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Trading Costs of Asset Pricing Anomalies

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1 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 information’s 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.

2 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

3 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 Tradeoff between expected tcost and tracking error. How does this vary across anomalies? (what a real arbitrageur would do) Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

4 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 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

5 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) Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

6 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 firm’s 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 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

7 Trade Execution Database
This picture shows our trade execution database. Last year’s data, the rest is in some nuclear-disaster-proof bunkers around the world Frazzini almost froze to death to take this photograph Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

8 Trade Execution Data, 1998 – 2013. Summary Stats
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

9 Summary Stats cont. Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

10 Summary Stats cont. Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

11 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 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

12 Measuring Market Impact: A Theoretical Example
(BPs) Execution Prices Temporary Impact Temporary Impact = 2.5 bps Pre-execution Market Impact Average Market Impact = 11 bps Permanent Impact Permanent Impact = 8.5 bps Time Execution Period Portfolio Formation Order Submission Portfolio Completed Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

13 Trade Execution Data, 1998 – 2011. Realized Trading Costs
Trading costs relative to theoretical prices = efficacy of strategy Trading costs relative to VWAP = costs vs. best price available

14 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. Only examine live trades of longer-term strategies, where portfolio formation process is separate from the trading process executing it. 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. Manager uses proprietary trading algorithms, but algorithms cannot make any buy or sell decisions. Only determine duration of trade (1-3 days). Exclude all high frequency trading. We also examine only the first trade from new inflows. Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

15 Exogenous Trades—Initial Trades from Inflows
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

16 Regression Results: Tcost Model
This table shows results from pooled regressions. The left-hand side is a trade’s 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). * * Use regression coefficients to compute predicted trading costs for all stocks Fix trade size (as a % of DTV) equal to the median size in our execution data Later, when running optimizations we’ll allow for variable (endogenous) trade size Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

17 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. Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

18 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 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

19 Optimized Portfolios So far, have ignored trading costs when building portfolios How can portfolios take into account trading costs to reduce total costs substantially? Can we change the portfolios to reduce trading costs without altering them significantly? Tradeoff between trading costs (market impact) and opportunity cost (tracking error) Construct portfolios that minimize trading costs while being close to the “benchmark” paper portfolios (SMB, HML, UMD, …) *Working on separating tracking error into style drift vs. idiosyncratic error (done) Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

20 Trading Cost vs. Tracking Error Frontier
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

21 Break-Even Sizes after Tcost Optimization
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

22 Conclusions Unique dataset of live trades to approximate the real trading costs of a large institutional trader/arbitrageur Our trading cost estimates are many times smaller (and break even capacities many times larger) than those previously claimed: Size, Val, Mom all survive tcosts at high capacity, but STR does not Fit a model from live traded data to compute expected trading costs based on observable firm and trade characteristics We plan to make the coefficients and the price impact breakpoints available to researchers to be used to evaluate trading costs Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

23 APPENDIX Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

24 Defining Trading Costs
Implementation shortfall (IS) and Market Impact (MI) as defined in Perold (1988) IS = difference between a theoretical or model price and traded price 𝑰𝑺=𝑸 + 𝑷 𝒆𝒙 − 𝑷 𝒕𝒉𝒆𝒐𝒓𝒚 + 𝑸 − 𝑷 𝒕𝒉𝒆𝒐𝒓𝒚 − 𝑷 𝒆𝒙 =𝑴𝑰+𝑷𝒓𝒆𝑻𝒓𝒂𝒅𝒆 MI = difference between arrival price and traded price 𝑴𝑰= 𝑸 + 𝑷 𝒆𝒙 − 𝑷 𝒔𝒕𝒂𝒓𝒕 + 𝑸 − 𝑷 𝒔𝒕𝒂𝒓𝒕 − 𝑷 𝒆𝒙 Our cost estimates measure how much of the theoretical returns to a strategy can actually be achieved in practice Other estimates: compare actual traded prices over the trading period to other possible traded prices that existed during the same period (e.g., VWAP). Tells us more about the effectiveness of a trader or trading strategy relative to other traders in the market at the same time, not the efficacy of an investment strategy Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

25 Realized Trading Costs by Trade Type
This table shows average Market Impact (MI).We compute average, median and dollar weighted average cost of all trades during the month and report time-series averages of the cross sectional estimates. Market Impact is in basis points. Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

26 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 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz

27 Returns Results – Optimized Portfolios, U.S.
* * * Break-even size (USD billion) 354.27 189.56 65.92 9.45 129.47 54.36 100 1,584.36 486.44 94.44 13.17 248.51 64.80 Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz


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