Quantitative Portfolio Theory & Performance Analysis

Transcription

1 Quanttatve Portfolo Theory & Perforance Analyss Week of Aprl 22, 2013 Portfolos of Fxed Incoe Securtes 1.1 Assgnent For Aprl 22 (Ths Week) Read: A&L, Chapter 8 Read: E&G Chapter 22 Probles E&G: 8.5; E&G: 16.3, 16.4 (Due Aprl 22) Project Defnton & Dscusson (Contnued) For Aprl 29 (Next Week) Read: A&L Chapter 7 Read: E&G Chapter 25&27 Last Day of Class: Wednesday, May 1 st Fnal Project Presentaton: Monday, May 13 th ; 9:00a Noon (Whtehead 203) 1.2 Quanttatve ethods for anagng bond portfolos are a ore recent developent than for anagng equtes Managng bond portfolos quanttatvely s uch ore prevalent than n equtes and growng faster Growth s both n style and scope In large part because of nnovatons n the dervatves arkets Also, because of advances n odelng the key sources of rsk faced by the bond PF anager We look at the partcular characterstcs of bond nvestents and the pact on the odelng approaches for perforance analyss 1.3 Bond Portfolos Sources of Rsk/Return Interest Rates the Ter Structure Coupon ncoe Gans or losses fro early lqudaton not held to aturty Prevalng levels of (coparable) rates Rollng Down the Yeld Curve Credt/Sector Qualty of ndvdual ssuer & the lkelhood of the payent of nterest and the return of prncpal Correlaton of Default Sector vs. Indvdual ssues Structure Lqudty 1.4 1

2 Bond Portfolos Sources of Rsk/Return Interest Rates Ter Structure Concepts and Models for nterest rates Man reason for the advance of quanttatve technques for bond portfolo anageent Concepts YTM/IRR, spot rates, dscount functon, ter structure, ter preu, forward rates, expected future spot rates, duraton, convexty Models statc, dynac, stochastc; spot rate & forward rates 1.5 Defnng the Rsks & Sources of Return Market Rsk Interest Rate (IR) Rsk duraton, convexty, etc. Prepayent (see structure rsk) Lqudty Rsk Modelng technques for the pact of IR rsk on the PF Factor Models for explanng YC shfts PCA analyss parallel, steepenng/flattenng, barbell Key rate senstvtes (correlatons) for DVBP analyss (JP Morgan) Forecastng Returns w/ horzon total return & (stochastc) horzon/scenaro analyss 1.6 Defnng the Rsks & Sources of Return Default/Credt Rsk The Rsk of Default wll drve the prce the arket wll set for the potental that nterest and prncpal ay not be pad n full Ths prce s expressed as a yeld or prce spread over otherwse equvalent, rsk-free ssues The spread, s, ay be approxated through the recovery, R, n the event of default and a easure of the lkelhood of default (the default ntensty per year, λ ) s = (1-R) x λ Ratng agences provde dscrete easures to express credt rsk - nvestent grade (AAA, AA, A, BBB; Aaa, Aa, A, Baa); wth sub-nvestent grades (BB, B, CCC, CC, C) 1.7 Defnng the Rsks & Sources of Return Default/Credt Rsk Methods of Approachng Default Rsk Fr-based (or structural) odels where the lkelhood of default s defned by the relatonshp between the value of a frs assets to relevant threshold Reduced For odels where the lkelhood of default s drawn fro hstorcal or pled (fro the arket) easures of a populaton of lke copanes Systeatc credt rsk or the nature of contagon credt rsk correlaton (ndustry, geography, qualty, etc.) 1.8 2

3 Defnng the Rsks & Sources of Return Structure Rsk Can be an nterplay between credt rsk and arket rsk Prepayent persson to a borrower usually pad for at te of ssue, but the te of the event s uncertan so the charge ay or ay not have been approprate Senor/subordnate and other fors of credt enhanceent Modeled through cash flow odels and Monte Carlo scenaro analyss provdes scenaro/horzon return easures Volatlty effects call structure/value 1.9 Analyss Fraework Portfolo Objectve and Constrants Asset Allocaton Dvdng the PF nto dfferent classes: sectors, duraton, actvepassve, dversfcaton, lqudty Benchark Choosng a Standard Benchark or Defnng the Bespoke Benchark Once the benchark s specfed, return objectves and rsk constrants ay be quantfed n ters of devatons fro the benchark 1.10 Bond Investng Strateges The constructon of a bond portfolo reles ore on the choce of, and allocaton to, (a) category(es) of bonds presentng the requred characterstcs (of duraton, credt, aturty, etc.) than on specfc choce of ndvdual bonds Strateges Actve prudent assupton of rsk to acheve addtonal return Assocated wth a ratonale (forecast) for takng on the rsk Passve replcatng a benchark Passve wth an actve overlay 1.11 Major Source of Rsk & Return n Bond PFs Foreost, the yeld curve To a large extent, donates any thoughts of MPT Never-the-less, to anage the bond PF one needs estates of future (next perod) returns and ther attendant rsk Then anage the PF to take the rsk or nsulate fro the rsk Bond returns have two sources Interest Incoe and P/L fro prce changes Prce changes fro the passage of te & the yeld curve Tradtonal easures of exposure to the yeld curve nclude Duraton & Convexty Convexty postve & negatve

4 Two technques for nsulatng an ndexed bond PF fro shfts n the yeld curve passve anageent Dedcaton the exact atchng of asset cash flows to a lablty requreent Usually, the lowest cost PF that does the job Surplus cash cash carry forward Rsks of dedcaton Assets default Renvestent rsk for cash carry forward Two technques for nsulatng an ndexed bond PF fro shfts n the yeld curve passve anageent Iunzaton Strateges Barbell vs. Focused Barbell allows bonds of duratons qute dfferent fro lablty requreent Focus requres bonds wth duratons close to lablty need Focus works uch better as non-parallel shfts are better unzed 1.15 Two technques for nsulatng an ndexed bond PF fro shfts n the yeld curve passve anageent Iunzaton atchng duraton (and other characterstcs) of the assets PF to the lablty requreent Rsks Rates rse loss on bonds wth reanng ter; renvest cash at a hgher rate Rates fall bond value gans, but renvest at a lower rate Sple exaples show a net cancelaton but not always/exactly Many anagers also atch convexty but at a cost

5 Two technques for nsulatng an ndexed bond PF fro shfts n the yeld curve passve anageent Iunzaton Dedcated PFs are Iunzed Dedcated PFs are ore expensve Many anagers wll use a dedcaton strategy on a porton of the PF and unze the reander 1.17 Bond PF anageent of yearly returns Many bond anagers are not concerned wth anagng aganst a partcular lablty, but are easured by ther yearly return Aganst an Index For Total Return When a anager s easured aganst an ndex, often eploy soe varaton of an ndex replcaton strategy The ndex often has thousands of bonds To replcate, the anager need only duplcate the bond proportons n the ndex But cannot because they are lkely not avalable Alternatve s to do cell atchng 1.18 Bond PF anageent of yearly returns Cell Matchng Delneate the portant characterstcs of the ndex, usually by duraton cell Duraton, coupon, ratng, sector Replcate as best as possble through avalable bonds Actve Bond Manageent Strateges Interest Rate forecastng Sector Selecton and Rotaton Indvdual bond selecton Bond PF anageent of yearly returns Interest Rate forecastng Shorten or lengthen duraton to gan exposure or lt exposure accordng to rates ovng down or up Manager has a ratonale for predctng and antcpatng these oves If rght 60% of te, bond PF can exhbt superor perforance vs. other alternatves Wll take a nuber of perods before luck vs. skll becoes apparent

6 Bond PF anageent of yearly returns Sector Selecton A anager ght have reason to beleve soe sector wll have superor perforance over others for exaple, hgh yeld and the pay-up for added default rsk ght be n excess of what the anager beleves s necessary Sector Rotaton Overweght a sector where perforance s expected to be superor n the next perod If wde spreads are expected to tghten as was the case edately after the credt crss, when wdenng was over done Volatlty s sprced for opton laden debt 1.21 Bond PF anageent of yearly returns Indvdual Selecton of sprced bonds Usually as t relates to credt ratng (too good or too bad) Best done wth relatve value odels for prce ( yeld or spread ) odels should nclude optonalty, aybe even ter or other rsk preus 1.22 Estatng Expected Return Coupon Incoe P/L fro ter structure Expectatons theory current 1-perod forward rates forecast expected forward rate n 1-perod Estatng Expected Return Exaple: 5-year bond, $8 nterest per perod, $100 prncpal, arket prce s $82 P 0Eqlbru =86.16 P 1Eqlbru =

7 Estatng Expected Return Prce n Equlbru = $86.16 Equlbru prce n 1-perod s $86.77 If arket prce was equlbru, 1-perod expected return s $8 nterest, $.61 captal gans, total return 8.61/86.16=10% If bond could have been bought at $82 and t returned to equlbru, 1-perod return would have been estated at ( )/82=15.57% Estatng Expected Return Lqudty Preu Theory for calculatng expected return Assued Forward rates (%) 1.25 FR w/lp reoved, stay the sae, reove 1 st LP s sld forward to get new FR w/lp to value 1.26 Estatng Expected Return Today s Equlbru Prce s the sae = $ perod Equlbru prce s now = $87.05 (vs. $86.77) 1-perod equlbru return s ( )/86.16 = 10.32% The extra 32 bps s due to the lqudty preu and pays the nvestor for takng ter rsk 1.27 Sngle-Index Models Total Return = Exp Return + Return Due to Unantcpated + e R R D Where we use a bonds duraton w/ unexpected % IR change Extendng the sple 1-factor odel fro stocks w/ ndex, R X R X R X D X R X D X R X D R D where D X D

8 Sngle-Index Models The return on bond s, R R D Solvng for and substtutng nto sngle ndex odel gves R R / D R R D e D R R R D D Where we can ake the assocaton,, where the ε are D assued ndependent of bond ndex cov RR Where the beta has the tradtonal eanng as 2 Except no need to estate an otherwse deternstc relatonshp, a rato of duratons 1.29 Mult-ndex odels Reasons for ult-ndex odels More accurately easure effect of IR Change n yeld spreads to Treasury Sector spreads Change n value of a call volatlty