Statistical Accommodement in the U. S. Equities Market Article

Statistical Arbitrage inside the U. S i9000. Equities Industry

Marco Avellaneda∗†and Jeong-Hyun Lee∗ Initial draft: September 11, 2008 This type: June 12-15, 2009

Abstract We study model-driven record arbitrage in U. S i9000. equities. The trading signs are produced in 2 different ways: using Primary Component Examination and employing sector ETFs. In both cases, we consider the residuals, or idiosyncratic aspects of stock results, and style them since mean-reverting procedures. This potential clients naturally to " contrarian” trading signs. The main contribution of the paper is the construction, back-testing and comparison of market-neutral PCA- and ETF- centered strategies placed on the wide-ranging universe of U. S. stocks. Back-testing shows that, following accounting for transaction costs, PCA-based tactics have an average annual Sharpe ratio of 1. 44 over the period 97 to 2007, with much stronger performances prior to 2003. During 2003-2007, the regular Sharpe percentage of PCA-based strategies was only 0. 9. Strategies based on ETFs achieved a Sharpe proportion of 1. one particular from 97 to 3 years ago, experiencing an identical degradation after 2002. All of us also bring in a method to be the cause of daily trading volume data in the indicators (which is definitely akin to applying " trading time” in contrast to calendar time), and watch significant improvement in functionality in the case of ETF-based signals. ETF strategies designed to use volume information achieve a Sharpe ratio of just one. 51 from 2003 to 2007. The paper also relates the performance of mean-reversion statistical arbitrage approaches with the currency markets cycle. Particularly, we analyze in detail the performance of the strategies during the liquidity problems of the summer season of 2007. We obtain results which are according to Khandani and Lo (2007) and validate their " unwinding” theory for the quant account drawdown of August 2007. ∗ Courant Institute of Mathematical Savoir, 251 Mercer Street, New york city, N. Sumado a. 10012 UNITED STATES †Fund Concepts, 49-51 Avenue Victor-Hugo, 75116 Rome, France.

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Introduction

The term record arbitrage has a variety of tactics and purchase programs. Their common features are: (i) trading indicators are methodical, or rules-based, as opposed to driven by basics, (ii) the trading book is market-neutral, in the sense that it has absolutely no beta while using market, and (iii) the mechanism to get generating extra returns is usually statistical. The concept is to make many wagers with great expected comes back, taking advantage of diversification across stocks, to produce a low-volatility investment strategy which is uncorrelated with the marketplace. Holding times range from a couple of seconds to days and nights, weeks or maybe longer. Pairs-trading is widely assumed as the " ancestor” of record arbitrage. In the event stocks G and Q are inside the same sector or have comparable characteristics (e. g. Exxon Mobile and Conoco Phillips), one expects the results of the two stocks in order to each other after controlling to get beta. Consequently, if Pt and Qt denote the corresponding price time series, after that we can model the system because ln(Pt /Pt0 ) = α(t − t0 ) + βln(Qt /Qt0 ) + Xt or, in its differential version, dQt dPt = αdt + β + dXt, Pt Qt (2) (1)

where Xt is a fixed, or mean-reverting, process. This procedure will be called the cointegration residual, or residual, for short, in the rest of the daily news. In many cases of interest, the go α is usually small compared to the fluctuations of Xt and may therefore become neglected. Which means that, after controlling for beta, the long-short portfolio oscillates near some statistical balance. The style suggests a contrarian purchase strategy through which we go long 1 dollar of stock L and brief β dollars of share Q in the event that Xt is usually small and, more over, go brief P and long Q if Xt is large. The stock portfolio is expected to produce a great return while valuations are coming (see Post (2007) for any comprehensive assessment on record arbitrage and co-integration). The mean-reversion paradigm is typically linked to market...

Referrals: Associated Press, Quant funds endure August turmoil. The Motley Mislead, December 6th, 2007. Barr, A., Relativement quake mixtures hedge-fund titans Goldman, Renaissance, AQR discover losses, although also impression opportunity, Marketwatch, August 13, 2007. Cont, R., Da Fonseca, M., Dynamics of implied volatility surfaces. Quantitative Finance, 2002, Vol 2, No 1, 45-60. Davis, G., Mallat, S. and Avellaneda, Meters., Adaptive greedy approximations. Helpful Approximations, 97, Vol. 13, No . you, 57-98. Jolliffe, I. To., Principal Parts Analysis, Springer Series in Statistics, Springer-Verlag, Heidelberg, 2002. Khandani, A. E. and Lo, A. W., So what happened to the quants in August 3 years ago? SSRN, 3 years ago. Laloux, D., Cizeau, G., Potters, M. and Bouchaud, J. L., Random matrix theory and financial correlations. International Record of Assumptive and Applied Finance, 2000, Vol. a few, No . three or more, 391-397. Lehmann, B., Fashions, martingales, and market efficiency. Quarterly Journal of Economics, 1990, Volume. 105, No . 1, 1-28. Litterman, R. and Scheinkman, J. A., Common factors affecting connection returns. Log of Fixed Income, June 1991, 54-61. Lo, A. W. and MacKinlay, A. C., The moment are contrarian profits as a result of stock market overreaction? The Review of Economic Studies, 1990, Vol. several, No . a couple of, 175-205. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. In., Guhr, Capital t. and Stanley,

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H. E., Arbitrary matrix way of cross correlations in п¬Ѓnancial data. Phys. Rev., 2002, E sixty-five, 066126. Post, A., Record arbitrage: Algorithmic trading insights and tactics, Wiley Fund, 2007. Poterba, J. M. and High seasons, L. L., Mean reversion in stock prices: proof and ramifications. Journal of economic Economics, 1988, Vol. twenty-two, 27-59. Potters, M., Bouchaud, J. G. and Laloux, L., Monetary application of unique matrix theory: old laces and new pieces. Rese?a Physica Polonica B, 2005, Vol. thirty six, No . on the lookout for, 2767. Rusli, E. M., Goldman Sachs Alpha to get corrupted?, Forbes. com, August being unfaithful, 2007. Scherer, K. L. and Avellaneda, M., Most for one and one for all those? A principal component evaluation of Latin American brady bond personal debt from year 1994 to 2150. International Journal of Assumptive and Utilized Finance, 2002, Vol. a few, No . one particular, 79-106.

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