Indexing and statistical arbitrage

There are two basic methodologies for portfolio optimization: tracking error variance (TEV) minimization (the industry standard for indexing), and a cointegration–optimal strategy (advocated by econometricians). Cointegration is a statistical tool that seeks to exploit a long–run equilibrium relationship between a portfolio and a benchmark, ensuring that the two are connected in the long term. For simple index tracking, the additional feature of cointegration is found to provide no clear advantages or disadvantages over TEV. Both models produce optimal portfolios that outperform a price–weighted benchmark during market crashes, assuming a long enough model calibration period. When tracking becomes more difficult, ensuring a cointegration relationship enhances performance. Cointegration–optimal portfolios dominate TEV equivalents for all the statistical arbitrage strategies based on enhanced indexation in all market circumstances.