Implementing 130/30 Equity Strategies: Diversification Among Quantitative Managers

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1 Implemening 130/30 Equiy Sraegies: Diversificaion Among Quaniaive Managers Absrac The high degree of correlaion among he reurns of quaniaive equiy sraegies during July and Augus 2007 has been exensively analyzed, and he lieraure o dae has focused largely upon reurn forecasing models as he source of ha correlaion. This opic is paricularly relevan o plan sponsors making allocaions o relaxed-long or 130/30 sraegies because, among oher hings, hose sraegies are predominanly implemened using quaniaive processes and generally arge higher levels of racking error han is he case for analogous long-only sraegies. This paper argues ha overlapping risk models consiue an overlooked source of correlaion among quaniaive equiy managers. In paricular, i demonsraes ha he deploymen of common risk models can grealy narrow he opporuniy se used in securiy selecion, and ha during a marke dislocaion conagion can spread among managers even in he absence of a high degree of overlap in heir forecasing models. The paper concludes by considering he implicaions of his analysis for boh invesmen managers and plan sponsors. Tony Foley Head of Quaniaive Research D. E. Shaw Invesmen Managemen, L.L.C. 39h Floor, Tower Wes Fory-Fifh Sree New York, NY March 28, 2008 The views expressed in his paper are solely hose of is auhor as of he dae of his paper and no of D. E. Shaw Invesmen Managemen, L.L.C., D. E. Shaw & Co., L.P., or any oher member of he D. E. Shaw group. This paper appears in Insiuional Invesor s Guide o 130/30 Sraegies (2008). Copyrigh 2008 D. E. Shaw & Co., L.P. ALL RIGHTS RESERVED.

2 1. Inroducion The performance of quaniaive equiy sraegies in July and Augus 2007 has been exensively analyzed. (See Khandani and Lo (2007) for an academic accoun and Rohman (2007) for an impressively imely analysis.) One red hread running hrough his work highlighs he high degree of correlaion among he excess reurns of quaniaive sraegies during his period. This was paricularly sriking given ha oher syles of equiy invesing did no experience anyhing close o he same degree of dislocaion. I cerainly fel as if he marke had urned ino a Quanron Bomb ha ook ou quaniaive equiy sraegies and lef everyhing else more or less unouched. The level of correlaion among quaniaive equiy managers is direcly relevan o plan sponsor decision making on relaxed-long or 130/30 equiy sraegies for hree primary reasons. Firs, many managers colonizing his invesmen space uilize quaniaive sraegies, and he bulk of 130/30 asses have been placed wih quaniaive managers. Second, plan sponsors ofen allocae o several managers in he 130/30 space because his approach o equiy invesing is relaively new. (I s no uncommon for a given plan o hire hree or four managers when implemening 130/30 sraegies.) Finally, since 130/30 sraegies generally afford managers more room o increase racking error wihou degrading he expeced informaion raio, such mandaes are ofen se a racking error arges ha exceed he long-only mandaes ha hey replace. A higher level of racking error increases he imporance of undersanding he correlaions of excess reurns among quaniaive managers and he implicaions of hose correlaions for he overall risk of allocaions o 130/30 equiy sraegies. 2. Risk Models as a Driver of Posiive Correlaion Similariy in alpha models has received op billing as he source of high correlaion among quaniaive equiy sraegies during Augus Boh references cied in his paper, and many ohers, have analyzed his facor in deail, and here is no need o repea ha analysis here. Page 1 Implemening 130/30 Equiy Sraegies

3 Anoher poenial source of correlaion ha has received far less aenion is similariy in he risk models deployed by quaniaive managers. Overlooking he impac of risk models on he performance of quaniaive equiy sraegies during Augus 2007 seems somewha odd. Afer all, while he degree of overlap in excess reurn models is difficul o ascerain (and, as will be argued below, is easy o overesimae), many quaniaive managers use no jus similar bu lierally idenical risk models and porfolio consrucion mehodologies obained from a relaively small se of exernal providers. Given hese circumsances, i s worh highlighing he poenial impac of idenical or very similar risk models on he concenraion of manager posiions. The dominan paradigm for he consrucion of muli-facor equiy risk models is he facor risk approach, which is loosely based on arbirage pricing heory (APT). This approach assumes ha he risk of a sock can be broken down ino a se of exposures o common risk facors and o a residual ha corresponds o he idiosyncraic risk of ha sock. (See he appendix for a mahemaical expression of his idea.) Like any consrain, his approach effecively rules ou some poenial porfolios and implies ha he opimal porfolio will be chosen from a subspace of he overall se of possible porfolios. To see how his works, consider a simple example in which price-o-book raio is he relevan risk facor and serves as a proxy for value syle exposure. Consider wo socks, one wih a higher han average price-o-book and one wih a below average price-o-book. Assume ha wihou a risk consrain, he manager s benchmark-relaive weighs would be in he ±1.0% range. Wih a sric risk consrain applied, some regions of his space will be unaainable. Figure 1 illusraes hese condiions. Page 2 Implemening 130/30 Equiy Sraegies

4 Figure 1: Impac of Facor Risk Consrain on Feasible Porfolio Choices All managers who consrain risk by using he same risk model end up selecing from he same smaller se of feasible porfolios. When his se of condiions is scaled up and applied o a larger universe of insrumens, he feasible space remains large, bu he basic principle sill applies: if a subgroup of managers uses he same risk model, hen each manager in ha subgroup will selec porfolios from he same, smaller subse of porfolio space. Cerainly, no all managers will consrain exposures o specific facors. Bu as long as managers deploy he same risk model, he same regions of porfolio space will be expensive or inexpensive for all of hem, and hus hey are more likely o find opimal areas in similar regions. Page 3 Implemening 130/30 Equiy Sraegies

5 Implici in his argumen is he noion ha managers using idenical risk models will also be using mean-variance opimizaion in one form or anoher. This assumpion would no seem o be overly heroic because major providers of risk models are also leading suppliers of porfolio opimizaion sofware, and he indusry is in any case dominaed by he mean-variance paradigm. A lack of diversiy in porfolio consrucion mehodology will clearly end o increase correlaions. Moreover, as many praciioners will appreciae, mean-variance opimizaions are no robus in heir raw sae. A small change in expeced reurns or risk inpus can lead o very large and no always paricularly inuiive changes in he opimal porfolio allocaion. As such, implemening meanvariance models requires a liany of consrains o ensure reasonable oucomes. This exacerbaes cross-manager correlaions because managers end o impose similar consrains, such as puing igh limis on benchmark-relaive acive sock or indusry misweighs and resricing facor risk in he manner already discussed. 3. Conagion wihou Direc Overlap in Forecasing Models All his nowihsanding, i is likely ha overlapping alpha models played a significan role in he marke evens of July and Augus 2007, and his has poenial implicaions for he implemenaion of 130/30 equiy sraegies. However, he very high excess reurn correlaions seen during his period may well oversae he degree of overlap in reurn forecasing models. In fac, i is perfecly possible for he kind of conagion winessed in he summer of 2007 o maerialize even in he absence of significan overlap in alpha models. For example, Manager A may have no overlap a all in forecasing models wih Manager C, bu if boh have some degree of forecasing model overlap wih Manager B, hen Manager B can serve as a conducor of conagion beween Manager A and Manager C. In such circumsances, he longer erm pair-wise excess reurn correlaion of Managers A and C would seriously underesimae he correlaion in he even ha Manager B decided o ake off leverage or oherwise reduce is acive exposure. Figure 2 illusraes his scenario. Page 4 Implemening 130/30 Equiy Sraegies

6 Figure 2: Poenial for Conagion In his sylized example, even a complee disclosure of he forecasing models used by Managers A and C would no have alered an observer o he common exposure o Manager B, unless ha observer also happened o know he deails of Manager B s invesmen process. 4. Conclusion The foregoing analysis suggess ha here is likely o be a lower bound on he excess reurn correlaions of quaniaive managers in imes of marke disrupion. All hings being equal, managers who do no rely upon generic risk models and widely known reurn drivers such as valuaion and momenum are less likely o be correlaed han oher managers. Bu he general expecaion should be ha mos managers will be unable o fully inoculae hemselves agains anoher liquidiy crisis like ha of July and Augus The difficulies generally experienced by quaniaive managers during his period are unlikely o sem he flow of invesmens ino 130/30 sraegies. Tha said, even if he case for making 130/30 invesmens has no changed, he Page 5 Implemening 130/30 Equiy Sraegies

7 answer on how o do 130/30 could be somewha differen. While recognizing ha quaniaive managers may be unable o reduce correlaions o de minimis levels, plan sponsors may now pay more aenion o hose feaures likely o leave managers mos exposed, in paricular he degree o which a given process relies on generic echnologies and porfolio consrucion mehodologies. Page 6 Implemening 130/30 Equiy Sraegies

8 5. Appendix The facor risk approach can be wrien as: r = X f + ε (1) where r is excess reurn, X is an N by F marix of exposures of he N socks n o a se of F common facors, f is an F by 1 vecor of facor exposures, ε is an N by 1 vecor of residual reurns, and is he esimaion horizon. In his framework, he co-variance marix is given by: V = X F X + Q (2) where V is porfolio variance, F is he F by F marix of facor variances (assumed o be diagonal because he risk facors are assumed o be uncorrelaed), and Q is he N by N diagonal marix of residual sock variances. Given his srucure, he racking error (σ ) of a porfolio can be wrien as: ( w X S ) ( S X w ) + w Q w σ = (3) where S is an F by F marix of facor risks, and w are he acive porfolio weighs. The produc w X S is a linear combinaion of he porfolio weighs, facor exposures, and facor sandard deviaions. Wihin his framework, a manager wishing o consrain is exposure o a given common risk facor can easily do so by imposing a linear consrain on he sum of he exposure muliplied by he associaed volailiy of ha risk facor. Page 7 Implemening 130/30 Equiy Sraegies

9 6. References [1] Khandani, Amir E. and Andrew W. Lo (2007). Wha Happened o he Quans in Augus 2007? Working Paper. MIT Sloan School of Managemen, Sepember 20, pp [2] Rohman, Mahew S. (2007). Turbulen Times in Quan Land. Marke Commenary. Lehman Brohers Equiy Research, Augus 9, pp Page 8 Implemening 130/30 Equiy Sraegies

10 The views expressed in his paper are solely hose of is auhor as of he dae of his paper and no of D. E. Shaw Invesmen Managemen, L.L.C., D. E. Shaw & Co., L.P., or any oher member of he D. E. Shaw group. Oher professionals in he D. E. Shaw group may have inconsisen or conflicing views. The views expressed in his paper are subjec o change wihou noice, and may no reflec he crieria employed by any company in he D. E. Shaw group o evaluae invesmens or invesmen sraegies. This paper is provided o you for informaional purposes only. This paper does no and is no inended o consiue invesmen advice, nor does i consiue an offer o sell or provide or a soliciaion of an offer o buy any securiy, invesmen produc, or service. This paper does no ake ino accoun any paricular invesor s invesmen objecives or olerance for risk. The informaion conained in his paper is presened solely wih respec o he dae of he preparaion of his paper, or as of such earlier dae specified in his paper, and may be changed or updaed a any ime wihou noice o any of he recipiens of his paper (wheher or no some oher recipiens receive changes or updaes o he informaion in his paper). No assurances can be made ha any aims, assumpions, expecaions, and/or objecives described in his paper would be realized or ha he invesmen sraegies described in his paper would mee heir objecives. None of he companies in he D. E. Shaw group; nor heir affiliaes; nor any shareholders, parners, members, managers, direcors, principals, personnel, rusees, or agens of any of he foregoing shall be liable for any errors (o he fulles exen permied by law and in he absence of willful misconduc) in he informaion, beliefs, and/or opinions included in his paper, or for he consequences of relying on such informaion, beliefs, or opinions. Page 9 Implemening 130/30 Equiy Sraegies

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