Trading Costs of Asset Pricing Anomalies

Transcription

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 AQR educational Capital purposes Management, only. LLC Two Greenwich Plaza, Third Floor Greenwich, CT T: F:

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 2

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 3

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 4

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) 5

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 6

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 7

8 Trade Execution Data, Summary Stats Panel A: Amount Traded (Billion USD) By region By size By portfolio type Year Total U.S. International Large Cap Small Cap Long short Long only 1998* ** Total 1, ,

9 Summary Stats cont. Panel B: Annual time series Mean Median Std Min Max Number of stocks per year 3,256 3,732 1, ,105 Number of countries per year Number of exchanges per year Panel C: Fama MacBeth averages Average trade size (1,000$) ,993 Fraction of average daily volume (%) Trade horizon (days)

10 Summary Stats cont. 10

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 11

12 Measuring Market Impact: A Theoretical Example Market Impact (BPs) 15 Execution Prices Temporary Impact 10 Preexecution Market Impact Temporary Impact = 2.5 bps 5 0 Average Market Impact = 11 bps Permanent Impact Permanent Impact = 8.5 bps Time -5 Click to edit Master title Execution style Portfolio Formation Order Submission Period Portfolio Completed 12

13 Trade Execution Data, Realized Trading Costs Trading costs relative to theoretical prices = efficacy of strategy Trading costs relative to VWAP = costs vs. best price available Panel B All By Region By Size By Portfolio type Recent sample: sample US US Int. Large cap Small cap Long short Long only Nyse- Amex Nasdaq MI mean # # # MI median 7.22 # # # MI vw mean # # # IS mean # # # IS median 9.29 # # # IS vw mean # # # Standard errors MI mean MI median MI vw mean IS mean IS median IS vw mean Full sample: All sample By Region By size By portfolio type US US Large Cap Small Cap Long Nyse- Nasdaq short Amex Long only MI mean 2.68 # # # MI median 2.29 # # # MI vw mean 3.13 # # # IS mean 2.68 # # # IS median 2.29 # # # IS vw-mean 3.13 # # # Standard errors MI mean MI median MI vw mean

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. 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

15 Average market impact (basis points) Exogenous Trades Initial Trades from Inflows All trades Large cap Small cap Inflows (long-only) All other long-only trades Long-only trades, Trade type Only All other Difference t-statistics inflows trades MI mean All trades MI median All trades MI vw mean All trades MI mean Large cap MI median Large cap MI vw mean Large cap MI mean Small cap MI median Small cap MI vw mean Small cap

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). All sample United States International (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Beta*IndexRet*buysell (17.37) (17.38) (17.38) (17.36) (8.43) (8.43) (8.43) (8.43) (24.03) (24.04) (24.04) (24.15) Time trend (Jun 1926 = 1) (2.34) -(1.61) -(1.92) -(1.33) -(0.51) -(0.08) -(0.24) -(0.02) -(5.23) -(4.11) -(4.88) -(3.80) Log of ME (Billion USD) (11.19) -(9.39) -(7.84) -(7.97) -(7.85) -(6.71) -(5.41) -(3.70) -(12.76) -(10.25) -(8.22) -(7.94) Fraction of daily volume (6.87) (3.39) (3.27). (3.28) (1.90) (1.84). (12.63) (4.53) (4.47) Sqrt(Fraction of daily volume) (3.50) (4.14).. (1.90) (2.10).. (5.68) (7.27) Idiosyncratic Volatility (2.06)... (0.70)... (6.02) Vix (4.47)... (2.62)... (3.53) Observations (1,000s) 2,125 2,125 2,125 2,125 1,005 1,005 1,005 1,005 1,120 1,120 1,120 1,120 Adjusted R Country Fixed Effects Yes Yes Yes Yes No No No No Yes Yes Yes Yes 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 we ll allow for variable (endogenous) trade size 16

17 Market impact (basis points) Market Impact by Fraction of Trading Volume, 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 Average market impact (MI) Fitted mean % 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% Average daily volume 17

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 Panel A: U.S. trade execution sample, Panel B: International trade execution sample, SMB HML UMD Combo SMB HML UMD Combo Dollar traded per month (Billion USD) Implied Fund size (Billion USD) Realized cost Break-even cost Realized minus breakeven t statistics (-7.78) (-18.55) (-12.59) (-21.81) (7.50) (-16.52) (-17.64) (-19.95) Return (Gross) (3.01) (1.12) (0.40) (3.17) (0.75) (1.83) (0.92) (2.88) Return (Net) (2.48) (0.80) -(0.14) (2.23) -(0.33) (1.32) (0.41) (1.86) Turnover (monthly) MI (bps) Sharpe ratio (gross) Sharpe ratio (net) Number of months

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, ) min Total Trading Cost (w) w Subject to: Tracking Error Constraint: w B Ω w B 1% $1 long and $1 short: w i = 0 and w i = 2 Trading Constraint: Fraction of daily volume <=5% *Working on separating tracking error into style drift vs. idiosyncratic error (done) 19

20 Sharpe Ratio (net) Sharpe Ratio (net) Total Trading Costs (Annual % ) Total Trading Costs (Annual % ) Trading Cost vs. Tracking Error Frontier Total trading costs, U.S. tradable sample Total trading costs, International tradable sample Ex-Ante Tracking (bps) SMB HML UMD Combo Ex-Ante Tracking (bps) SMB HML UMD Combo 0.7 Sharpe Ratio (net), U.S. tradable sample 0.8 Sharpe Ratio (net), International tradable sample Ex-Ante Tracking (bps) SMB HML UMD Combo Ex-Ante Tracking (bps) SMB HML UMD Combo 20

21 Break-Even Sizes after Tcost Optimization 21

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 22

23 APPENDIX 23

24 Defining Trading Costs 24

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 timeseries averages of the cross sectional estimates. Market Impact is in basis points. Panel B: Market Impact by Trade Type % of sample All sample By Region By Size Dollars Trades U.S. INT Large Cap Small Cap MI (VW-mean) Buy Long Buy Cover Sell Long Sell Short Differences Buy Cover - Buy Long Sell Short - Sell Cover t-statistics Buy Cover - Buy Long Sell Short - Sell Cover

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 Panle A: All stocks, United States, Panel B: All international stocks, SMB HML UMD Combo SMB HML UMD Combo Realized cost Break-even cost Realized minus breakeven t statistics ( ) ( ) ( ) ( ) (26.51) (-96.72) (-84.88) (-94.68) Return (Gross) (2.72) (3.10) (4.79) (9.14) (-0.12) (3.01) (2.98) (5.22) Return (Net) (2.10) (2.64) (3.77) (7.73) (-0.74) (2.49) (2.18) (3.95) Turnover (monthly) MI (bps) Sharpe ratio (gross) Sharpe ratio (net) Observations 1,039 1,039 1,039 1,

27 Returns Results Optimized Portfolios, U.S. Panel B: Tradable Stocks U.S. - Starting NAV 200M SMB HML UMD STR ValMom Combo Starting Nav (Million, USD) Ending Nav (Million, USD) 1, , , , , * * * Non-optimized Excess Return (Gross) (1.31) (1.68) (1.75) (1.98) (3.89) (4.81) Optimized Exess Return (Gross) (1.58) (1.60) (1.70) (1.01) (3.58) (4.30) Optimized Excess Return (Net) (1.42) (1.26) (0.75) -(2.68) (2.45) (1.50) Total trading costs (non-optimized) Total trading costs Turnover (non-optimized) Turnover MI (non-optimized, bps) MI (bps) Sharpe ratio (gross, non-optimized) Sharpe ratio (gross) Sharpe ratio (net) Beta to non-optimized Tracking error to non-optimized (%) Portfolio volatility Obs Break-even size (USD billion) ,