Study on Stock Index Futures’ Mean Reversion Effect and Arbitrage in China Based on High-Frequency Data

Affiliation(s)

School of Management, Graduate University of Chinese Academy of Sciences, Beijing, China.

School of Economics and Management, Beijing University of Posts and Telecmmunication, Beijing, China.

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.

School of Management, Graduate University of Chinese Academy of Sciences, Beijing, China.

School of Economics and Management, Beijing University of Posts and Telecmmunication, Beijing, China.

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.

ABSTRACT

Based on 1 minute high frequency data, this paper constructs no-arbitrage band for CSI300 index futures, and empirically studies the futures-spot arbitrage. Furthermore, the mean reversion and its time effect are analyzed by ADF model for the first time in Chinese index futures market and a logit model is used to investigate the related factors of arbitrage opportunities. We find that CSI300 index futures have cash-and-carry arbitrage opportunities; the existence of mean reversion effect of index futures when arbitrage is absent; cash-and-carry arbitrage has a significant impact for mean reversion of the mispricing, while the reverse has insignificant effect. As for the time effect of mean reversion, it indicates that the time which arbitrage effect reversion most is mispricing shows 14 minutes later. The probability of arbitrage opportunities is positive correlated to first-order lagged of volume, and negative correlated to the volume; the time to expiration, the highest price and lowest price differences are also positive related to arbitrage opportunities.

Based on 1 minute high frequency data, this paper constructs no-arbitrage band for CSI300 index futures, and empirically studies the futures-spot arbitrage. Furthermore, the mean reversion and its time effect are analyzed by ADF model for the first time in Chinese index futures market and a logit model is used to investigate the related factors of arbitrage opportunities. We find that CSI300 index futures have cash-and-carry arbitrage opportunities; the existence of mean reversion effect of index futures when arbitrage is absent; cash-and-carry arbitrage has a significant impact for mean reversion of the mispricing, while the reverse has insignificant effect. As for the time effect of mean reversion, it indicates that the time which arbitrage effect reversion most is mispricing shows 14 minutes later. The probability of arbitrage opportunities is positive correlated to first-order lagged of volume, and negative correlated to the volume; the time to expiration, the highest price and lowest price differences are also positive related to arbitrage opportunities.

Cite this paper

W. Zhuo, X. Zhao, Z. Zhou and S. Wang, "Study on Stock Index Futures’ Mean Reversion Effect and Arbitrage in China Based on High-Frequency Data,"*iBusiness*, Vol. 4 No. 1, 2012, pp. 78-83. doi: 10.4236/ib.2012.41009.

W. Zhuo, X. Zhao, Z. Zhou and S. Wang, "Study on Stock Index Futures’ Mean Reversion Effect and Arbitrage in China Based on High-Frequency Data,"

References

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[19] Y. Tse, “Index Arbitrage with Heterogeneous Investors: A Smooth Transition Error Correction Analysis,” Journal of Banking & Finance, Vol. 25, No. 10, 2001, pp. 1829- 1855. doi:10.1016/S0378-4266(00)00162-X

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[23] P. Kumar and D. Seppi, “Information and Index Arbitrage,” Journal of Business, Vol. 67, No. 4, 1994, pp. 481-509.

[24] C. W. Holden, “Index Arbitrage as Cross-Sectional Mar- ket Making,” Journal of Futures Markets, Vol. 15, No. 4, 1995, pp. 423-455.

[25] C. W. Holden, “Intertemporal Arbitrage Trading: Theory and Empirical Tests,” Working Paper, Indiana University, Bloomington, 1990.

[26] A. Kraus and H. R. Stoll, “Price Impacts of Block Trad- ing on the New York Stock Exchange,” Journal of Fi- nance, Vol. 27, No. 3, 1972, pp. 569-588.

[27] B. Biais, P. Hillion and C. Spatt, “An Empirical Analysis of the Limit Order Book in the Paris Bourse,” Journal of Finance, Vol. 50, No. 5, 1985, pp. 1655-1689.

[28] M. H. Miller, J. Muthuswamy and R. E. Whaley, “Mean Reversion of Standard & Poor’s 500 Index Basis Changes: Arbitrage-Induced or Statistical Illusion?” Journal of Fi- nance, Vol. 49, No. 2, 1994, pp. 479-513. doi:10.2307/2329160

[29] P. Alphonse, “Mispricing Persistence and the Effective- ness of Arbitrage Trading,” Multinational Finance Jour- nal, Vol. 11, No. 1-2, 2007, pp. 123-56.

[30] G. P. Dwyer, P. Locke and W. Yu, “Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash,” Review of Financial Studies, Vol. 9, No. 1, 1996, pp. 301-312. doi:10.1093/rfs/9.1.301

[31] Y. W. Cheung and H. G. Fung, “Information Flows be- tween Eurodollar Spot and Futures Markets,” Multina- tional Finance Journal, Vol. 1, No. 4, 1997, pp. 255-271.

[32] J. Merrick Jr., “Volume Determination in Stock and Stock Index Futures Markets: An Analysis of Arbitrage and Vola- tility Effects,” Journal of Futures Markets, Vol. 7, No. 5, 1987, pp. 483-496. doi:10.1002/fut.3990070503

[1] B. Cornell and K. R. French, “The Pricing of Stock Index Futures,” Journal of Futures Markets, Vol. 3, No. 1, 1983, pp. 1-14. doi:10.1002/fut.3990030102

[2] S. Figlewski, “Hedging Performance and Basis Risk in Stock Index Futures,” Journal of Finance, Vol. 39, No. 3, 1984, pp. 657-669. doi:10.2307/2327924

[3] L. Harris, “The October 1987 S&P 500 Stock-Futures Ba- sis,” Journal of Finance, Vol. 44, No. 1, 1989, pp. 77-99. doi:10.2307/2328276

[4] M. J. Brennan and E. S. Schwartz, “Arbitrage in Stock Index Futures,” Journal of Business, Vol. 63, No. 1, 1990, pp. 7-31. doi:10.1086/296491

[5] Y. P. Chung, “A Transactions Data Test of Stock Index Futures Market Efficiency and Index Arbitrage Profitabil- ity,” Journal of Finance, Vol. 46, No. 5, 1991, pp. 1791- 1809. doi:10.2307/2328573

[6] N. Richie, R. Daigler and K. C. Gleason, “The Limit to Stock Index Arbitrage: Examing S&P 500 Futures and SPDRS,” Journal of Futures Markets, Vol. 28, No. 12, 2008, pp. 1182-1205. doi:10.1002/fut.20365

[7] A. Fremault, “Stock Index Futures and Index Arbitrage in a Rational Expectations Model,” Journal of Business, Vol. 64, No. 4, 1991, pp. 523-525.

[8] C. Sutcliffe, “Stock Index Futures,” 3rd Edition, Ashgate Publishing Company, Surrey, 2006.

[9] D. G. McMillan and N. ülkü, “Persistent Mispricing in a Recently Opened Emerging Index Futures Market: Arbi- trageurs Invited,” Journal of Futures Markets, Vol. 29, No. 3, 2009, pp. 218-243. doi:10.1002/fut.20355

[10] A. C. MacKinlay and K. Ramaswamy, “Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices,” Review of Financial Studies, Vol. 1, No. 2, 1988, pp. 137- 158. doi:10.1093/rfs/1.2.137

[11] K. G. Lim, “Arbitrage and Price Behavior of the Nikkei Stock Index Futures,” Journal of Futures Markets, Vol. 12, No. 2, 1992, pp. 151-161. doi:10.1002/fut.3990120204

[12] P. K. Yadav and P. F. Pope, “Stock Index Futures Mis- pricing: Profit Opportunities or Risk Premia,” Journal of Banking & Finance, Vol. 18, No. 5, 1994, pp. 921-953. doi:10.1016/0378-4266(94)00026-3

[13] R. Neal, “Direct Tests of Index Arbitrage Models,” Jour- nal of Financial and Quantitative Analysis, Vol. 31, No. 4, 1996, pp. 541-562.

[14] K. D. Garbade and W. L. Silber, “Price Movements and Price Discovery in Futures and Cash Markets,” Review of Economics and Statistics, Vol. 65, No. 21983, pp. 289-297.

[15] K. A. Chan, “Further Analysis of the Lead Lag Relation- ship between the Cash Market and Index Futures Mar- ket,” Review of Financial Studies, Vol. 5, No. 1, 1992, pp. 123-151. doi:10.1093/rfs/5.1.123

[16] I. G. Kawaller, P. D. Koch and T. W. Koch, “The Tem- poral Price Relationship between the S&P 500 Futures and the S&P 500 Index,” Journal of Finance, Vol. 42, No. 5, 1987, pp. 1309-1329.

[17] H. R. Stoll and R. E. Whaley, “The Dynamics of Stock Index and Stock Index Futures Returns,” Journal of Fi- nancial and Quantitative Analysis, Vol. 25, No. 4, 1990, pp. 441-468. doi:10.2307/2331010

[18] I. G. Kawaller, “Determining the Relevant Fair Value(S) of S&P 500 Futures: A Case Study Approach,” Journal of Futures Markets, Vol. 11, No. 4, 1991, pp. 453-460. doi:10.1002/fut.3990110405

[19] Y. Tse, “Index Arbitrage with Heterogeneous Investors: A Smooth Transition Error Correction Analysis,” Journal of Banking & Finance, Vol. 25, No. 10, 2001, pp. 1829- 1855. doi:10.1016/S0378-4266(00)00162-X

[20] P. K. Yadav and P F. Pope, “Stock Index Futures Arbi- trage: International Evidence,” Journal of Futures Mar- kets, Vol. 10, No. 6, 1990, pp. 573-603. doi:10.1002/fut.3990100603

[21] A. Kempf, “Short Selling, Unwinding, and Mispricing,” Journal of Futures Markets, Vol. 18, No. 8, 1998, pp. 903- 923. doi:10.1002/(SICI)1096-9934(199812)18:8<903::AID-FUT2>3.0.CO;2-V

[22] A. K. Fung, D. M. Mok and K. Lam, “Intraday Price Re- versals for Index Futures in the US and Hong Kong,” Journal of Banking & Finance, Vol. 24, No. 7, 2000, pp. 1179-1201. doi:10.1016/S0378-4266(99)00072-2

[23] P. Kumar and D. Seppi, “Information and Index Arbitrage,” Journal of Business, Vol. 67, No. 4, 1994, pp. 481-509.

[24] C. W. Holden, “Index Arbitrage as Cross-Sectional Mar- ket Making,” Journal of Futures Markets, Vol. 15, No. 4, 1995, pp. 423-455.

[25] C. W. Holden, “Intertemporal Arbitrage Trading: Theory and Empirical Tests,” Working Paper, Indiana University, Bloomington, 1990.

[26] A. Kraus and H. R. Stoll, “Price Impacts of Block Trad- ing on the New York Stock Exchange,” Journal of Fi- nance, Vol. 27, No. 3, 1972, pp. 569-588.

[27] B. Biais, P. Hillion and C. Spatt, “An Empirical Analysis of the Limit Order Book in the Paris Bourse,” Journal of Finance, Vol. 50, No. 5, 1985, pp. 1655-1689.

[28] M. H. Miller, J. Muthuswamy and R. E. Whaley, “Mean Reversion of Standard & Poor’s 500 Index Basis Changes: Arbitrage-Induced or Statistical Illusion?” Journal of Fi- nance, Vol. 49, No. 2, 1994, pp. 479-513. doi:10.2307/2329160

[29] P. Alphonse, “Mispricing Persistence and the Effective- ness of Arbitrage Trading,” Multinational Finance Jour- nal, Vol. 11, No. 1-2, 2007, pp. 123-56.

[30] G. P. Dwyer, P. Locke and W. Yu, “Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash,” Review of Financial Studies, Vol. 9, No. 1, 1996, pp. 301-312. doi:10.1093/rfs/9.1.301

[31] Y. W. Cheung and H. G. Fung, “Information Flows be- tween Eurodollar Spot and Futures Markets,” Multina- tional Finance Journal, Vol. 1, No. 4, 1997, pp. 255-271.

[32] J. Merrick Jr., “Volume Determination in Stock and Stock Index Futures Markets: An Analysis of Arbitrage and Vola- tility Effects,” Journal of Futures Markets, Vol. 7, No. 5, 1987, pp. 483-496. doi:10.1002/fut.3990070503