Statistical Arbitrage Trading Model Abstract: An important tool for financial traders in this technology age is effective models that can systematically assist them in making decisions. As many traders do not have academic backgrounds in engineering, mathematics or statistics, developing a quantitative model that can capture statistical miss-pricings can be challenging. They are also exposed to human errors, emotional distractions and over-reliance on intuitions but do not have the resources to develop a decision tool to assist them. To provide a solution for these problems, we have developed a statistical arbitrage model that is affordable, robust and reliable. We have employed a statistical approach using mean-reversion techniques to evaluate relative mispricing of equity prices. The model is able to capture movement trends that can be used to exploit market prices discrepancies. Using a two-engine system, the model takes in the input of equity prices and transaction volume while generates systematic signals for users to “sell” and “buy” an asset. The model then computes a market-neutral strategy to minimize the general-market exposure that may underline the trade’s performance. University of Pennsylvania Department of Electrical and Systems Engineering TEAM 14 Authors: Xiang-li Lim (SSE) Lu Tian (SSE) Xiaobin Zhang (SSE) Advisors: Dr. Alejandro Ribeiro (ESE) Dr. Tony Smith (ESE) DEMO TIMES: Thursday, April 21 st, 2011 AM: 11: :30 PM: 02: :00 Problem Statement Human errors are unavoidable due to emotional disturbances and mental fatigue. Large financial institutions developed trading models as a decision- making tool but most of these models are proprietary and expensive. Thus, smaller firms do not have the resources nor the capabilities to develop such a tool. This model attempts to solve these problems for these smaller firms by serving as a decision tool in equities trading that is effective yet reasonable. Solution: Stat-Arb Approach The concept of statistical arbitrage from the relative mispricing of two or more assets. For example, consider a game 1.Flip a coin and collects $1 for heads or pays $0.50 for tails [biased coin]. 2.In any flip, it is uncertain if one will win or lose money, thus having some element of risk. 3.Statistically speaking, however, the expected value is $1 x 50% as revenue and $0.50 x 50% as cost which yields $0.25 profit for each flip. 4.After numerous flips, the mean return will approach this expected value due to the law of large numbers (Source: Algoet, 1994) The features of a statistical arbitrage model are (Source: Avellaneda and Lee, 2008) : Trading signals are systematic. The trading book is market-neutral. The mechanism for generating excess returns is statistical. Source: Algoet, P.H. "The strong law of large numbers for sequential decisions under uncertainty." IEEE Transactions on Information Theory; Volume: 40 Issue:3, Project Goals Our objective is to use the statistical arbitrage concept to design a prototype of a decision tool that can provide a systematic approach for users in equities- trading. Our Goals are as follow: 1.Outperform the benchmark in profitability by at least 2% This is tested using a data set from 2002 to 2006 containing over 1500 data points. 2.Insensitivity to transaction cost Model considers a transaction cost of 5 basis points of the total asset value. 3.Robustness Model’s performance is validated over the short run and the long run. 4.Market neutral returns, Model’s performance should have minimal correlations with the S&P 500 performance. Results: Figure 4: Performance of Model against Benchmark Conclusion The prototype model is profitable while taking transaction cost into account, shown market neutrality and robust, thus achieving all of our stated objectives and goals. A further development into a full-fledge operational software can be executed using this prototype to achieve better efficiency, more sophisticated interface and to incorporate database from live-sources. Figure 1: System Block Diagram Engine 1: Trading Signals Generator Two key variables are considered in executing Engine 1; Asset Price and Transaction Cost. A Database of 150 Stocks and 15 ETFs was compiled as follow: Using 60 days of moving-historical data for asset prices and 30 days for transaction volume, the following parameters (Source: Avellaneda and Lee, 2008) were computed: System Block Diagram Engine 2 – Calibrating Market Neutral Trade and Transaction Cost Each transaction amount is calibrated with the Beta computed in Engine 1. Thus the transaction amount for each ETF traded is the multiplication of Beta and the particular Stock Price The transaction cost of 5 basis points for each transaction was also computed and incorporated for each transaction. Figure 3: A Sample of Model’s Database Figure 2: Industry Sectors Representation Signals Threshold Two signals (drift and no drift) were computed: The following threshold were followed: Long if the s-score <-1.25 Short if the s-score > 1.25 Close long position if the s-score > -0.5 Close short position if the s-score<0.75 Close long position means nullifying the long position, thus selling the current amount of shares. Close short position is the same applied to a short position. Figure 5: Summary of Key Statistics Source: Avellaneda, Marco, and Jeong-Hyun Lee. Statistical Arbitrage in the U.S. Equities Market. Academic, New York: New York University, 2008.