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
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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
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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
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
3
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
4
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
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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 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
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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
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Trade Execution Data, 1998 – 2013. Summary Stats
Panel A: Amount Traded
(Billion USD)
By region
Year
U.S. International
1998*
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013**
Total
Total
By size
By portfolio type
Large Cap
Small Cap
Long short
Long only
2.96
5.29
1.99
1.08
4.21
5.43
10.00
16.16
67.01
129.46
108.29
111.12
117.17
146.50
179.09
141.18
1.29
1.99
0.76
0.55
0.71
2.69
2.95
8.06
34.79
50.70
25.06
18.58
29.15
56.62
121.39
92.87
1.67
3.30
1.23
0.53
3.50
2.75
7.05
8.10
32.22
78.76
83.24
92.54
88.02
89.88
57.70
48.31
2.96
5.29
1.99
1.08
4.21
5.43
9.99
15.75
64.23
125.21
104.27
108.12
113.78
141.93
173.41
136.04
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.41
2.78
4.25
4.02
2.99
3.38
4.58
5.68
5.14
2.96
5.29
1.86
1.00
1.40
4.17
6.38
11.45
44.69
96.65
69.30
85.50
91.94
115.69
141.97
95.21
0.00
0.00
0.13
0.08
2.81
1.26
3.62
4.71
22.31
32.81
38.99
25.62
25.23
30.81
37.13
45.98
1,046.94
448.15
598.79
1,013.69
33.25
775.46
271.48
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
8
Summary Stats cont.
Panel B: Annual time series
Number of stocks per year
Number of countries per year
Number of exchanges per year
Panel C: Fama MacBeth averages
Average trade size (1,000$)
Fraction of average daily volume (%)
Trade horizon (days)
Mean
Median
Std
Min
Max
3,256
17.5
24.6
3,732
19.0
26.0
1,592
4.2
7.1
386
8.0
11.0
5,105
21.0
34.0
658
1.1
2.0
345
0.5
1.1
990
2.0
2.1
53
0.1
0.0
5,993
13.1
8.8
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
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
11
Measuring Market Impact: A Theoretical Example
Market Impact
(BPs)
15
Temporary
Impact
Execution
Prices
10
Preexecution
Market
Impact
Average
Market
Impact =
11 bps
5
0
Temporary
Impact =
2.5 bps
Permanent
Impact
Permanent
Impact =
8.5 bps
Time
Execution
Click to edit Master title
style
Period
-5
Portfolio
Formation
Order
Submission
Portfolio
Completed
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
12
Trade Execution Data, 1998 – 2011. Realized Trading Costs
Panel B
Recent sample:
2003-2013
Trading costs
relative to
theoretical
prices =
efficacy of
strategy
Trading costs
relative to
VWAP = costs
vs. best price
available
All
sample
By Region
US
NyseAmex
US
Nasdaq
Int.
By Size
By Portfolio type
Large cap Small cap
Long short Long only
MI mean
MI median
MI vw mean
11.21 #
7.22 #
16.91 #
8.92
6.09
14.47
11.84
6.12
16.83
12.41 #
8.55 #
17.44 #
10.18
6.62
16.35
21.21 #
15.15 #
25.80 #
9.23
6.12
16.15
15.56
10.08
17.37
IS mean
IS median
IS vw mean
11.88 #
9.29 #
18.18 #
9.22
7.49
16.10
11.73
7.63
19.12
13.54 #
11.15 #
18.58 #
10.92
8.64
17.60
21.17 #
17.19 #
28.35 #
10.39
8.11
17.42
15.14
12.06
18.35
Standard errors
MI mean
MI median
MI vw mean
0.67
0.45
1.00
0.74
0.52
1.21
1.01
0.55
1.67
0.83
0.61
1.03
0.70
0.47
1.00
1.35
1.18
1.88
0.70
0.50
1.17
0.94
0.80
1.02
IS mean
IS median
IS vw mean
0.99
0.70
1.31
1.05
0.79
1.74
1.28
0.81
2.16
1.20
0.96
1.22
1.03
0.73
1.32
1.63
1.59
2.14
1.11
0.77
1.45
1.19
0.99
1.28
Full sample: 1998 2013
All sample
By Region
US
NyseAmex
By size
US
Nasdaq
By portfolio type
Large Cap Small Cap
Long Long only
short
MI mean
MI median
MI vw mean
2.68 #
2.29 #
3.13 #
2.22
2.29
2.15
3.57 #
2.29 #
3.18 #
1.96
1.88
2.74
7.28 #
5.63 #
6.78 #
2.64
2.15
3.16
2.83
2.94
0.95
IS mean
IS median
IS vw-mean
2.68 #
2.29 #
3.13 #
2.22
2.29
2.15
3.57 #
2.29 #
3.18 #
1.96
1.88
2.74
7.28 #
5.63 #
6.78 #
2.64
2.15
3.16
2.83
2.94
0.95
2.71
0.22
1.41
3.74
0.21
9.02
1.40
0.26
1.70
2.98
0.24
1.55
1.04
0.81
0.70
0.93
0.23
1.05
11.10
0.59
17.38
Standard errors
MI mean
MI median
MI vw mean
13
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.
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
14
Exogenous Trades—Initial Trades from Inflows
25.0
Average market impact (basis points)
20.0
15.0
10.0
5.0
0.0
All trades
Large cap
Inflows (long-only)
Long-only trades, 1998 - 2013
Trade type
MI mean
MI median
MI vw mean
MI mean
MI median
MI vw mean
MI mean
MI median
MI vw mean
All trades
All trades
All trades
Large cap
Large cap
Large cap
Small cap
Small cap
Small cap
Small cap
All other long-only trades
Only
inflows
16.95
12.51
19.30
14.76
9.88
11.59
20.94
17.08
26.29
All other Difference
trades
15.54
1.40
10.23
2.28
17.22
2.08
13.83
0.93
9.13
0.75
16.71
-5.12
20.56
0.37
14.59
2.48
24.47
1.82
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
t -statistics
0.20
0.35
0.31
0.11
0.09
-0.66
0.07
0.54
0.25
15
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
(1)
Beta*IndexRet*buysell
Time trend (Jun 1926 = 1)
Log of ME (Billion USD)
* Fraction of daily volume
* Sqrt(Fraction of daily volume)
Idiosyncratic Volatility
(3)
(4)
(5)
(6)
International
(7)
(8)
(9)
(10)
(11)
(12)
0.21
0.21
0.21
0.21
0.21
0.21
0.21
0.21
0.20
0.20
0.20
0.20
(17.37)
(17.38)
(17.38)
(17.36)
(8.43)
(8.43)
(8.43)
(8.43)
(24.03)
(24.04)
(24.04)
(24.15)
-0.08
-0.05
-0.07
-0.05
-0.03
0.00
-0.02
0.00
-0.13
-0.10
-0.12
-0.09
-(2.34)
-(1.61)
-(1.92)
-(1.33)
-(0.51)
-(0.08)
-(0.24)
-(0.02)
-(5.23)
-(4.11)
-(4.88)
-(3.80)
-4.10
-3.40
-2.72
-1.86
-3.62
-3.09
-2.35
-1.83
-4.88
-3.97
-3.35
-1.95
-(11.19)
-(9.39)
-(7.84)
-(7.97)
-(7.85)
-(6.71)
-(5.41)
-(3.70)
-(12.76)
-(10.25)
-(8.22)
-(7.94)
.
.
.
1.54
0.81
0.80
(6.87)
(3.39)
(3.27)
.
.
.
.
.
.
.
Vix
(2)
United States
7.81
(4.14)
.
.
.
.
6.50
(3.50)
0.10
(2.06)
.
.
.
0.27
(4.47)
.
.
.
.
1.45
0.83
0.82
(3.28)
(1.90)
(1.84)
.
.
.
.
.
.
.
7.83
(2.10)
.
.
.
.
6.73
(1.90)
0.05
(0.70)
.
.
.
0.19
(2.62)
.
.
.
.
1.61
0.76
0.72
(12.63)
(4.53)
(4.47)
.
.
.
.
.
.
.
8.14
(7.27)
.
.
.
.
6.61
(5.68)
0.22
(6.02)
.
.
.
0.32
(3.53)
.
Observations (1,000s)
Adjusted R2
2,125
0.071
2,125
0.072
2,125
0.072
2,125
0.072
1,005
0.068
1,005
0.069
1,005
0.069
1,005
0.069
1,120
0.074
1,120
0.075
1,120
0.075
1,120
0.076
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
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
16
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.
40
Market impact (basis points)
35
Average market impact (MI)
Fitted mean
30
25
20
15
10
5
0
0.00%
2.00%
4.00%
6.00%
Average daily volume
8.00%
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
10.00%
12.00%
17
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, 1998 - 2013
Panel B: International trade execution sample, 1998 - 2013
SMB
9.69
18.18
HML
5.97
9.42
UMD
6.18
5.21
Combo
9.69
16.91
SMB
11.80
17.88
HML
7.15
10.09
UMD
8.38
6.85
Combo
12.77
19.74
Realized cost
Break-even cost
Realized minus breakeven
t statistics
1.47
2.95
-1.48
1.35
4.95
-3.61
3.03
8.20
-5.17
1.46
5.39
-3.93
1.70
-0.17
1.87
1.54
5.78
-4.24
2.24
7.65
-5.40
1.24
4.68
-3.44
(-7.78)
(-18.55)
(-12.59)
(-21.81)
(7.50)
(-16.52)
(-17.64)
(-19.95)
Return (Gross)
7.98
4.86
2.26
5.04
1.17
5.59
4.02
3.59
(3.01)
(1.12)
(0.40)
(3.17)
(0.75)
(1.83)
(0.92)
(2.88)
6.52
3.51
-0.77
3.58
-0.53
4.05
1.78
2.35
(2.48)
(0.80)
-(0.14)
(2.23)
-(0.33)
(1.32)
(0.41)
(1.86)
Turnover (monthly)
MI (bps)
0.53
22.94
0.63
17.71
1.19
21.30
0.57
21.22
0.66
21.42
0.71
18.12
1.22
15.27
0.65
16.02
Sharpe ratio (gross)
Sharpe ratio (net)
0.78
0.65
0.29
0.21
0.10
-0.04
0.82
0.58
0.20
-0.09
0.47
0.34
0.24
0.11
0.75
0.48
Number of months
178
178
178
178
178
178
178
178
Dollar traded per month (Billion USD)
Implied Fund size (Billion USD)
Return (Net)
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
18
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:
$1 long and $1 short:
𝒘 − 𝑩 𝛀 𝒘 − 𝑩 ≤ 1%
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)
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
19
Trading Cost vs. Tracking Error Frontier
4.0
5.0
Total trading costs, International tradable sample
Total trading costs, U.S. tradable sample
3.5
4.0
Total Trading Costs (Annual % )
Total Trading Costs (Annual % )
4.5
3.5
3.0
2.5
2.0
1.5
1.0
0.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
50
75
SMB
100
125
Ex-Ante Tracking (bps)
HML
UMD
150
200
0.0
0
50
75
100
125
Ex-Ante Tracking (bps)
200
Combo
SMB
0.7
150
0.8
Sharpe Ratio (net), U.S. tradable sample
HML
UMD
Combo
Sharpe Ratio (net), International tradable sample
0.7
0.6
0.6
0.5
Sharpe Ratio (net)
Sharpe Ratio (net)
0.5
0.4
0.3
0.2
0.4
0.3
0.2
0.1
0.0
0.1
0
50
75
100
125
150
200
-0.1
0.0
0
50
75
SMB
100
Ex-Ante Tracking (bps)
HML
125
150
200
-0.2
Trading
CostsCombo
of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
SMB
UMD
Ex-Ante Tracking (bps)
HML
UMD
Combo
20
Break-Even Sizes after Tcost Optimization
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
21
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
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APPENDIX
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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Defining Trading Costs
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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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
Dollars
Trades
0.35
0.15
0.32
0.18
0.32
0.17
0.34
0.18
By Region
By Size
U.S.
INT
Large Cap Small Cap
12.22
19.53
19.74
23.47
14.05
20.12
12.97
10.31
10.43
18.92
23.36
29.99
10.87
19.20
19.25
23.16
32.72
27.71
28.12
29.64
MI (VW-mean)
Buy Long
Buy Cover
Sell Long
Sell Short
Differences
Buy Cover - Buy Long
Sell Short - Sell Cover
7.31
3.73
6.07
-2.67
8.49
6.62
8.33
3.91
-5.01
1.52
t-statistics
Buy Cover - Buy Long
Sell Short - Sell Cover
1.82
1.10
1.07
-0.50
1.89
1.37
1.95
1.08
-0.26
0.07
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
Panle A: All stocks, United States, 1926 - 2013
SMB
HML
UMD
Combo
Realized cost
Break-even cost
Realized minus breakeven
t statistics
Return (Gross)
Return (Net)
Panel B: All international stocks, 1986 - 2013
SMB
HML
UMD
Combo
0.69
3.03
-2.33
0.75
4.93
-4.18
1.71
8.20
-6.49
0.84
5.39
-4.55
0.90
-0.17
1.07
1.03
5.78
-4.75
2.04
7.65
-5.60
1.08
4.42
-3.34
(-106.00)
(-195.82)
(-140.45)
(-228.11)
(26.51)
(-96.72)
(-84.88)
(-94.68)
3.03
4.93
8.20
5.39
-0.17
5.78
7.65
4.42
(2.72)
(3.10)
(4.79)
(9.14)
(-0.12)
(3.01)
(2.98)
(5.22)
2.33
4.18
6.49
4.55
-1.07
4.75
5.60
3.34
(2.10)
(2.64)
(3.77)
(7.73)
(-0.74)
(2.49)
(2.18)
(3.95)
Turnover (monthly)
MI (bps)
0.38
15.17
0.42
14.79
1.05
13.56
0.51
13.78
0.47
15.87
0.52
16.54
1.11
15.40
0.58
15.56
Sharpe ratio (gross)
Sharpe ratio (net)
0.29
0.23
0.33
0.28
0.51
0.41
0.98
0.83
-0.02
-0.14
0.57
0.47
0.57
0.41
1.00
0.75
1,039
1,039
1,039
1,039
331
331
331
331
Observations
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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Returns Results – Optimized Portfolios, U.S.
Panel B: Tradable Stocks 1980- 2011 - U.S. - Starting NAV 200M
Starting Nav (Million, USD)
Ending Nav (Million, USD)
*
Non-optimized Excess Return (Gross)
*
Optimized Exess Return (Gross)
*
Optimized Excess Return (Net)
SMB
HML
UMD
STR
ValMom
Combo
200.00
1,710.52
200.00
1,854.77
200.00
1,275.90
200.00
152.16
200.00
2,433.47
200.00
1,475.60
1.99
3.96
4.96
4.23
4.46
3.79
(1.31)
(1.68)
(1.75)
(1.98)
(3.89)
(4.81)
2.32
3.56
4.57
2.03
4.56
4.18
(1.58)
(1.60)
(1.70)
(1.01)
(3.58)
(4.30)
2.08
2.81
2.00
-5.27
3.12
1.43
(1.42)
(1.26)
(0.75)
-(2.68)
(2.45)
(1.50)
Total trading costs (non-optimized)
Total trading costs
1.24
0.25
2.88
0.76
5.83
2.56
12.31
7.30
5.54
1.44
8.85
2.75
Turnover (non-optimized)
Turnover
0.27
0.11
0.47
0.25
1.09
0.68
3.01
1.97
0.97
0.41
1.70
0.72
MI (non-optimized, bps)
MI (bps)
38.53
19.39
51.51
25.57
44.34
31.28
34.12
30.84
47.81
28.95
43.46
31.94
Sharpe ratio (gross, non-optimized)
Sharpe ratio (gross)
Sharpe ratio (net)
0.23
0.28
0.25
0.30
0.28
0.22
0.31
0.30
0.13
0.35
0.18
-0.48
0.69
0.64
0.43
0.85
0.76
0.27
Beta to non-optimized
Tracking error to non-optimized (%)
Portfolio volatility
0.95
1.71
8.29
0.94
2.00
12.56
0.94
2.05
15.15
0.90
2.64
11.09
1.07
2.10
7.20
1.13
2.08
5.39
Obs
382
382
382
382
382
382
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
64.80
Break-even size (USD billion)
Trading Costs of Asset Pricing Anomalies - Frazzini, Israel, and Moskowitz
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