Trading Costs of Asset Pricing Anomalies - PowerPoint Presentation

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Trading Costs of Asset Pricing Anomalies

Andrea FrazziniAQR Capital ManagementRonen IsraelAQR Capital ManagementTobias J. MoskowitzUniversity of Chicago and NBER

Copyright 2012 © 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. Slide2

MotivationCross-section of expected returns typically analyzed gross of transactions costsQuestions regarding market efficiency should be net of transactions costsAre profits within trading cost bounds?Measure of limits to arbitrage?

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?How does the tradeoff between expected returns and trading costs vary across anomalies?Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz2Slide3

ObjectivesMeasure trading costs of an “arbitrageur”Quantify limits to arbitrageUnderstand the cross-section of

net returns on anomalies Model of trading costs for descriptive and prescriptive purposesConstruct optimized portfolios3

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What We DoTake all (longer-term) equity orders and executions from AQR Capital1998 to 2011, $721 billion worth of trades, traded using automated algorithmsData just updated through September 2013 > $1.1 trillion worth of tradesU.S.

(NYSE and NASDAQ) and 18 international markets—*Exclude “high frequency” (intra-day) tradesUse actual trade sizes and prices as well intended trade sizes and prices to calculate Price impact and implementation shortfall (e.g., Perold (1988)), which includes “opportunity cost” of not tradingMore accurate picture of real-world transactions costs and tradeoffsGet vastly different measures than those in the literature [e.g., Chen, Stanzl, and Watanabe (2002), Korajczyk and Sadka (2004), Lesmond, Schill, and Zhou (2003)]Actual costs are 1/10 the size of those estimated in the literature (break-even fund sizes more than an order of magnitude larger)Why? 1) Average trading cost ≠ cost facing an arbitrageur

2)

Design portfolios

that endogenously respond to expected trading costs

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Measuring Trading CostsLiterature 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

)

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Key Differences with the LiteratureBased on our live, realized trading cost data, we find very different resultsActual costs are 1/10 the size of those estimated in the literatureBreak even fund sizes more than an order of magnitude largerWhy?Models used in the literature too

conservativeData represents the average trade (aggregated over all informed, retail, and institutional traders), our costs closer to the marginal traderPortfolios considered do not address tcosts in any way (or in a very limited way)In addition we provideUnique look at intent of the trade (model price), novel estimates for shorting, covering, etc.tcosts internationally (18 markets) on same strategies simultaneouslyAre there simple changes that can be made to a portfolio that increase net returns? What are the tradeoffs?6

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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 decisionsMerely determines duration of a trade (most within 1 day, max is 3 days)

The trades are executed using proprietary, automated trading algorithms designed and built by the “manager” (aka Ronen)Direct market access through electronic exchangesProvide rather than demand liquidity using a systematic approach that sets opportunistic, liquidity-providing limit ordersBreak up total orders into smaller orders and dynamically manage themRandomize size, time, orders, etc. to limit market impactLimit prices are set to buy stocks at bid or below and sell stocks at ask or above generallyWe consider all of the above as part of the “trading cost” of a large arbitrageur7

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Trading Execution DatabaseTrade execution database from AQR Capital ManagementInstitutional investor, around 90.2 billion USD in assets (November 2013)Data compiled by the execution desk and covers all trades executed algorithmically in any of the firm’s funds since

inception (excluding HFTs)Information on orders, execution prices and quantities, and intended prices and quantitiesAugust 1998 to December 2011 (being updated through 2013)Common stocks only: restrict to cash equity and equity swaps19 Developed markets (drop emerging markets trades) Drop high frequency/statistical arbitrage tradesResult: 9,128 global stocks , 0.72 trillion USD worth of trades (updated to 1.1 trillion USD)Price, return and volume dataUnion of the CRSP tapes and the XpressFeed Global databaseAll available common stocks between July 1926 and December 20118

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Trade Execution DatabaseThis picture shows our trade execution database.This is just for the last 2 years, the rest is in some nuclear-disaster-proof bunkers around the worldFrazzini almost froze to death to take this photograph

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Trade Execution Data, 1998 – 2011. Summary Stats10

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Updated Summary Stats through 201311

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Defining Trading CostsImplementation shortfall (IS) and Market Impact (MI) as defined in Perold (1988)IS = difference between a theoretical or

model price and traded price MI = difference between arrival price and traded price

Our

cost estimates measure how much of the theoretical returns to a strategy can actually be achieved in

practice

O

ther 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

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13

Market Impact(BPs)Time

Portfolio Formation

Order Submission

Portfolio

Completed

Execution

Period

Pre-execution

Execution

Prices

Market Impact

Permanent

Impact

Temporary

Impact

Measuring

M

arket Impact: A

Theoretical

Example

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

Average

Market Impact = 9 bps

Temporary

Impact =

2.5 bps

Permanent

Impact =

6.5 bps

Perold

(

1988):

IS = difference between a theoretical or model price and traded price

MI

= difference between arrival price and traded

price, where IS = MI + pre-trade

Our

cost estimates measure how much of the theoretical returns to a strategy can actually be achieved in practice

 Slide14

Trade Execution Data, 1998 – 2011. Realized Trading CostsThis figure shows average Market Impact (MI). Each calendar month, we compute the average cost of all trade baskets executed during the month. This table reports time-series averages of the cross sectional estimates.

14Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and MoskowitzSlide15

Trade Execution Data, 1998 – 2011. Realized Trading Costs15

Trading costs relative to theoretical prices = efficacy of strategyTrading costs relative to VWAP = costs vs. best price available Slide16

InterpretationHow 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.

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Exogenous Trades—Initial Trades from Inflows17

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Regression Results: Tcost ModelThis 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).

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

*

*

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 Slide19

Market Impact by Fraction of Trading Volume, 1998 – 2011This 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.

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Portfolios and SamplesOur portfolio construction closely follows Fama and French (1992, 1993, and 1996) and Asness and Frazzini (2012)Consider SMB, HML, UMD, STR, ValMom and Combo of all four Form portfolios within country and compute a global factor by weighting each country’s portfolio by the country’s total (lagged) market

capitalizationTrading Execution sample , 1998-2011All stocks with trading cost data over the prior 6 months at portfolio formation20

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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

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Trade Execution Sample – Global

22Slide23

Optimized PortfoliosSo 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)23

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Returns Results – Optimized Portfolios, U.S. 24

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

*

*

*

Break-even size (USD billion)

0

354.27

189.56

65.92

9.45

129.47

54.36

100

1,584.36

486.44

94.44

13.17

248.51

64.80Slide25

Trading Cost vs. Tracking Error Frontier, U.S.25

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Trading Cost vs. Tracking Error Frontier, U.S.26

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Trading Cost vs. Tracking Error Frontier, U.S.

As we allow even just a bit of tracking error (50bps-100bps), trading costs (net SRs) decrease (increase) substantiallyBased on our model (estimated using actual trading costs) break even sizes are much largerFor example: we estimate ValMom capacity at 250B (1.77% of total US cap of around 14 trillion) with 100 bps of tracking error, which is more than twice capacity at zero tracking error 27

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Trading Cost vs. Tracking Error Frontier, Global28

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Trading Cost vs. Tracking Error Frontier, Global29

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Trading Cost vs. Tracking Error Frontier, Global

ValMom capacity now climbs to 415B globally.30

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Realized Trading Costs updated to 2013.

31Trading costs relative to theoretical prices = efficacy of strategySlide32

ConclusionsUnique dataset of live trades to approximate the real trading costs of a large arbitrageur and apply them to standard asset pricing anomaliesOur trading cost estimates are many times smaller (and break even capacities many times larger) than those

previously claimed:Not average trading costs, but closer to marginal trader’s costConstruct portfolios to significantly reduce costs without incurring much tracking errorSize, Val, Mom all survive tcosts at high capacity, but STR does notFit a model from live traded data to compute expected trading costs based on observable firm and trade characteristicsWe plan to make the coefficients and the price impact breakpoints available to researchers to be used to evaluate trading costs32

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APPENDIX33

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Comparison to Other Tcost MeasuresKorajczyk and Sadka (2004) estimate only $2-5 billion break even size for long-only momentumUsing their methodology and TAQ data updated through 2013 we also get about $3-5 billionUsing our data, we get break even size 10-20

times larger (about $50 billion)Repeat same exercise for Russell 1000 and 2000 (estimate alphas to be about 36 bps and 2.5%) KS break-even fund size = $785 billion for R1000; $127 billion for R2000Our break-even fund size = $4,655 billion for R1000; $1,114 billion for R2000Actual sizes? $4,146 in R1000 and $898 billion in R2000 (using ICI and Sensoy (2009) estimates)Our money manager has also been running long-only momentum indexes in large and small cap U.S. and international stocks since July 2009. The live realized price impact costs in these funds have been 8, 18.2, and 5.9 basis points in large cap, small cap, and international momentum, respectively.

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Portfolios and SamplesOur portfolio construction closely follows Fama and French (1992, 1993, and 1996) and Asness and Frazzini (2012)Consider SMB, HML, UMD, STR, ValMom and Combo of all four Form portfolios within country and compute a global factor by weighting each country’s portfolio by the country’s total (lagged) market capitalization

Trading Execution sample , 1998-2011All stocks with trading cost data over the prior 6 months at portfolio formationAll Stocks sample , 1926 -2011Non missing 1-year volume and market cap at portfolio formationTradable sample, 1980 – 2011Top liquid 2,000 Stocks (U.S. and International separately) ranked on a 50-50 blend rank of average daily volume and market capitalization at portfolio formation35

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Realized Trading Costs by Trade TypeThis 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.

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Trade Execution Data, 2003 – 2011. Realized Trading CostsThis table shows average Market Impact (MI) and Implementation Shortfall (IS). 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 (we

weight each monthly observation by the number of stocks traded during the month). Market Impact and Implementation Shortfall are in basis points and standard errors are reported in the bottom panel. 37

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Relative to VWAPThis table shows average Market Impact (MI) relative to VWAP rather than theoretical prices. 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 (we weight each monthly observation by the number of stocks traded during the month). Market Impact is in basis points and standard errors are reported in the bottom panel.

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Realized Trading Costs by Time period and Trade TypeThis 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.

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Out of Sample Tcost Estimates40

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Trade Execution Data, 1998 – 2011. Realized Trading Costs, InternationallyThis figure shows average Market Impact (MI). Each calendar month, we compute the average cost of all trade baskets executed during the month. This table reports time-series averages of the cross sectional estimates.

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Returns Results - Full Sample, 1926 - 2011. U.S.We forecast trading costs based on our full regression modelFix trade size at the median trade size in our data and use max(actual, forecast) when both available

This gives trading costs for an investor as big as our manager (in % of DTV) over the full sample42

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Returns Results - Full Sample, 1982 - 2011. Global

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