Statistical Arbitrage: A Critical View

Przemysław Jaśko

Abstract


 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.



Keywords


statistical arbitrage, cointegration, conditional heteroscedasticity, VECM-MGARCH, Breitung cointegration test

Full Text:

PDF

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.




DOI: https://doi.org/10.15678/AOC.2016.1505