bod prce wth respect to the yeld: 2 B c = (.4) 2 y The fudato dea of mmuzato theory s the to match both the covexty ad the durato of the assets wth the labltes, usg specfc bods wth lqudty. I moder facal terms, mmusato (or dedcato) theory s smlar to a sem-statc hedge for a bod portfolo. It s a passve strategy that guaratees that the bod portfolo bares hardly ay rsk. Occasoally the portfolo maager may eed to re-hedge as t s oly a secod order hedge. Hgher momets may o the log term affect the portfolo. As tme passes, the durato ad covexty of the portfolo ad the labltes may shft. The portfolo must check perodcally the qualty of the mmusato For hgh yeld bod, mmusato plays a mportat role, as terest rsk ca be qute substatal. Immusato gores at frst sght ay credt valuato of couterparty. I order to gauge the vulerablty of ther portfolos to terest rate rsk, fud maagers may do varous scearo aalyses ad stress testg.

4 Ths prelmary aalyss would help them structure approprate mmusato strateges. Oe eeds also to model accurately ay embedded opto the bod as the bod s durato ad covexty ca be cosderable modfed by the opto compoet. Etry category: mathematcal models Related artcles: yeld curve modellg. Erc Behamou Swaps Strategy, Lodo, FICC, Goldma Sachs Iteratoal The vews ad opos expressed here are the oes of the author s ad do ot ecessarly reflect those of Goldma Sachs

5 Refereces Fabozz ad Pollack, Hadbook of Fxed Icome Securtes