Indexing and Statistical Arbitrage

Carol Alexander · Anca Dimitriu

109 citations0/0 files storedThe Journal of Portfolio Management

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Financial Markets and Investment Strategies Financial Risk and Volatility Modeling Risk and Portfolio Optimization

Abstract

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.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1993Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency 1991Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models 1979Distribution of the Estimators for Autoregressive Time Series With a Unit Root 1965The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets 1985Does the Stock Market Overreact?1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]

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