Indexation of Principal Protection

Transcription

1 March 2008 Indexaion of Principal Proecion A S&P 500 Proecive Pu Index Concep Srikan Dash, CFA, FRM srikan_dash@sandp.com (212) Berlinda Liu berlinda_liu@sandp.com (212) Principal proeced invesmens are a saple offering in insurance and srucured produc disribuion channels for invesors seeking exposure o an asse wih limied downside risk o he iniial invesmen. Principal proeced S&P 500 index producs are among he mos popular srucured producs issued o reail invesors. Given reail invesors limied undersanding of opions pricing and general aversion o risk, hese producs sell briskly a relaively high loads and expenses. In his paper, we discuss he concep of a possible S&P 500 Proecive Pu index, which could be a benchmark for he legions of principal proeced producs available in he reail marke, or be he basis of a lower cos index linked produc. There are muliple insrumens and echniques used o execue principal proecion or porfolio insurance. For purposes of ransparency and replicabiliy, we use he liquid, publicly raded opions marke and explore various mauriy, financing and srike scenarios. Our simple S&P 500 Proecive Pu Index concep, based on 2% collars, offers approximaely wo-hirds of marke reurn a one-hird overall risk. Downside risk as measured by maximum drawdown and Sorino raio is significanly lower han he S&P 500 index.

2 Inroducion Principal proeced invesmens are a saple offering in insurance and srucured produc disribuion channels for invesors seeking exposure o an asse or asse class wih limied downside risk o he iniial invesmen. The users of such producs are concerned abou principal risk and are willing o forgo some upside or yield in exchange for downside proecion. There are muliple insrumens and echniques used o execue principal proecion or porfolio insurance, and such echniques have been widely used in he invesmen communiy for more han 25 years. In his paper, we do no conribue anyhing new o he body of lieraure surrounding principal proecion sraegies. Raher, we explore he indexaion of such sraegies. Equiy indexaion has radiionally covered whole markes or marke segmens ha have disinguishable characerisics. The overriding feaure of such broad indices is ha hey aemp o provide represenaion of heir respecive marke or segmen. Increasingly, invesmen sraegies and echniques incorporaing acive risks are packaged ino an index framework. Such sraegy indexes provide ransparency and replicaion efficiency, and lower he cos for acive producs. The indexes we explore in his paper fi in ha mould of sraegy indexes. We explore a ransparen framework for indexaion of a pu proeced S&P 500 index sraegy. We explore he rade-offs associaed wih various financing and mauriy opions while saying wihin he confines of liquid segmens of he opions marke. Sandard & Poor s 2

3 Pu Proecion 101 An opion is a financial conrac beween wo paries, he buyer and he seller. A pu gives he buyer he righ bu no he obligaion o sell he underlying securiy o he seller of he opion a a cerain ime (he expiraion dae) for a cerain price (he srike price). A call gives he buyer he righ bu no he obligaion o buy he underlying securiy from he seller of he opion a a cerain ime (he expiraion dae) for a cerain price (he srike price). The invesing raionale for buying pu opions is o proec a long posiion in he asse and o limi downside risk. A porfolio wih long posiions is always exposed o he downside risk of he marke. For example, if you buy an index a $100, you ll face a poenial loss of up o $100. By going long a pu a $95, however, you may exercise your opion and sell your index a he srike once he index plunged below $95. Therefore, your maximum loss is limied o $5 curbed. The cos of he proecion is he premium you paid upfron. Exhibi 1: Buy Pu o Proec Principal Long Index Long Pu Index + Pu pu srike spo share price a mauriy Exhibi 1 illusraes how pu opions proec porfolio principal. The blue line shows he profi of a naked long posiion of index. I has unlimied upside poenial and downside risk driven by he spo of he index. A long pu posiion is illusraed in green. The invesor pays a premium regardless of he share price a mauriy, bu will benefi from he predeermined floor se by pu srike if he index declines. The combined posiion of index and pu sill has he unlimied upside poenial, bu he profi from he pu offse he loss from he index once Sandard & Poor s 3

4 he index goes below he srike. The maximum loss of he combined posiion is limied o he difference beween he spo and srike, plus he premium paid upfron. In addiion o sraigh pu opions, one could finance he pu by shoring ou of he money (OTM) calls. This implies ha one is willing o give up some of he upside in reurn for lowering he cos of he proecion. Exhibi 2 illusraes he effec of financing a long pu by selling a call opion. If one believes ha he underlying will no go above he call srike by he expiraion dae, he may op o shor he call and pocke he premium. This premium will reduce he cos of he pu opion and hence decrease he maximum downside exposure. However, if he index does exceed he call srike, he loss from he call will offse he profi from he index. Therefore, he maximum profi is also capped. Exhibi 2: Finance Pu wih Shor Call Posiion Long Index Long Pu Shor Call Index + Collar pu srike spo call srike share price a mauriy Sandard & Poor s 4

5 Research Mehodology We measure he impac of various combinaions of pu proecion for S&P 500 over a 15 year period ending Scope: Liquidiy and cos are he major consideraions in limiing he scope of our research in erms of breadh of mauriies and opion srikes. The longer daed he opion and he closer he srike is o curren index level, he higher he opion cos. Similarly, liquidiy fades of as one moves away from a he money (ATM) srikes and as one considers longer mauriies. Given his, we consider ATM, 2% OTM, and 5% OTM opions wih a mauriy of one monh or hree monhs. Calculaion: The performance of each sraegy is evaluaed by he accumulaed oal reurn of he combined posiion, i.e. he long S&P 500 index posiion, dividends from he index, a long pu posiion and a shor call posiion, if applicable. On Day 1, we selec he pu and call opions. The srike arge is calculaed based on he opening price of he S&P 500 index. For boh pu and call opions, we selec he conracs immediaely above he srike arge. We se he iniial value of he oal reurn index (I) as 100. For he underlying securiy, we only have he open and close prices. Inra-day price and volume daa are no available. Therefore, we assume ha he opion srikes are deermined by he open price of he rading day. In realiy, he opion raders may use he volume weighed average prices or oher derived prices as heir basis. On any subsequen non-expiraion day, we calculae he accumulaed oal reurn on a closeo-close basis as follows: PX + DVD + C R = PX + C I = R 1 * I 1 C pu call pu call 1 C 1 Sandard & Poor s 5

6 where PX = index closing price DVD = index dividend poins C = opion close price On he opion expiraion day, we close he expiring opions and buy new opions for he nex period. We only have open and close opion prices of he opions. Alhough one could buy and sell opions in several rades a differen prices, we close he expiraion conracs a heir selemen value calculaed from he SOQ (Special Opening Quoaion), and roll o he new conracs based on heir opening prices. The daily reurns of he expiring opions are denoed as Ra. We assume ha he new opions are bough a open based on he open price of he underlying. Their inra-day reurns are denoed as Rb. The oal reurn index shall be calculaed as follows: where SOQ + DVD + V Ra = PX PX + C Rb = SOQ + O R = Ra* Rb = R* I 1 V old pu old call old pu old call 1 + C 1 C 1 new pu new pu C O I new call newcall V V old pu old call = max(0, K old pu = max(0, SOQ K SOQ) old call ) V = opion value a expiraion K = opion srike a he ime of posiion esablishmen O = opion open price SOQ = CBOE s special opening quoaion The new pu and call opions are seleced based on he moneyness and mauriy consrains in a similar way as on Day 1. We purchase he new conracs a he open of he expiraion dae. To incorporae a realisic price of buying a pu or selling a call, we Sandard & Poor s 6

7 do no use opening prices by hemselves. Raher, we devise an opening ask for he pu opion we are buying and an opening bid for he call opion we are selling. For pu opions, we add a spread o he open price. For calls, we subrac a spread from he open price. The spread we use is half of a hisorical average of he closing bid/ask spreads. (An alernaive would be o purchase he new conracs someime in he middle of he day and use a volume weighed average price a a cerain window.) Sandard & Poor s 7

8 Resuls We evaluae our resuls among hree differen dimensions: Impac of rollover frequency Impac of pu srike Impac of financing choice Impac of rollover frequency. As expeced, quarerly rollover is more efficien han monhly rollover. As we can see from Exhibi 4, for ATM opions, quarerly rollover has almos he same volailiy as monhly, bu is average reurn is increased from 2.52% o 4.27%. This is also he case for OTM opions. The average annual reurn of 5% OTM pu proecion increases from 5.62% o 6.72% if he rollover frequency is changed from monhly o quarerly. Source: Sandard & Poor's. Exhibi 4: Impac of rollover ATM Pu 5% OTM Pu Monhly Quarerly Monhly Quarerly Average Annulized Reurn 2.52% 4.27% 5.62% 6.72% Volailiy 7.87% 8.40% 12.16% 10.99% Median Yearly Reurn 2.20% 4.22% 6.22% 8.24% Max Yearly Reurn 18.61% 27.27% 34.45% 33.80% Min Yearly Reurn % -9.20% % % One migh consider longer daed conracs such as six monh opions or LEAPS (Long-Term Equiy Anicipaion Securiies, i.e. publicly raded opions wih expiraion daes ha are longer han one year). Unforunaely, liquidiy drops off afer hree monhs and longer daed conracs are far less liquid. For example, on 12/20/2007, he June 08 pu conracs were no raded a all a srike 1460 (ATM) or 1290 (5% OTM). Impac of moneyness. The naïve approach is o buy sraigh ATM pu opions o proec full value of he underlying. ATM opions are usually he mos acively raded in he opion marke. However, ATM opions also have he riches premium, resuling in exremely high insurance coss. Sandard & Poor s 8

9 Exhibi 5 shows he risk-reurn rade-off of differen srike prices. If he conracs are rolled quarerly, giving up 5% proecion will increase he average reurn from 4.27% o 6.72%. I also comes wih higher risk, bu he increase in volailiy is relaively mild (an increase from 8.40% o 10.99%). Source: Sandard & Poor's. Exhibi 5: Impac of moneyness. Quarerly Pu ATM 2% OTM 5% OTM Annulized Reurn 4.27% 5.25% 6.72% Annualized Volailiy 8.40% 9.36% 10.99% Median Yearly Reurn 4.22% 5.33% 8.24% Max Yearly Reurn 27.27% 30.59% 33.80% Min Yearly Reurn -9.20% % % Opions furher away from 5% are less liquid. For example, on January 18, 2008, March % OTM pu were no raded unil four days laer. Impac of financing: The cos of pus could be financed by selling calls. We summarize he resuls of various such collar sraegies in Exhibi 6. Exhibi 6: Impac of Financing 2% OTM Pu (Quarerly) 5% OTM Pu (Quarerly) S&P 500 Sraigh Pu Collar Sraigh Pu Collar Annulized Reurn 10.34% 5.25% 6.57% 6.72% 6.00% Annualized Volailiy 16.22% 9.36% 5.54% 10.99% 8.15% Median Yearly Reurn 13.01% 5.33% 9.27% 8.24% 6.58% Max Yearly Reurn 38.13% 30.59% 12.53% 33.80% 23.41% Min Yearly Reurn % % 1.29% % -4.65% Source: Sandard & Poor's. From Exhibi 6, we can see ha 5% collar is no a big improvemen over he 5% sraigh pu since he 5% calls are no sufficien o cover he cos of he pus. Therefore, no big difference in he average reurn is observed in he pase 15 years. However, if we move a lile closer o he srike and use 2% OTM collars, he corresponding calls sar o improve boh he reurn and he volailiy. Sandard & Poor s 9

10 A S&P 500 Proecive Pu Index Concep Principal proeced S&P 500 index producs are among he mos popular srucured producs issued o reail invesors. For example, a cursory search of an indusry daabase ( showed more han 175 various proeced S&P 500 index linked producs. Given reail invesors limied undersanding of opions and general aversion o risk, hese producs are a saple offering sold a relaively high loads and expenses. Given our resuls, we explore a possible S&P 500 Proecive Pu index using 2% collars. This index could poenially be a benchmark for he legions of principal proeced producs available in he reail marke, or be he basis of a lower cos index linked produc. Exhibi 7 summarizes he performance of he 2% quarerly collar in he pas 15 years. I offers approximaely 2/3 marke reurn a 1/3 overall risk, and significanly lower downside risk as measured by maximum drawdown and Sorino raio. Source: Sandard & Poor's. Exhibi 7: Possible S&P 500 Proeced Index Saisics S&P 500 S&P 500 Proeced Pu Annulized Reurn 10.34% 6.57% Annualized Volailiy 16.22% 5.54% Sharpe Raio Sorino Raio Max Drawdown % -5.09% Exhibi 8 shows he proeced pu indices based on accumulaed oal reurns of his index. The sabiliy of he line char for he S&P 500 Proecive Pu index is sriking. Sandard & Poor s 10

11 Exhibi 8: Performance of S&P 500 Proecive Pu Index 600 S&P 500 Proeced Pu Index S&P S&P ATM Pu S&P 500 Proeced Pu Index Dec-92 Dec-95 Dec-98 Dec-01 Dec-04 Dec-07 Source: Sandard & Poor's. Sandard & Poor s 11

12 Conclusions Principal proeced S&P 500 index producs are among he mos popular srucured producs issued o reail invesors. Given reail invesors limied undersanding of opions pricing and general aversion o risk, hese producs sell briskly a relaively high loads and expenses. In his paper, we discussed he concep of a possible S&P 500 Proecive Pu index, which could be a benchmark for he legions of principal proeced producs available in he reail marke, or be he basis of a lower cos index linked produc. There are muliple insrumens and echniques used o execue principal proecion or porfolio insurance. For purposes of ransparency and replicabiliy, we use he liquid, publicly raded opions marke and explore various mauriy, financing and srike scenarios. Our simple S&P 500 Proecive Pu Index concep, based on 2% collars, offers approximaely wo-hird of marke reurn a one-hird of overall risk. Downside risk as measured by maximum drawdown and Sorino raio is significanly lower han he S&P 500 index. This is cerainly no he only manner in which o implemen such a concep. One could choose a differen combinaion of opions, or could use a combinaion of risk free asses and fuures in he radiional porfolio insurance framework. Separaely, one could exend he idea we presen o ap ino he large annuiies marke by adding a fixed disribuion o he S&P 500 Principal Proeced index. Sandard & Poor s 12

13 Disclaimer This repor is published by Sandard & Poor s, 55 Waer Sree, New York, NY Copyrigh Sandard & Poor s (S&P) is a division of The McGraw-Hill Companies, Inc. All righs reserved. Sandard & Poor s does no underake o advise of changes in he informaion in his documen. These maerials have been prepared solely for informaional purposes based upon informaion generally available o he public from sources believed o be reliable. Sandard & Poor s makes no represenaion wih respec o he accuracy or compleeness of hese maerials, whose conen may change wihou noice. Sandard & Poor s disclaims any and all liabiliy relaing o hese maerials, and makes no express or implied represenaions or warranies concerning he saemens made in, or omissions from, hese maerials. No porion of his publicaion may be reproduced in any forma or by any means including elecronically or mechanically, by phoocopying, recording or by any informaion sorage or rerieval sysem, or by any oher form or manner whasoever, wihou he prior wrien consen of Sandard & Poor s. Sandard & Poor s does no guaranee he accuracy and/or compleeness of any Sandard & Poor s Index, any daa included herein, or any daa from which i is based, and Sandard & Poor s shall have no liabiliy for any errors, omissions, or inerrupions herein. Sandard & Poor s makes no warrany, express or implied, as o resuls o be obained from he use of he S&P Indices. Sandard & Poor s makes no express or implied warranies, and expressly disclaims all warranies of merchanabiliy or finess for a paricular purpose or use wih respec o he S&P Indices or any daa included herein. Wihou limiing any of he foregoing, in no even shall Sandard & Poor s have any liabiliy for any special, puniive, indirec, or consequenial damages (including los profis), even if noified of he possibiliy of such damages. Sandard & Poor s does no sponsor, endorse, sell, or promoe any invesmen fund or oher vehicle ha is offered by hird paries and ha seeks o provide an invesmen reurn based on he reurns of S&P Indices. A decision o inves in any such invesmen fund or oher vehicle should no be made in reliance on any of he saemens se forh in his documen. Prospecive invesors are advised o make an invesmen in any such fund or vehicle only afer carefully considering he risks associaed wih invesing in such funds, as deailed in an offering memorandum or similar documen ha is prepared by or on behalf of he issuer of he invesmen fund or vehicle. Sandard & Poor s 13