Statistical Arbitrage: A Critical View
DOI:
https://doi.org/10.15678/AOC.2016.1505Keywords:
statistical arbitrage, cointegration, conditional heteroscedasticity, VECM-MGARCH, Breitung cointegration testAbstract
Statistical arbitrage dynamics is driven by a stationary, autoregressive process known as mispricing. This process approximates the value in time of a portfolio weighted equally to the elements of a cointegration vector of the log-prices processes of related instruments. Statistical arbitrage involves taking either long or short positions on a portfolio according to predictions of mispricing. This paper offers a theoretical analysis of cointegration testing under the conditional heteroscedasticity of the innovations process. Cointegration testing is used in the procedure of searching for the log-price processes of the related instruments that will form a statistical arbitrage portfolio. We also investigate dynamic characteristics of the mispricing process, which is a linear combination (cointegration vector elements are coefficients of it) of related log-
-prices processes for which the (T)VECM-MGARCH model class is assumed. Under this model assumptions making precise predictions on mispricing process based on past realizations are difficult. This paper can be treated as a starting point for an empirical analysis of statistical arbitrage portfolio construction. Reference is made to theory to describe the challenges which can be faced in constructing a statistical arbitrage portfolio based on cointegration, in modelling the dynamics of mispricing, and in prediction where the innovation process is conditionally heteroscedastic.
References
Balke, N. S. and Fomby, T. B. (1997) “Threshold Cointegration”. International Economic Review 38(3): 627–45, https://doi.org/10.2307/2527284.
Breitung, J. (2002) “Nonparametric Tests for Unit Roots and Cointegration”. Journal of Econometrics 108 (2): 343–63, https://doi.org/10.1016/s0304-4076(01)00139-7.
Burgess, A. N. (2000) A Computational Methodology for Modelling the Dynamics of Statistical Arbitrage. PhD dissertation. London: University of London.
Cavaliere, G., Rahbek, A. and Taylor, A. M. R. (2008) Testing for Co-integration in Vector Autoregressions with Non-stationary Volatility. CREATES Research Paper No. 2008–50, Copenhagen: University of Copenhagen.
Cavaliere, G., Rahbek, A. and Taylor, A. M. R. (2010) “Cointegration Rank Testing under Conditional Heteroskedasticity”. Econometric Theory 26 (6): 1719–60, https://doi.org/10.1017/s0266466609990776.
Chan, N. H. (2011) Time Series: Applications to Finance with R and S-Plus. New York: John Wiley & Sons.
Davidson, J. (1994) Stochastic Limit Theory: An Introduction for Econometricians. Oxford: Oxford University Press.
Jarrow, R., Teo, M., Tse, Y. K. and Warachka, M. (2012) “An Improved Test for Statistical Arbitrage”. Journal of Financial Markets 15 (1): 47–80, https://doi.org/10.1016/j.finmar.2011.08.003.
Johansen, S. (1995) Likelihood-based Inference in Cointegrated Vector Autoregressive Models. Oxford–New York: Oxford University Press.
Maki, D. (2013) “The Influence of Heteroskedastic Variances on Cointegration Tests: A Comparison Using Monte Carlo Simulations”. Computational Statistics 28 (1): 179–98, https://doi.org/10.1007/s00180-011-0293-x.
Swensen, A. R. (2006) “Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models”. Econometrica 74 (6): 1699–1714, https://doi.org/10.1111/j.1468-0262.2006.00723.x.
