: erm Srucure and Hedging Gonçalo Faria (1),* and Rober Kosowski (2),* (1) CEF.UP, Universiy of Poro; (2) Imperial College Business School, CEPR, Oxford-Man Insiue of Quaniaive Finance. Nespar Inernaional Pension Workshop Amserdam January 30 h, 2015 * We graefully acknowledge financial suppor from Nespar, INQUIRE Europe and he BNP Paribas Hedge Fund Cenre. 1
Presenaion Ouline I. Moivaion II. Main findings III. Relaed lieraure IV. Calculaion of he correlaion risk facor V. Daa VI. Empirical resuls VII. Relevance of his research projec VIII. Concluding remarks References Appendices 2
I. Moivaion raders are speculaing on correlaion among equiies, already he highes since he crash of 1987, will increase as he hrea of a banking crisis in Europe drowns ou news abou individual companies. Equiy prices moving in unison have hur reurns for money managers who seek relaive value among socks and indusries, leaving hedge fund managers wih fewer ways o bea heir benchmark measures. Fear drives correlaions. Bloomberg News, 16 h Sep 2011. 3
I. Moivaion 1. Diversificaion benefis can suddenly evaporae when correlaions unexpecedly increase: 2. Need for early warning sress signals. Promising area: derivaives reflecing marke expecaions of volailiy and correlaion; 3. Volailiy indices (e.g. VIX) have been exensively used. Bu he area of correlaion swaps is relaively unexplored. his is surprising! 4
I. Moivaion 5
II. Main findings 1. Documen and compare differen correlaion risk measures and heir dynamics, for he S&P500 Index; 2. Analysis of he erm srucure of implied correlaion and correlaion risk facor (30d, 60d, 91d, 182d, 365d and 730d) reveals shifs in he slope of correlaion erm srucure; 3. CBOE Implied Correlaion Indices can be accuraely replicaed by means of synheic correlaion swap raes, despie differences regarding mauriies and consiuens; 4. Analysis of uncondiional and condiional correlaion hedging sraegies shows only some condiional correlaion hedging sraegies add value. 6
III. Relaed lieraure Srucural models: endogenous correlaion risk carrying a risk premium (Buraschi, rojani and Vedolin (2014), Piai (2014) and Marin (2013)); Empirical evidence: significan risk premium, sysemic naure, diversificaion consrains (Driessen, Maenhou and Vilkov (2012) and Buraschi, Kosowski and rojani (2014)); Opimal porfolio decisions: Relevance of he absolue correlaion hedging demand (Buraschi, Porchia and rojani (2010)). 7
IV. Calculaion of he correlaion risk facor For an equiy index, he correlaion risk facor CR for he ime period (,) : where: RC, is he average pair-wise realized correlaion of equiy index Q consiuens and RC is risk-neural expecaion. Q RC compuaion: E, E, CR RC E RC (1) Q,, equal o he correlaion swap rae quoe SC,, if available; If SC, is no available: synhesized from he cross-secion of index and individual sock opions. => Mehodology we use o obain synheic correlaion swap raes. (more in Appendix I) 8
V. Daa ime window: January 1996 unil January 2013 (daily frequency). Focus: S&P500 Index and is consiuens. Robusness es: 100 larges consiuens (by marke capializaion) of he S&P500 Index. Daa resources include: (i) a comprehensive daa se of opions on he S&P500 Index and is consiuens; (ii) Daily quoaion of he S&P500 Index and is consiuens; (iii) se of OC correlaion swap quoes wih differen mauriies; (iv) CBOE Implied Correlaion Indices quoaions; (v) -Bill raes ime series. Daabases: For (i) and (ii): Compusa, CRSP and Opionmerics; For (iii): unique daa se of correlaion swap quoes for various mauriies (since March 2000 unil July 2012) from a major bank in London; For (iv) and (v): publicly available informaion from CBOE and Federal Reserve. 9
VI. Main resuls: Real vs. Synheic Correlaion Swap Raes 1. Level and dynamics of correlaion swap quoes (Q.IC) for he S&P500 Index for differen mauriies are accuraely replicaed by he synheic correlaion swap raes (S.IC) esimaed from opion prices. For 03.2000 07.2012: 10
VI. Main resuls: Implied Correlaion (IC) erm srucure 2. Upward sloping during normal marke regimes; IC erm srucure flaens or even wih negaive slope during urbulen periods. he IC and is erm srucure change significanly over ime. 11
VI. Main resuls: Implied Correlaion (IC) erm srucure 12
VI. Main resuls: Correlaion Risk facor (CR) erm srucure 3. Downward sloping during normal marke regimes; during urbulen periods, CR erm srucure flaens or even wih posiive slope. CR facor and is erm srucure change significanly over ime. [CR given by equaion (1)] 13
VI. Main resuls: Replicaion of CBOE IC Indices 4. CBOE Implied Correlaion Indices can be accuraely replicaed by means of synheic correlaion swap raes, despie differences regarding mauriies and consiuens. Noe: CBOE Implied Correlaion Indices includes only opions on 50 larges capializaion socks of he S&P500 Index. 14
VI. Main resuls: Replicaion of CBOE IC Indices 15
VI. Main resuls: Correlaion Hedging Sraegies Compared wih a sraegy long in he S&P500 wih no hedging (full sample). 5. Uncondiional correlaion hedging sraegies using correlaion swaps srongly underperform. Cumulaive growh of a $1 invesmen saring in January 1996: 16
VI. Main resuls: Correlaion Hedging Sraegies 6. he condiional Cash sraegy delivers good resuls, specially wih rading signals relaed wih he level of he correlaion risk facor and wih he dispersion rade reurns. Cumulaive growh of a $1 invesmen saring in January 1996: 17
VII. Relevance of his research projec 1. Informaional conen in IC and CR erm srucure in equiy markes: useful for he design of early warning signals of financial sress; 2. For he design of risk managemen sraegies by asse managers, paricularly: Long erm oriened, such as pension funds, hose more exposed o he correlaion risk, such as hedge funds. 3. Imporan for regulaors and supervisors when assessing: he sysemic risk a macro level; risk managemen policies a micro level. 4. Correlaion risk carries a significan premium: some insiuional invesors may be ineresed in supplying correlaion proecion o he marke place. 18
VIII. Concluding Remarks 1. his paper is a conribuion o he recen lieraure on early warning indicaors of financial sress and equiy marke correlaion risk premium; 2. Analysis of alernaive measures of correlaion risk and heir erm srucure; 3. Analysis of uncondiional and condiional hedging sraegies: only some condiional correlaion hedging sraegies add value; 4. Exensions: Develop a srucural model (general equilibrium model) ha derives correlaion risk endogenously for differen mauriies; Addiional performance measures o evaluae differen correlaion hedging sraegies. 19
References Bakshi, G. S., Kapadia, N. and D.B. Madan, 2003, Sock Reurns Characerisics, Skew Laws, and he Differenial Pricing of Individual Equiy Opions, he Review of Financial Sudies, 16, 101-143. Brien-Jones, M. and A. Neuberger, 2000, Opion Prices, Implied Price Processes, and Sochasic Volailiy, Journal of Finance 55, 839-866. Buraschi, A., Kosowski,R. and F. rojani, 2014, When here is no place o hide : Correlaion risk and he Cross secion of Hedge Fund Reurns, Review of Financial Sudies 27, 581-616. Buraschi, A., Porchia, P. and F. rojani, 2010, Correlaion Risk and Opimal Porfolio Choice, Journal of Finance 65, 393-420. Buraschi, A., rojani, F. and A. Vedolin, 2014, When uncerainy blows in he orchard: comovemen and equilibrium variance risk premia, Journal of Finance, 69 (1),101-137. Carr, P. and L. Wu, 2009, Variance Risk Premiums. he Review of Financial Sudies 22(3), 1311-1341 Driessen, J., Maenhou, P. and G. Vilkov, 2009, he price of correlaion risk: evidence from equiy opions, Journal of Finance 64 (3), 1377-1406. Driessen, J., Maenhou, P. and G. Vilkov, 2012, Opion-Implied Correlaions and he Price of Correlaion Risk, Working paper. Marin, I., 2013, he Lucas Orchard, Economerica 81(1), 55-111. Piai, I., 2014, Heerogeneous Beliefs abou Rare Even Risk in he Lucas Orchard, Working paper. 20
Appendix I - Synheic correlaion swap quoe When correlaion swap quoes are no available, i can be approximaed using he concep of implied correlaion IC (e.g. Buraschi, Kosowski and rojani (2014) and Driessen, Maenhou and Vilkov (2009)): IC E Q i j I n 2 Q i RV, w i1 i E RV, Q i Q j w w E RV E RV i j,, SV I, i j w w i j n 2 i w i1 i SV, SV i, SV j, (2) where: RV RV SV SV w i I, i, I, i, Re alized variance of Re alized variance of Variance swap rae for Index over ime span sock i over ime span Index over ime span markecapializa ion weigh of sock i;,,, Variance swap rae for sock i over ime span, ; ; ; ; 21
and he variance swap raes are compued using he mehodology of Bakshi, Kapadia and Madan (2003): where: is he marke price of OM European Call a ime, wih ime o mauriy of ( - ), and wih srike price K. is he marke price of OM European Pu a ime, wih ime o mauriy of ( - ), and wih srike price K. 22 ) (3, ;, ln 1 2 ;, ln 1 2 0 2 2, s s dk K P K K S dk K C K S K SV K C ;, K P ;, Appendix I - Synheic correlaion swap quoe
Appendix I - Synheic correlaion swap quoe If variance swap quoes are no available, he variance swap rae SV, for he index (or individual socks) can be synhesized from lised vanilla opions prices (see, for e.g., Brien-Jones and Neuberger (2000), Bakshia, Kapadia and Madan (2003) and Carr and Wu (2009)) as well as using inerpolaed implied volailiy surfaces for a range of sandard mauriies and se of opion dela poins (for, e.g, as compued by Opionmerics). Wha we do: We use Opionmerics volailiy surface o obain a smoohed implied volailiy surface for a range of mauriies and opion dela poins; We only use OM calls ( dela <= 0.5) and OM pus (dela >= - 0.5); Afer applying hose filers we use 13 OM call and 13 OM pu implied volailiy from he surface daa for each mauriy and each day; hen a oal of 1001 grid poins in he moneyness range from 1/3 o 3 is filled in; hen opion prices are calculaed from inerpolaed and exrapolaed volailiies, using he know ineres rae for a given mauriy; hose are he opion prices used o compue he synheic variance swap rae using Bakshia, Kapadia and Madan (2003) formula (3). 23
Appendix II - IC and CR: Summary Saisics 24