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Momentum in Investment StrategiesMomemtum Basics

US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes

Momentum Crashes

Kent Daniel† & Tobias Moskowitz‡

†Columbia Business School & NBER‡Chicago – Booth & NBER

Society of Quantitative AnalystsFall Seminar

October 16, 2014

Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014

IntroductionProperties of Cross-Sectional Momentum

Momentum

Momentum is employed by most quantitative managers(Swaminathan 2010)

Grinblatt and Titman (1989, 1993), Carhart (1997), andsubsequent empirical work suggests that mutual funds alsoemploy momentum.

Historically, momentum strategies deliver high premia.Over the post WWII period, through 2008, the long-shortUS equity momentum strategy we’ll examine had anaverage return of 16.5%/year, a market beta of -0.125, andan annualized Sharpe-ratio of 0.82.

Evidence of Momentum

Momentum is pervasive:US Equities: Jegadeesh and Titman (1993, 2001).Developed Equities: Rouwenhorst (1998)Emerging Equities: Rouwenhorst (1999)Victorian Era Equities: Chabot, Remy, and Jagannathan(2009) – 1866-1907 British data.Industries & Firm Specific (Equity): Moskowitz andGrinblatt (1999), Grundy and Martin (2001).Country Equity Indices: Asness, Liew, and Stevens (1997)Currencies: Okunev and White (2003)Commodities: Erb and Harvey (2006)Futures: Asness, Moskowitz, and Pedersen (2013),Moskowitz, Ooi, and Pedersen (2012).

Momentum Drawdowns

Momentum strategies perform well, but exhibit significantnegative skewness:

e.g., in March-May 2009, equity and other momentumstrategies suffered severe losses.

The April 2009 return was the worst since August, 1932.Monthly momentum return skewness is -6.3.

For comparison, HML is +1.8, and the market is -0.58

The maximum monthly momentum return in our sample is26.1%.

The 5 worst are -79%, -60%, -46%, -44%, and -42%.

Much like “carry-trade” strategies in currencies, momentumstrategies are sometimes perceived like selling out-of-themoney put options (see, e.g., Brunnermeier, Nagel, andPedersen (2008))

Momentum Drawdowns

The 5 worst are -79%, -60%, -46%, -44%, and -42%.

Momentum Drawdowns

The 5 worst are -79%, -60%, -46%, -44%, and -42%.

Literature ReviewPortfolio ConstructionCrash Characterization

Literature Review

Behavioral theories of momentum:Barberis, Shleifer, and Vishny (1998) Daniel, Hirshleifer,and Subrahmanyam (1998), Hong and Stein (1999),George and Hwang (2004), Grinblatt and Han (2005)

Time dependence in momentum risk:Time dependence in momentum returns:“Optionality” in past return sorted portfolios:

Literature Review

Behavioral theories of momentum:Time dependence in momentum risk:

Kothari and Shanken (1992) show that the market beta ofpast-return based strategies should be, and are highlydependent on the lagged market return.Grundy and Martin (2001) show this for momentumstrategies, and further argue that a momentum portfoliowhich hedges out market & size risk exhibits consistentlygood performance. (using ex-post βs).

Time dependence in momentum returns:“Optionality” in past return sorted portfolios:

Literature Review

Behavioral theories of momentum:Time dependence in momentum risk:Time dependence in momentum returns:

Cooper, Gutierrez, and Hameed (2004) demonstrate thestate dependence of momentum strategy returnsThey don’t control for conditional variations in risk.

“Optionality” in past return sorted portfolios:

Literature Review

Behavioral theories of momentum:Time dependence in momentum risk:Time dependence in momentum returns:“Optionality” in past return sorted portfolios:

Rouwenhorst (1998), Chan (1988), DeBondt and Thaler(1987), Boguth, Carlson, Fisher, and Simutin (2010).We’ll show the state dependence of this optionality, and thepresence in non-equity strategies.

Momentum: Portfolio Construction

At the end of each month, we form 10 value-weightedmomenutum portfolios on the basis of prior (12,2) return:t-12 t-2 t

Ranking PeriodHoldingPeriod

(11 months) (1 mo.)

April '09FebruaryApr. '08 (March)

Over the one-month holding period, we will evaluate thereturn of the top and bottom (“winner” and “loser”) deciles.We also consider the long-short portfolio that invests $1 inthe winner portfolio, and shorts $1 worth of the loserportfolio (=WML)

(11 months) (1 mo.)

At the end of each month, we re-form the portfolios based onthe updated ranking-period return:

t-12 t-2 t

(11 months) (1 mo.)

t-12 t-2 t

(11 months) (1 mo.)

May '09MarchMay. '08 (April)

While the portfolio are reblanced at the end of each month,we generate daily returns for each of the ten portfolios.

This is necessary to accurately estimate the conditional riskof the portfolios.

For a firm to be included in the portfolio, we require that:The firm remain be listed on the NYSE, AMEX or NASDAQ.The shares be common shares only (share-code 10 or 11)The firm have valid prices and share data during theformation period (for value weighting).

Long-Only Investment Strategy Returns

1949 1959 1969 1979 1989 1999date

$15.62

Cumulative Gains from Investments, 1947:01-2006:12

risk-free

1949 1959 1969 1979 1989 1999date

$15.62

$754.11

risk-freemarket

1949 1959 1969 1979 1989 1999date

$15.62

$754.11

risk-freemarketpast losers

1949 1959 1969 1979 1989 1999date

$15.62

$754.11

$53829.84

risk-freemarketpast loserspast winners

2009-13 Momentum Performance

Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 Feb 2012 Aug 2012 Feb 2013date

Cumulative Gains from Investments, Mar 09, 2009 - Mar 28, 2013

Momentum in the Great Depression

1933 1934 1935 1936 1937 1938 1939date

Cumulative Gains from Investments, Jun 01, 1932 - Dec 30, 1939

Cumulative Momentum Returns

1929 1939 1949 1959 1969 1979 1989 1999 2009date

Cumulative Momentum Strategy Returns, Jan 1927-Mar 2013

15 Worst Monthly Momentum ReturnsRANK MONTH MOMt MKT-2Y MKTt

1 1932-08 -74.36 -69.39 36.492 1932-07 -60.98 -76.22 33.483 2001-01 -49.19 -9.95 2.584 2009-04 -45.52 -46.33 10.185 1939-09 -43.83 -21.34 16.646 1933-04 -43.14 -60.33 37.677 2009-03 -42.28 -50.61 8.938 2002-11 -37.04 -43.85 5.849 1938-06 -33.36 -28.29 23.69

10 2009-08 -30.54 -32.15 3.3111 1931-06 -29.72 -53.25 13.6112 1933-05 -28.90 -39.39 21.2613 2001-11 -25.31 -34.50 7.3714 2001-10 -24.98 -32.27 2.2515 1974-01 -24.04 -23.71 -0.80

MKT-2Y is the lagged 2-year market returnMKTt is the contemporaneous (1-month) market return.

Bear Market Momentum Performance

The preceding table shows that the momentum strategysuffers its worst performance at “turning points,” followinglarge market declines:

In June 1932, the market “bottomed.”in July-August 1932, the market rose by 82%.Over these 2 months, losers outperform winners by 206%.losers gain 236%, winners gain 30%.

On March 9, 2009 the US equity market bottomed.In March-May 2009, the market was up by 29%.losers outperform winners by 149%.losers gain 156%, winners gain 6.5%.

Market BetaWML “Option”Dynamic Strategy Performance

Momentum Beta

As of March 2009, many the firms in the Loser portfoliohad fallen by 90% or more.

These were firms like Citigroup, Bank of America, Ford,GM, and International Paper (which was levered)In contrast, the Winner portfolio was composed ofdefensive or counter-cyclical firms like Autozone.

The loser firms, in particular, were often extremely levered,and at risk of bankruptcy.

Their common stock was effectively an out-of-the-moneyoption on the firm value (à là (Merton 1974))

This suggests that there were potentially large differencesin the market betas of the winner and loser portfolios

Momentum Beta

Market Beta and Momentum - 1927-1940

19281929

19301931

19321933

19341935

19361937

19381939

Rolling 126-day betas, 1927:06 - 1940:02

Market Beta and Momentum - 1999-2013

20002001

20022003

20042005

20062007

20082009

20102011

20122013

Rolling 126-day betas, 1999:01 - 2013:03

Estimating BetaThere is a strong Up- and Down-β differential in bear markets:

RWML,t = [α0 + αBIB] +[β0 + βBIB + βB,U(IB · IU)

m,t + εt

Estimated Coefficients(t-statistics in parentheses)

Coeff. Variable (1) (2) (3) (4)α0 1 0.019 0.020 0.020 0.020

(7.3) (7.7) (7.8) (8.4)αB IB -0.021 0.005

(-3.5) (0.6)β0 Re

m,t -0.577 -0.032 -0.032 -0.034(-12.5) (-0.5) (-0.5) (-0.6)

βB IB ·Rem,t -1.136 -0.668 -0.710

(-13.4) (-5.0) (-6.2)βB,U IB ·IU ·Re

m,t -0.810 -0.734(-4.5) (-5.7)

R2_adj 0.130 0.271 0.284 0.285

IB = 1 when the past 2-year market return is non-positive – there are 186 Bear-market months.

IU = 1 when Rm,t > 0. This is not an ex-ante variable.

m,t + εt

Coeff. Variable (1) (2) (3) (4)α0 1 0.019 0.020 0.020 0.020

(7.3) (7.7) (7.8) (8.4)αB IB -0.021 0.005

(-3.5) (0.6)β0 Re

m,t -0.577 -0.032 -0.032 -0.034(-12.5) (-0.5) (-0.5) (-0.6)

βB IB ·Rem,t -1.136 -0.668 -0.710

(-13.4) (-5.0) (-6.2)βB,U IB ·IU ·Re

m,t -0.810 -0.734(-4.5) (-5.7)

R2_adj 0.130 0.271 0.284 0.285

m,t + εt

Coeff. Variable (1) (2) (3) (4)α0 1 0.019 0.020 0.020 0.020

(7.3) (7.7) (7.8) (8.4)αB IB -0.021 0.005

(-3.5) (0.6)β0 Re

m,t -0.577 -0.032 -0.032 -0.034(-12.5) (-0.5) (-0.5) (-0.6)

βB IB ·Rem,t -1.136 -0.668 -0.710

(-13.4) (-5.0) (-6.2)βB,U IB ·IU ·Re

m,t -0.810 -0.734(-4.5) (-5.7)

R2_adj 0.130 0.271 0.284 0.285

m,t + εt

Coeff. Variable (1) (2) (3) (4)α0 1 0.019 0.020 0.020 0.020

(7.3) (7.7) (7.8) (8.4)αB IB -0.021 0.005

(-3.5) (0.6)β0 Re

m,t -0.577 -0.032 -0.032 -0.034(-12.5) (-0.5) (-0.5) (-0.6)

βB IB ·Rem,t -1.136 -0.668 -0.710

(-13.4) (-5.0) (-6.2)βB,U IB ·IU ·Re

m,t -0.810 -0.734(-4.5) (-5.7)

R2_adj 0.130 0.271 0.284 0.285

Where is the Option?

This optionality is mostly in the loser portfolio:For the past-loser portfolio, βB,U = 0.60.For the past-winner portfolio, βB,U = −0.21.

The optionality is not present in BulL markets:For past-loser portfolio, βL,U = 0.02.

WML “Option”

0 +10%

+10%-10%

MarketReturn

WinnerReturn

LoserReturn

WMLReturn

MarketReturn

Forecasting Crashes

We have seen that the payoff associated with the WMLportfolio has short-option-like characteristics.It seems likely this this option will be more costly whenmarket variance is higher

This would also be consistent with a behavioral motivationfor our forecasting variable.

Based on this we investigate whether other variablesassociated with perceived risk affect the payoff tomomentum strategies.

Specifically we look at market volatility – related to the VIX.

Forecasting Crashes

Forecasting Momentum Returns

rWML,t = γ0 + γB · IB,t−1 + γσ2m· σ2

m,t−1 + γint · IB,t−1 · σ2m,t−1 + εt

(1) (2) (3) (4) (5)γ0 0.020 0.036 0.033 0.021 0.022

(6.6) (6.6) (6.0) (7.1) (3.3)γB -0.027 -0.014 0.025

(-3.8) (-1.8) (1.5)γσ2

m-0.009 -0.007 -0.001(-4.4) (-2.9) (-0.5)

γint -0.009 -0.013(-5.2) (-2.8)

Exposure to variance riskRHS Vars. (1) (2) (3)α 31.48 29.94 30.39

(4.7) (4.8) (4.9)IBσ2 -58.62 -49.26 -55.01

(-5.2) (-4.8) (-5.3)r em 0.109 0.105

(4.5) (3.3)IBσ2 · r e

m,t -0.518 -0.629(-28.4) (-24.7)

rvs,t -0.008(-0.2)

IBσ2 · rvs,t -0.101(-4.8)

Daily Regressions, January 2, 1990 to March 28, 2013.rvs,t is the return to a variance-swap on the S&P 500.α and IBσ2 coeffficients are ×252×100 (i.e., in %/year)

Exposure to variance riskRHS Vars. (1) (2) (3)α 31.48 29.94 30.39

(4.7) (4.8) (4.9)IBσ2 -58.62 -49.26 -55.01

(-5.2) (-4.8) (-5.3)r em 0.109 0.105

(4.5) (3.3)IBσ2 · r e

m,t -0.518 -0.629(-28.4) (-24.7)

rvs,t -0.008(-0.2)

IBσ2 · rvs,t -0.101(-4.8)

Daily Regressions, January 2, 1990 to March 28, 2013.rvs,t is the return to a variance-swap on the S&P 500.α and IBσ2 coeffficients are ×252×100 (i.e., in %/year)

Dynamic Strategy ReturnsWe next evalulate the performance of a strategy whichdynamically adjusts the weight on the basic wml strategybased on the forecast return and volatility of the wmlstrategy.

Et−1[rwml,t ] is forecast using the interaction on thepreceding slide (regression 4)σ2

wml,t−1 is forecast using a GARCH-like procedure appliedto daily wml returns:

The weight on wml at at the start of period t is:

wwml,t−1 = κ ·Et−1[rwml,t ]

σ2wml,t−1

Each strategy is scaled to give an unconditional volatility of19%

equal to σmkt over the full sample.

σ2wml,t−1

WML & Dynamic Strategy Returns

1929 1939 1949 1959 1969 1979 1989 1999 2009date

Cumulative Normalized Strategy Returns (19% ann. vol.) -- 1927:07-2013:03

wmldynamicc_vol

WML & Dynamic Strategy Returns - Subsamples

1929 1934 1939 1944 19490.2

1.21926-1949

wmldynamic

1954 1959 1964 1969 19740.5

3.51950-1974

wmldynamic

1979 1984 1989 1994 19990.5

4.01975-1999

wmldynamic

2001 2003 2005 2007 2009 2011 2013

2000-2013

wmldynamic

Dynamic Strategy Returns

Strategy S.R.Subperiod WML const. σ dynamic1927:01-2013:03 0.60 1.01 1.181927:01-1949:12 0.27 0.63 0.681950:01-1974:12 1.31 1.51 1.671975:01-1999:12 1.48 1.69 1.852000:01-2013:03 0.27 0.59 0.96

The dynamic strategy almost doubles the Sharpe Ratio of the staticmomentum strategy.

Moreover, the improvement is strong in each subperiod.A constant volatility strategy provides a substantial improvement overstandard momentum.

See Barroso and Santa-Clara (2012).However, exploiting the strong forecastability of the meangets you still superior performance.

Dynamic Strategy Returns

Strategy S.R.Subperiod WML const. σ dynamic1927:01-2013:03 0.60 1.01 1.181927:01-1949:12 0.27 0.63 0.681950:01-1974:12 1.31 1.51 1.671975:01-1999:12 1.48 1.69 1.852000:01-2013:03 0.27 0.59 0.96

The dynamic strategy almost doubles the Sharpe Ratio of the staticmomentum strategy.

Moreover, the improvement is strong in each subperiod.A constant volatility strategy provides a substantial improvement overstandard momentum.

See Barroso and Santa-Clara (2012).However, exploiting the strong forecastability of the meangets you still superior performance.

Dynamic Strategy Returns – Skewness

Strategy S.R./(skewness)Subperiod WML const. σ dynamic1927:01-2013:03 0.60 1.01 1.18

(-4.70) (-0.76) (0.09)1927:01-1949:12 0.27 0.63 0.68

(-3.38) (-1.25) (-0.99)1950:01-1974:12 1.31 1.51 1.67

(-1.16) (-0.54) (-0.05)1975:01-1999:12 1.48 1.69 1.85

(-0.78) (-0.41) (0.18)2000:01-2013:03 0.27 0.59 0.96

(-1.50) (-0.68) (0.14)

The dynamic strategy also exhibits considerably less negativeskewness.

International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work

Momentum in Other MarketsThe remarkably strong results for predictability in US equitymarkets is consistent across the four quarter-centurysubsamples.To further assesss the robustness of the phenonmena wedocument, we also investigate whether the predictabilityand optionality patterns are also present in other marketsWe examine 3 other equity markets, and 4 other assetclasses.

Data is similar to that in Asness, Moskowitz, and Pedersen(2013).

Our momentum measure is 12-2 in each marketmomentum portfolio is long top third, short bottom third.

We use a market return that corresponds to the assetuniverse in which the momentum strategy is constructed.

Portfolios are VW for equities, EW for other asset classes.

International EquitiesOther Asset Classes

CommoditiesCurrenciesBondsEquities

International EquitiesUS, UK, Continental Europe, and Japan

In each market, universe is largest market capitalizationfirms, such that we include 90% of the total market cap.comprises 15-20% of names in each market.

Other Asset ClassesCommoditiesCurrenciesBondsEquities

Commodities27 commodities from 8 exchanges.Oil and Gas, Metals, Agricultural.

CurrenciesBondsEquities

CommoditiesCurrencies

9 Currencies.Australia, Canada, Germany (spliced with the Euro), Japan,New Zealand, Norway, Sweden, Switzerland, and U.K.

BondsEquities

CommoditiesCurrenciesBonds

10 Government Bonds.Australia, Canada, Denmark, Germany, Japan, Norway,Sweden, Switzerland, U.K., and U.S.

Equities

18 Equity IndicesAustralia, Austria, Belgium, Canada, Denmark, France,Germany, Hong Kong, Italy, Japan, Netherlands, Norway,Portugal, Spain, Sweden, Switzerland, U.K., and U.S.

International Equity Market Momentum

Past Market Returns and Market Variance

Rmomt = [α0 + αBIB + αV σ

2m] + [β0 + βBIB + βV σ

em,t + εt .

Europe Japan UK US globalα0 0.010 0.005 0.009 0.008 0.007

(4.2) (1.4) (3.5) (3.2) (4.7)αB 0.003 0.002 -0.001 0.007 0.002

(0.5) (0.4) (-0.1) (1.2) (0.4)αV -0.143 -0.150 -0.141 -0.197 -0.116

(-2.7) (-2.3) (-2.3) (-3.3) (-3.1)β0 0.109 0.242 0.069 0.216 0.052

(2.4) (4.4) (1.6) (3.6) (1.4)βB -0.372 -0.539 -0.092 -0.523 -0.201

(-4.3) (-6.8) (-1.2) (-5.0) (-2.8)βV -1.787 0.449 -2.390 -1.836 -1.011

(-3.0) (0.5) (-2.9) (-2.1) (-1.9)

2m] + [β0 + βBIB + βV σ

em,t + εt .

Europe Japan UK US globalα0 0.010 0.005 0.009 0.008 0.007

(4.2) (1.4) (3.5) (3.2) (4.7)αB 0.003 0.002 -0.001 0.007 0.002

(0.5) (0.4) (-0.1) (1.2) (0.4)αV -0.143 -0.150 -0.141 -0.197 -0.116

(-2.7) (-2.3) (-2.3) (-3.3) (-3.1)β0 0.109 0.242 0.069 0.216 0.052

(2.4) (4.4) (1.6) (3.6) (1.4)βB -0.372 -0.539 -0.092 -0.523 -0.201

(-4.3) (-6.8) (-1.2) (-5.0) (-2.8)βV -1.787 0.449 -2.390 -1.836 -1.011

(-3.0) (0.5) (-2.9) (-2.1) (-1.9)

Optionality in Bear Markets

Rmomt = [α0 + αBIB] +

[β0 + βBIB + βB,U(IB · IU)

m,t + εt

Europe Japan UK US globalα0 0.007 -0.001 0.006 0.003 0.005

(3.0) (-0.3) (2.6) (1.2) (3.2)αB 0.012 0.013 0.004 0.005 0.005

(1.8) (1.8) (0.6) (0.5) (1.0)β0 0.075 0.248 0.026 0.167 0.029

(1.7) (4.7) (0.6) (2.9) (0.8)βB -0.305 -0.284 0.016 -0.556 -0.092

(-2.6) (-2.0) (0.1) (-3.2) (-0.9)βB,U -0.443 -0.392 -0.329 -0.085 -0.338

(-2.5) (-2.1) (-2.2) (-0.3) (-2.2)

Other Asset Class Momentum

2m] + [β0 + βBIB + βV σ

em,t + εt

Bonds Commod’s Currencies Equities all all+stockα0 0.001 0.013 0.006 0.008 0.004 0.005

(1.2) (3.2) (2.8) (3.8) (4.4) (5.5)αB -0.000 -0.007 -0.009 -0.001 -0.001 0.000

(-0.0) (-1.0) (-3.0) (-0.2) (-0.4) (0.0)αV -0.029 -0.059 -0.013 -0.020 -0.025 -0.049

(-1.4) (-0.7) (-0.4) (-0.5) (-1.2) (-2.3)β0 0.290 0.250 0.267 0.300 0.188 0.109

(3.7) (2.7) (2.9) (6.2) (2.7) (2.3)βB -0.448 -0.718 -0.987 -0.585 -0.360 -0.238

(-2.9) (-4.1) (-7.3) (-7.0) (-2.6) (-2.4)βV -1.145 0.876 0.173 -0.957 -1.558 -1.363

(-0.8) (0.5) (0.2) (-1.4) (-1.5) (-1.9)

2m] + [β0 + βBIB + βV σ

em,t + εt

Bonds Commod’s Currencies Equities all all+stockα0 0.001 0.013 0.006 0.008 0.004 0.005

(1.2) (3.2) (2.8) (3.8) (4.4) (5.5)αB -0.000 -0.007 -0.009 -0.001 -0.001 0.000

(-0.0) (-1.0) (-3.0) (-0.2) (-0.4) (0.0)αV -0.029 -0.059 -0.013 -0.020 -0.025 -0.049

(-1.4) (-0.7) (-0.4) (-0.5) (-1.2) (-2.3)β0 0.290 0.250 0.267 0.300 0.188 0.109

(3.7) (2.7) (2.9) (6.2) (2.7) (2.3)βB -0.448 -0.718 -0.987 -0.585 -0.360 -0.238

(-2.9) (-4.1) (-7.3) (-7.0) (-2.6) (-2.4)βV -1.145 0.876 0.173 -0.957 -1.558 -1.363

(-0.8) (0.5) (0.2) (-1.4) (-1.5) (-1.9)

Optionality in Bear Markets

Rmomt = [α0 + αBIB] +

[β0 + βBIB + βB,U(IB · IU)

m,t + εt

Bonds Commod’s Currencies Equities all all+stockα0 -0.002 0.009 0.003 0.005 0.002 0.003

(-1.5) (2.4) (1.7) (2.4) (2.3) (3.4)αB 0.005 0.017 0.008 0.010 0.008 0.007

(1.5) (1.8) (2.0) (2.1) (2.7) (2.3)β0 0.287 0.288 0.302 0.283 0.183 0.094

(4.5) (3.7) (3.4) (6.1) (2.8) (2.1)βB -0.346 0.040 -0.498 -0.474 0.260 -0.024

(-0.9) (0.1) (-1.8) (-4.2) (0.8) (-0.2)βB,U -0.211 -1.327 -0.889 -0.338 -1.138 -0.692

(-0.4) (-2.6) (-2.4) (-1.9) (-2.7) (-3.2)

Dynamic Strategy Performance: Equity Strategies

Annualized Strategy SR (skewness) by Region

EU JP UK US GEstart 06/90 06/90 06/90 07/72 07/72end 05/13 05/13 05/13 05/13 05/13

Static WML 0.462 0.067 0.465 0.283 0.513(-0.34) (0.02) (-0.62) (-0.04) (-0.34)

Const. σ 0.886 0.160 0.751 0.519 0.732(0.55) (-0.13) (-0.02) (-0.09) (0.13)

Dynamic 1.130 0.416 0.891 0.646 0.752(0.97) (1.41) (0.36) (0.08) (0.33)

Full-dynamic WML 0.956(1.11)