AQR Capital Management, LLC|Two Greenwich Plaza, Third Floor | Greenwich, CT 06830 |T: 203.742.3600 | F: 203.742.3100 | www.aqr.com Trading Costs of Asset

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  • AQR Capital Management, LLC|Two Greenwich Plaza, Third Floor | Greenwich, CT 06830 |T: 203.742.3600 | F: 203.742.3100 | www.aqr.com Trading Costs of Asset Pricing Anomalies Andrea Frazzini AQR Capital Management Ronen Israel AQR Capital Management Tobias J. Moskowitz University of Chicago, NBER, and AQR Copyright 2014 by Andrea Frazzini, Ronen Israel, and Tobias J. Moskowitz. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC its affiliates, or its employees. The information set forth herein has been obtained or derived from sources believed by author to be reliable. However, the author does not make any representation or warranty, express or implied, as to the informations accuracy or completeness, nor does the author recommend that the attached information serve as the basis of any investment decision. This document is intended exclusively for the use of the person to whom it has been delivered by the author, and it is not to be reproduced or redistributed to any other person. This presentation is strictly for educational purposes only.
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  • Motivation Cross-section of expected returns typically analyzed gross of transactions costs Questions regarding market efficiency should be net of transactions costs Are profits within trading costs? Research Questions: How large are trading costs faced by large arbitrageurs? How robust are anomalies in the literature after realistic trading costs? At what size do trading costs start to constrain arbitrage capital? What happens if we take transactions costs into account ex ante? Tradeoff between expected returns and trading costs varies across anomalies Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz 2
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  • Objectives Measure trading costs of an arbitrageur Understand the cross-section of net returns on anomalies Model of trading costs for descriptive and prescriptive purposes Constructing optimized portfolios Conclusion 3 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • What We Do Take all (longer-term) equity orders and executions from AQR Capital 1998 to 2013, $1.1 trillion worth of trades, traded using automated algorithms U.S. (NYSE and NASDAQ) and 18 international markets *Exclude high frequency (intra-day) trades Use actual trade sizes and prices to calculate Price impact and implementation shortfall (e.g., Perold (1988)) More accurate picture of real-world transactions costs and tradeoffs Get vastly different measures than the literature Actual costs are 1/10 the size of those estimated in the literature Why? 1) Average trading cost cost facing an arbitrageur 2) Design portfolios that endogenously respond to expected trading costs 4 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Measuring Trading Costs Literature has used a variety of models and types of data to approximate trading costs: Daily spread and volume data [Roll (1984), Huang and Stoll (1996), Chordia, Roll, and Subrahmanyam (2000), Amihud (2002), Acharya and Pedersen (2005), Pastor and Stambaugh (2003), Watanabe and Watanabe (2006), Fujimoto (2003), Korajczyk and Sadka (2008), Hasbrouck (2009), and Bekaert, Harvey, and Lundblad (2007)] Transaction-level data (TAQ, Rule 605, broker) [Hasbrouck (1991a, 1991b), Huberman and Stanzl (2000), Breen, Hodrick, and Korajczyk (2002), Loeb (1983), Keim and Madhavan (1996), Knez and Ready (1996), Goyenko (2006), Sadka (2006), Holden (2009), Goyenko, Holden, and Trzcinka (2009), Lesmond, Ogden, and Trzcinka (1999), Lesmond (2005), Lehmann (2003), Werner (2003), Hasbrouck (2009), and Goyenko, Holden, and Trzcinka (2009)] Proprietary broker data [ Keim (1995), Keim and Madhavan (1997), Engle, Ferstenberg, and Russell (2008) ] Several papers have applied trading cost models to anomalies, chiefly size, value, and momentum. Most find costs are significantly binding. Chen, Stanzl, and Watanabe (2002) Korajczyk and Sadka (2004) Lesmond, Schill, and Zhou (2003) 5Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Trading Execution Database Trade execution database from AQR Capital Management Institutional investor, around 118 billion USD in assets (October 2014) Data compiled by the execution desk and covers all trades executed algorithmically in any of the firms funds since inception (*excluding stat arb trades) Information on orders, execution prices and quantities Common stocks only: restrict to cash equity and equity swaps 19 Developed markets (drop emerging markets trades) Drop liqudity/statistical arbitrage trades Result: ~9,300 global stocks, 1.1 trillion USD worth of trades Price, return and volume data Union of the CRSP tapes and the XpressFeed Global database 6Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Trade Execution Database This picture shows our trade execution database. Last years data, the rest is in some nuclear-disaster-proof bunkers around the world Frazzini almost froze to death to take this photograph 7 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Trade Execution Data, 1998 2013. Summary Stats 8 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Summary Stats cont. 9 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Summary Stats cont. 10 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Trading Execution Algorithm *The portfolio generation process is separate from the trading process - algorithms do not make any explicit aggregate buy or sell decisions Merely determine duration of a trade (most within 1 day) The trades are executed using proprietary, automated trading algorithms designed and built by the manager (aka Ronen) Direct market access through electronic exchanges Provide rather than demand liquidity using a systematic approach that sets opportunistic, liquidity-providing limit orders Break up total orders into smaller orders and dynamically manage them Randomize size, time, orders, etc. to limit market impact Limit prices are set to buy stocks at bid or below and sell stocks at ask or above generally We consider all of the above as part of the trading cost of a large arbitrageur 11 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Click to edit Master title style 12 Market Impact (BPs) Time Portfolio Formation Order Submission Portfolio Completed Execution Period Pre- execution Execution Prices Market Impact Permanent Impact Temporary Impact Measuring Market Impact: A Theoretical Example Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz Average Market Impact = 11 bps Temporary Impact = 2.5 bps Permanent Impact = 8.5 bps
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  • Trade Execution Data, 1998 2011. Realized Trading Costs 13 Trading costs relative to theoretical prices = efficacy of strategy Trading costs relative to VWAP = costs vs. best price available
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  • Interpretation How generalizable are the results? How exogenous are trading costs to the portfolios being traded by our manager? Trading costs we estimate are fairly independent from the portfolios being traded. 1.Only examine live trades of longer-term strategies, where portfolio formation process is separate from the trading process executing it. 2.Set of intended trades is primarily created from specific client mandates that often adhere to a benchmark subject to a tracking error constraint of a few percent. 3.Manager uses proprietary trading algorithms, but algorithms cannot make any buy or sell decisions. Only determine duration of trade (1-3 days). 4.Exclude all high frequency trading. We also examine only the first trade from new inflows. 14 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Exogenous TradesInitial Trades from Inflows 15 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Regression Results: Tcost Model This table shows results from pooled regressions. The left-hand side is a trades Market Impact (MI), in basis points. The explanatory variables include the contemporaneous market returns, firm size, volatility and trade size (all measured at order submission). 16 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz * * Use regression coefficients to compute predicted trading costs for all stocks 1.Fix trade size (as a % of DTV) equal to the median size in our execution data 2.Later, when running optimizations well allow for variable (endogenous) trade size
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  • Market Impact by Fraction of Trading Volume, 1998 2011 This figure shows average Market Impact (MI). We sort all trades in our datasets into 30 bins based on their fraction of daily volume and compute average and median market impact for each bucket. 17 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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  • Returns Results Trade Execution Sample U.S. Actual dollar traded in each portfolio (past 6 month) to estimate trading costs at each rebalance Trading costs and implied fund size are based on actual traded sizes 18 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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