A Comparison of Cointegration & Tracking Error Models for Mutual Funds & Hedge Funds

Abstract

We present a detailed study of portfolio optimisation based on cointegration, a statistical tool that here exploits a long-run equilibrium relationship between stock prices and an index price. We compare the theoretical and empirical properties of cointegration optimal equity portfolios with those of portfolios optimised on the tracking error variance. From an eleven year out of sample performance analysis we find that for simple index tracking the additional feature of cointegration between the tracking portfolio and the index has no clear advantages or disadvantages relative to the tracking error variance (TEV) minimization model. However ensuring a cointegration relationship does pay off when the tracking task becomes more difficult. Cointegration optimal portfolios clearly dominate the TEV equivalents for all of the statistical arbitrage strategies based on enhanced indexation, in all market circumstancescointegration, tracking error, index tracking, statistical arbitrage