Post on 06-Feb-2017
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
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
IntroductionProperties of Cross-Sectional Momentum
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).
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
IntroductionProperties of Cross-Sectional Momentum
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))
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
IntroductionProperties of Cross-Sectional Momentum
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))
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
IntroductionProperties of Cross-Sectional Momentum
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))
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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:
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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:
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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:
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Momentum: Portfolio Construction
At the end of each month, we re-form the portfolios based onthe updated ranking-period return:
t-12 t-2 t
Ranking PeriodHoldingPeriod
(11 months) (1 mo.)
April '09FebruaryApr. '08 (March)
t-12 t-2 t
Ranking PeriodHoldingPeriod
(11 months) (1 mo.)
May '09MarchMay. '08 (April)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Momentum: Portfolio Construction
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).
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Long-Only Investment Strategy Returns
1949 1959 1969 1979 1989 1999date
10-2
10-1
100
101
102
103
104
105
$ v
alu
e o
f in
vest
ment
$15.62
Cumulative Gains from Investments, 1947:01-2006:12
risk-free
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Long-Only Investment Strategy Returns
1949 1959 1969 1979 1989 1999date
10-2
10-1
100
101
102
103
104
105
$ v
alu
e o
f in
vest
ment
$15.62
$754.11
Cumulative Gains from Investments, 1947:01-2006:12
risk-freemarket
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Long-Only Investment Strategy Returns
1949 1959 1969 1979 1989 1999date
10-2
10-1
100
101
102
103
104
105
$ v
alu
e o
f in
vest
ment
$15.62
$754.11
$0.04
Cumulative Gains from Investments, 1947:01-2006:12
risk-freemarketpast losers
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Long-Only Investment Strategy Returns
1949 1959 1969 1979 1989 1999date
10-2
10-1
100
101
102
103
104
105
$ v
alu
e o
f in
vest
ment
$15.62
$754.11
$0.04
$53829.84
Cumulative Gains from Investments, 1947:01-2006:12
risk-freemarketpast loserspast winners
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
2009-13 Momentum Performance
Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 Feb 2012 Aug 2012 Feb 2013date
1
2
3
4
5
6
($ v
alu
e o
f in
vest
ment)
Cumulative Gains from Investments, Mar 09, 2009 - Mar 28, 2013
risk-freemarketpast loserspast winners
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Momentum in the Great Depression
1933 1934 1935 1936 1937 1938 1939date
1
2
3
4
5
6
($ v
alu
e o
f in
vest
ment)
Cumulative Gains from Investments, Jun 01, 1932 - Dec 30, 1939
risk-freemarketpast loserspast winners
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
Cumulative Momentum Returns
1929 1939 1949 1959 1969 1979 1989 1999 2009date
10-1
100
101
102
103
104
105
106
107
Port
folio
Valu
e
Cumulative Momentum Strategy Returns, Jan 1927-Mar 2013
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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%.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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%.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Literature ReviewPortfolio ConstructionCrash Characterization
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%.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Market Beta and Momentum - 1927-1940
19281929
19301931
19321933
19341935
19361937
19381939
1940
date
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
126 d
ay (
rolli
ng)
beta
Rolling 126-day betas, 1927:06 - 1940:02
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Market Beta and Momentum - 1999-2013
20002001
20022003
20042005
20062007
20082009
20102011
20122013
date
0
1
2
3
4
5
12
6 d
ay (
rolli
ng)
beta
Rolling 126-day betas, 1999:01 - 2013:03
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Estimating BetaThere is a strong Up- and Down-β differential in bear markets:
RWML,t = [α0 + αBIB] +[β0 + βBIB + βB,U(IB · IU)
]Re
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Estimating BetaThere is a strong Up- and Down-β differential in bear markets:
RWML,t = [α0 + αBIB] +[β0 + βBIB + βB,U(IB · IU)
]Re
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Estimating BetaThere is a strong Up- and Down-β differential in bear markets:
RWML,t = [α0 + αBIB] +[β0 + βBIB + βB,U(IB · IU)
]Re
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
Estimating BetaThere is a strong Up- and Down-β differential in bear markets:
RWML,t = [α0 + αBIB] +[β0 + βBIB + βB,U(IB · IU)
]Re
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
WML “Option”
0
0
0 +10%
+10%
+10%-10%
-10%
-10%
MarketReturn
0
0
0
WinnerReturn
LoserReturn
WMLReturn
MarketReturn
MarketReturn
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
WML & Dynamic Strategy Returns
1929 1939 1949 1959 1969 1979 1989 1999 2009date
100
101
102
103
104
105
106
107
108
109
Port
folio
Valu
e (
$)
Cumulative Normalized Strategy Returns (19% ann. vol.) -- 1927:07-2013:03
wmldynamicc_vol
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy Performance
WML & Dynamic Strategy Returns - Subsamples
1929 1934 1939 1944 19490.2
0.0
0.2
0.4
0.6
0.8
1.0
1.21926-1949
wmldynamic
1954 1959 1964 1969 19740.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.51950-1974
wmldynamic
1979 1984 1989 1994 19990.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.01975-1999
wmldynamic
2001 2003 2005 2007 2009 2011 2013
0.0
0.2
0.4
0.6
0.8
2000-2013
wmldynamic
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy 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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy 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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
Market BetaWML “Option”Dynamic Strategy 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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
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.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
CommoditiesCurrenciesBondsEquities
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
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
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
CommoditiesCurrenciesBondsEquities
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
Commodities27 commodities from 8 exchanges.Oil and Gas, Metals, Agricultural.
CurrenciesBondsEquities
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
CommoditiesCurrencies
9 Currencies.Australia, Canada, Germany (spliced with the Euro), Japan,New Zealand, Norway, Sweden, Switzerland, and U.K.
BondsEquities
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
CommoditiesCurrenciesBonds
10 Government Bonds.Australia, Canada, Denmark, Germany, Japan, Norway,Sweden, Switzerland, U.K., and U.S.
Equities
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Data
International EquitiesOther Asset Classes
CommoditiesCurrenciesBondsEquities
18 Equity IndicesAustralia, Austria, Belgium, Canada, Denmark, France,Germany, Hong Kong, Italy, Japan, Netherlands, Norway,Portugal, Spain, Sweden, Switzerland, U.K., and U.S.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
International Equity Market Momentum
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Past Market Returns and Market Variance
Rmomt = [α0 + αBIB + αV σ
2m] + [β0 + βBIB + βV σ
2m]R
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Past Market Returns and Market Variance
Rmomt = [α0 + αBIB + αV σ
2m] + [β0 + βBIB + βV σ
2m]R
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Optionality in Bear Markets
Rmomt = [α0 + αBIB] +
[β0 + βBIB + βB,U(IB · IU)
]Re
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Other Asset Class Momentum
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Past Market Returns and Market Variance
Rmomt = [α0 + αBIB + αV σ
2m] + [β0 + βBIB + βV σ
2m]R
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Past Market Returns and Market Variance
Rmomt = [α0 + αBIB + αV σ
2m] + [β0 + βBIB + βV σ
2m]R
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Optionality in Bear Markets
Rmomt = [α0 + αBIB] +
[β0 + βBIB + βB,U(IB · IU)
]Re
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
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)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Dynamic Strategy Performance in Other AssetClasses
Annualized Strategy SR (skewness) by Asset Class:
FI CM FX EQ GA GAllstart 06/83 02/73 02/80 02/79 02/73 02/73end 05/13 05/13 05/13 05/13 05/13 05/13
Static WML 0.004 0.587 0.296 0.705 0.676 0.754(-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33)
Const. σ WML 0.020 0.686 0.423 0.800 0.791 0.942(-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18)
Dynamic WML 0.066 0.803 0.653 0.843 0.973 1.139(0.06) (0.39) (-0.20) (0.25) (0.11) (0.20)
Full-dynamic WML 1.028 1.223(-0.19) (0.44)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Dynamic Strategy Performance in Other AssetClasses
Annualized Strategy SR (skewness) by Asset Class:
FI CM FX EQ GA GAllstart 06/83 02/73 02/80 02/79 02/73 02/73end 05/13 05/13 05/13 05/13 05/13 05/13
Static WML 0.004 0.587 0.296 0.705 0.676 0.754(-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33)
Const. σ WML 0.020 0.686 0.423 0.800 0.791 0.942(-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18)
Dynamic WML 0.066 0.803 0.653 0.843 0.973 1.139(0.06) (0.39) (-0.20) (0.25) (0.11) (0.20)
Full-dynamic WML 1.028 1.223(-0.19) (0.44)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Dynamic Strategy Performance in Other AssetClasses
Annualized Strategy SR (skewness) by Asset Class:
FI CM FX EQ GA GAllstart 06/83 02/73 02/80 02/79 02/73 02/73end 05/13 05/13 05/13 05/13 05/13 05/13
Static WML 0.004 0.587 0.296 0.705 0.676 0.754(-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33)
Const. σ WML 0.020 0.686 0.423 0.800 0.791 0.942(-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18)
Dynamic WML 0.066 0.803 0.653 0.843 0.973 1.139(0.06) (0.39) (-0.20) (0.25) (0.11) (0.20)
Full-dynamic WML 1.028 1.223(-0.19) (0.44)
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Conclusions & Future Work
1 In “normal” environments, the market appears tounderreact to public information, resulting in consistentprice momentum.
2 However, in “panic” states, the market prices of severe pastlosers embody a very high premium.
When market conditions ameliorate, these losersexperience strong gains, resulting in a momentum crash.
The expected gains from the loser portfolio are related toboth past market losses, and lagged market volatility.
3 Market risk of momentum portfolios varies dramatically, butdoes not appear to explain the variation in the premiumearned by momentum.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Conclusions & Future Work
1 In “normal” environments, the market appears tounderreact to public information, resulting in consistentprice momentum.
2 However, in “panic” states, the market prices of severe pastlosers embody a very high premium.
When market conditions ameliorate, these losersexperience strong gains, resulting in a momentum crash.
The expected gains from the loser portfolio are related toboth past market losses, and lagged market volatility.
3 Market risk of momentum portfolios varies dramatically, butdoes not appear to explain the variation in the premiumearned by momentum.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
Conclusions & Future Work
1 In “normal” environments, the market appears tounderreact to public information, resulting in consistentprice momentum.
2 However, in “panic” states, the market prices of severe pastlosers embody a very high premium.
When market conditions ameliorate, these losersexperience strong gains, resulting in a momentum crash.
The expected gains from the loser portfolio are related toboth past market losses, and lagged market volatility.
3 Market risk of momentum portfolios varies dramatically, butdoes not appear to explain the variation in the premiumearned by momentum.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
References I
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Asness, Clifford S., Toby J. Moskowitz, and Lasse Heje Pedersen, 2013, Value and momentum everywhere, TheJournal of Finance 58, 929–895.
Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment, Journal of FinancialEconomics 49, 307–343.
Barroso, Pedro, and Pedro Santa-Clara, 2012, Managing the risk of momentum, Nova School of Business andEconomics working paper.
Boguth, Oliver, Murray Carlson, Adalai Fisher, and Mikhail Simutin, 2010, Conditional risk and performanceevaluation: Volatility timing, overconditioning, and new estimates of momentum alphas, Journal of FinancialEconomics, forthcoming.
Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen, 2008, Carry trades and currency crashes, NBERMacroeconomics Annual.
Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 57–82.
Chabot, Benjamin, Eric Remy, Ghysels, and Ravi Jagannathan, 2009, Momentum cycles and limits to arbitrage -evidence from victorian england and post-depression us stock markets, Working Paper.
Chan, K.C., 1988, On the contrarian investment strategy, Journal of Business 61, 147–163.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
References II
Cooper, Michael J., Roberto C. Gutierrez, and Allaudeen Hameed, 2004, Market states and momentum, Journal ofFinance 59, 1345–1365.
Daniel, Kent D., David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psychology and security marketunder- and over-reactions, Journal of Finance 53, 1839–1886.
DeBondt, Werner F. M., and Richard H. Thaler, 1987, Further evidence on investor overreaction and stock marketseasonality, Journal of Finance 42, 557–581.
Erb, Claude B., and Campbell R. Harvey, 2006, The strategic and tactical value of commodity futures, FinancialAnalysts Journal 62, 69–97.
George, Thomas J., and Chuan-Yang Hwang, 2004, The 52-week high and momentum investing, The Journal ofFinance 59, 2145–2176.
Grinblatt, Mark, and Bing Han, 2005, Prospect theory, mental accounting and momentum, Journal of FinancialEconomics 78, 311–339.
Grundy, Bruce, and J. Spencer Martin, 2001, Understanding the nature of the risks and the source of the rewards tomomentum investing, Review of Financial Studies 14, 29–78.
Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, momentum trading and overreactionin asset markets, Journal of Finance 54, 2143–2184.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
References III
Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications forstock market efficiency, Journal of Finance 48, 65–91.
, 2001, Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance56, 699–720.
Kothari, S.P., and Jay Shanken, 1992, Stock return variation and expected dividends, Journal of FinancialEconomics 31, 177–210.
Merton, Robert C., 1974, On the pricing of corporate debt: The risk structure of interest rates, The Journal ofFinance 29, 449–470.
Moskowitz, Tobias J., and Mark Grinblatt, 1999, Do industries explain momentum?, The Journal of Finance 54,1249–1290.
Moskowitz, Tobias J., Yoa Hua Ooi, and Lasse H. Pedersen, 2012, Time series momentum, Journal of FinancialEconomics 104, 228–250.
Okunev, John, and Derek White, 2003, Do momentum-based strategies still work in foreign currency markets?,Journal of Financial and Quantitative Analysis 38, 425–447.
Rottenstreich, Yuval, and Chris K. Hsee, 2001, Money, kisses, and electric shocks: On the affective psychology ofrisk, Psychological Science 12, 185–190.
Rouwenhorst, K. Geert, 1998, International momentum strategies, Journal of Finance 53, 267–284.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014
Momentum in Investment StrategiesMomemtum Basics
US Equity Momentum: Risk & ReturnInternational Equities/Other Asset Classes
International Equity MarketsOther Asset Class MomentumDynamic Strategy in Other Asset ClassesConclusions & Future Work
References IV
, 1999, Local return factors and turnover in emerging stock markets, Journal of Finance 54, 1439–1464.
Swaminathan, Bhaskaran, 2010, Qunatitative money management: A practical application of behavioral finance,Working Paper.
Daniel & Moskowitz, Momentum Crashes SQA Fall Seminar · 16·October·2014