High and low frequency correlations in global equity markets

Transcription

1 BIS CCA May 2010 High and low frequency correlaions in global equiy markes A presenaion prepared for he BIS CCA Conference on Sysemic risk, bank behaviour and regulaion over he business cycle Buenos Aires, March 2010 Auhors*: Rober F Engle and Jose Gonzalo Rangel Affiliaion: New York Universiy and Bank of Mexico rengle@sern.nyu.edu, jgrangel@banxico.org.mx * This presenaion reflecs he views of he auhors and no necessarily hose of he BIS or of cenral banks paricipaing in he meeing.

2 High and Low Frequency Correlaions in Global Equiy Markes Rober Engle and José Gonzalo Rangel NYU and Banco de México Sysemic risk, bank behaviour and regulaion over he business cycle Buenos Aires March 19, 2010

3 Marke Volailiy and Comovemens in Inernaional Sock Markes % Marke Volailiy Index VIX Average Correlaions Across Inernaional Sock Markes / One-year moving average correlaion based on weekly reurns (Jan:2000-Feb:2010)

4 Implicaions: Inernaional asse allocaion Changes in he scope of diversificaion opporuniies. Opimal porfolio sraegies and hedging demands. Capial flows due o changes in he naure of risk. Asse pricing Derivaives based on porfolios of securiies. Why do correlaions change? Some empirical resuls: correlaions change wih marke condiions and he business cycle (e.g., Erb,Harvey and Viskana, 1995, Longin and Solnik, 1995, 2001, Ang and Bekaer, 2002) More fundamenally, correlaions change wih news evens abou fundamenals (Engle, 2009) News abou fuure dividends: counry-indusry linkages. News abou discoun facors: macroeconomic news, moneary policy, inflaion, ineres raes.

5 How can a model capure hese economic effecs? Pracical issues: The business cycle is only measured a low frequencies. News evens are observed a high frequencies. Popular approaches o model inernaional correlaions: Correlaion models based on high frequency daa are well suied o capure high frequency news effecs (e.g., Capiello, Engle and Sheppard, 2003). Bu no so informaive abou long-erm effecs. More aggregaed correlaion models can approximae low frequency behavior (Ang and Bekaer, 2002, Bekaer, Hodrick, and Zhang, 2008). Bu no informaive abou high frequency dynamics. Limied applicaion in forecasing problems.

6 Can we have hese feaures in a unified framework? Yes, his paper presens an approach o characerize high and low frequency correlaion componens in inernaional markes. Anoher issue: Inernaional daa is unsynchronized. This paper addresses his problem and allows he use of daily daa o characerize erm-variaion in he correlaion srucure. Model is easy o implemen in forecasing applicaions. Highlighs furher key quesions for modeling and forecasing correlaions: Are correlaions mean-revering? Do hey mean-rever o a consan?

7 Facor Models and Correlaion Srucure Consider a K facor APT model r E ( r ) ' F u, F ( f,..., f )' i, 1 i, i i, 1, K, and he following sandard resricions in a facor srucure: (1) Euu ( ) 0, i j (2) E( f u ) 0, i, k If (1), (2) and (3) hold condiionally: K V ( f 1,, -1, ) k ik jk k i, j, K 2 K 2 V V V V i k, j i (3) E( f f ) 0, k l k, l, ( u -1, ) (, -1, ) ( -1, ) (, -1, ) i f i k k u j f j k k k1 k1

8 High Frequency Covariance Relaxing (1) condiionally incorporaes he effec of laen unobserved facors. Relaxing (2) condiionally incorporaes he effec of ime varying beas. cov ( r, f ) E ( u f ). 1 i, k, 1 i, k, ik,, ik, V 1 ( fk, ) V 1 ( fk, ) Relaxing (3) allows for dynamic ineracions across facors. Hence, we can define he high frequency covariance and correlaion as: V ( r ) H BF B ' Bcov ( F, u ) cov ( u, F) B 1, 1 1 u, 1 1 HF , 1 N, R D H D, D diag{ V ( r ),..., V ( r )}

9 Low Frequency Correlaion Following Engle and Rangel (2008), facors are described by asymmeric spline-garch processes: V (1) 1 ( f ) k, f, k, g f, j, g ~ Asymmeric GARCH, ~ Exponenial Cuadraic Splin Also, idiosyncraic erms show asymmeric spline-garch dynamics: V 1 ( ui, ) i, gi, (2) g ~ Asymmeric GARCH, ~ Exponenial Cuadraic Spline The ypical low frequency correlaion componen is: (3) f, j, i, LF i, j, K k 1 ik, jk, i, Eu ( u ) f, k, i, j K 2 K 2 i, k 1 ik, f, k, j, k1 jk, f, k, The ypical elemen of R HF (high-frequency correlaion) mean-revers oward he LFC. HF LF (4) i, j, i, j, f, j, e

10 Inernaional daa and synchronizaion Daa: marke reurns of 43 counries (include developed and emerging markes), reurns in US dollars, weekly and daily frequencies from January 1995 o December Three global facors: marke reurns in America, Europe, and Asia (S&P500, MSCI Europe, and MSCI Asia Ex Japan). Problem: Non-synchronous rading aciviy biases esimaion of loadings and correlaions. Scholes and Williams (1977), Lo and MacKinlay (1990), Burns, Engle, and Mezrich (1998). Soluion: Use weekly daa. Synchronize daily observaions.

11 Esimaion Resuls: weekly daa (summary) Correlaion persisence = 0.94, updaing correlaion parameer = Variance persisence = 0.73, updaing variance parameer = 0.08 Average spline knos: 2.2 Example: High and Low Frequency Correlaions of Germany and Japan (From Weekly Daa) LFC HFC

12 Average FSG-DCC Correlaions vs Model Free Benchmark Ge average correlaion of each counry wih respec o all he res, hen average across counries. Model-Free Benchmark: sample correlaion marix for every half year in he sample from weekly daa (e.g., Bekaer, Hodrick and Zhang (2008)) sample 6 monhs lfc_weekly hfc_weekly Feb-95 Aug-95 Feb-96 Aug-96 Feb-97 Aug-97 Feb-98 Aug-98 Feb-99 Aug-99 Feb-00 Aug-00 Feb-01 Aug-01 Feb-02 Aug-02 Feb-03 Aug-03 Feb-04 Aug-04 Feb-05 Aug-05 Feb-06 Aug-06 Feb-07 Aug-07 Feb-08 Aug-08 Average Correlaion Dae

13 Synchronizing Reurns -2-1 US US E E A A - Synchronized reurn: s r E E 1 Reurns Close-Close US - Esimaed synchronized reurn: se re 1, where E ( r { r, r, r }, ) E, 1 US, E, A, A ν -1 ξ E ν Open Close ξ - In a mulivariae seup follow Burns e al. (1998) r M 1, V 1 ( ) H, s ( I M), V ( s ) ( I M) H ( I M) 1,

14 Global correlaions and curren financial urmoil Compue average correlaions in hree subperiods: 08/03/2006 o 08/03/2007, 08/06/2007 o 09/12/2008, 09/15/2008 o 12/15/2008 From Lehman s Bankrupcy o December Sample Period From he Credi-Crunch o Lehman s Bankrupcy Before he Credi-Crunch (Augus 2006-Augus 2007) Average Correlaions (High Freq) Average Correlaions (Low Freq) Correlaions

15 Disribuion of changes on average low frequency correlaions across counries Average % change Peru Colombia Newzealand Philippines Czech Rep. Hungary Japan Korea Poland India Ausria Turkey Mexico China UK Souhafrica Indonesia Chile Denmark France Malaysia Neherlands Thailand Ausralia Singapore Venezuela Germany Swiss Hong Kong Sweden Greece Taiwan Belgium Brazil Argenina Spain Russia Porugal Norway Ireland Ialy Finland Canada % Change

16 Disribuion of changes on average high frequency correlaions across counries Venezuela Newzealan Philippines India Colombia China Peru Poland Taiwan Porugal Thailand Turkey Hungary Chile Malaysia Souhafrica Ireland Denmark Indonesia Ausralia Greece Japan Czech Rep. Mexico Singapore Hong Kong Korea Ausria Norway Swiss Finland UK Brazil Spain Canada Sweden Belgium Argenina France Neherland Ialy Germany Russia % Change Average % change

17 Concluding Remarks This paper inroduces a unified framework o model high and low frequency dynamics of global equiy correlaions. The framework allows us o exploi high frequency available informaion o measure such inernaional correlaions. The wo erm componens of global correlaions have shown subsanial increases on average, especially during he recen financial urmoil. However, such effecs have no been equally disribued across counries. The effec has been larger in emerging markes. This has imporan implicaions for diversificaion of global risk.