Momentum Crashes. Society of Quantitative Analysts SQA Fall Seminar 16 October Kent Daniel & Tobias Moskowitz

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1 Momentum Crashes Kent Daniel & Tobias Moskowitz Columbia Business School & NBER Chicago Booth & NBER Society of Quantitative Analysts Fall Seminar October 16, 2014

2 Momentum Momentum in Investment Strategies Introduction Properties of Cross-Sectional Momentum Momentum is employed by most quantitative managers (Swaminathan 2010) Grinblatt and Titman (1989, 1993), Carhart (1997), and subsequent empirical work suggests that mutual funds also employ momentum. Historically, momentum strategies deliver high premia. Over the post WWII period, through 2008, the long-short US equity momentum strategy we ll examine had an average return of 16.5%/year, a market beta of , and an annualized Sharpe-ratio of 0.82.

3 Evidence of Momentum Introduction Properties of Cross-Sectional 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) British data. Industries & Firm Specific (Equity): Moskowitz and Grinblatt (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).

4 Momentum Drawdowns Introduction Properties of Cross-Sectional Momentum Momentum strategies perform well, but exhibit significant negative skewness: e.g., in March-May 2009, equity and other momentum strategies suffered severe losses. The April 2009 return was the worst since August, Monthly momentum return skewness is For comparison, HML is +1.8, and the market is The maximum monthly momentum return in our sample is 26.1%. The 5 worst are -79%, -60%, -46%, -44%, and -42%. Much like carry-trade strategies in currencies, momentum strategies are sometimes perceived like selling out-of-the money put options (see, e.g., Brunnermeier, Nagel, and Pedersen (2008))

5 Momentum Drawdowns Introduction Properties of Cross-Sectional Momentum Momentum strategies perform well, but exhibit significant negative skewness: e.g., in March-May 2009, equity and other momentum strategies suffered severe losses. The April 2009 return was the worst since August, Monthly momentum return skewness is For comparison, HML is +1.8, and the market is The maximum monthly momentum return in our sample is 26.1%. The 5 worst are -79%, -60%, -46%, -44%, and -42%. Much like carry-trade strategies in currencies, momentum strategies are sometimes perceived like selling out-of-the money put options (see, e.g., Brunnermeier, Nagel, and Pedersen (2008))

6 Momentum Drawdowns Introduction Properties of Cross-Sectional Momentum Momentum strategies perform well, but exhibit significant negative skewness: e.g., in March-May 2009, equity and other momentum strategies suffered severe losses. The April 2009 return was the worst since August, Monthly momentum return skewness is For comparison, HML is +1.8, and the market is The maximum monthly momentum return in our sample is 26.1%. The 5 worst are -79%, -60%, -46%, -44%, and -42%. Much like carry-trade strategies in currencies, momentum strategies are sometimes perceived like selling out-of-the money put options (see, e.g., Brunnermeier, Nagel, and Pedersen (2008))

7 Literature Review Literature Review Portfolio Construction Crash Characterization 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:

8 Literature Review Literature Review Portfolio Construction Crash Characterization Behavioral theories of momentum: Time dependence in momentum risk: Kothari and Shanken (1992) show that the market beta of past-return based strategies should be, and are highly dependent on the lagged market return. Grundy and Martin (2001) show this for momentum strategies, and further argue that a momentum portfolio which hedges out market & size risk exhibits consistently good performance. (using ex-post ˆβs). Time dependence in momentum returns: Optionality in past return sorted portfolios:

9 Literature Review Literature Review Portfolio Construction Crash Characterization Behavioral theories of momentum: Time dependence in momentum risk: Time dependence in momentum returns: Cooper, Gutierrez, and Hameed (2004) demonstrate the state dependence of momentum strategy returns They don t control for conditional variations in risk. Optionality in past return sorted portfolios:

10 Literature Review Literature Review Portfolio Construction Crash Characterization 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 the presence in non-equity strategies.

11 Literature Review Portfolio Construction Crash Characterization Momentum: Portfolio Construction At the end of each month, we form 10 value-weighted momenutum portfolios on the basis of prior (12,2) return: t-12 t-2 t Apr. '08 February (March) April '09 Ranking Period Holding Period (11 months) (1 mo.) Over the one-month holding period, we will evaluate the return of the top and bottom ( winner and loser ) deciles. We also consider the long-short portfolio that invests $1 in the winner portfolio, and shorts $1 worth of the loser portfolio (=WML)

12 Literature Review Portfolio Construction Crash Characterization Momentum: Portfolio Construction At the end of each month, we form 10 value-weighted momenutum portfolios on the basis of prior (12,2) return: t-12 t-2 t Apr. '08 February (March) April '09 Ranking Period Holding Period (11 months) (1 mo.) Over the one-month holding period, we will evaluate the return of the top and bottom ( winner and loser ) deciles. We also consider the long-short portfolio that invests $1 in the winner portfolio, and shorts $1 worth of the loser portfolio (=WML)

13 Literature Review Portfolio Construction Crash Characterization Momentum: Portfolio Construction At the end of each month, we form 10 value-weighted momenutum portfolios on the basis of prior (12,2) return: t-12 t-2 t Apr. '08 February (March) April '09 Ranking Period Holding Period (11 months) (1 mo.) Over the one-month holding period, we will evaluate the return of the top and bottom ( winner and loser ) deciles. We also consider the long-short portfolio that invests $1 in the winner portfolio, and shorts $1 worth of the loser portfolio (=WML)

14 Literature Review Portfolio Construction Crash Characterization Momentum: Portfolio Construction At the end of each month, we re-form the portfolios based on the updated ranking-period return: t-12 t-2 t Apr. '08 February (March) April '09 Ranking Period Holding Period (11 months) (1 mo.) t-12 t-2 t May. '08 March (April) May '09 Ranking Period Holding Period (11 months) (1 mo.)

15 Literature Review Portfolio Construction Crash 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 risk of 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 the formation period (for value weighting).

16 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns risk-free Cumulative Gains from Investments, 1947: : $ value of investment $ date

17 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns risk-free market Cumulative Gains from Investments, 1947: :12 $ value of investment $ $ date

18 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns risk-free market past losers Cumulative Gains from Investments, 1947: :12 $ value of investment $ $ $ date

19 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns risk-free market past losers past winners Cumulative Gains from Investments, 1947: :12 $ $ $ value of investment $ $ date

20 Literature Review Portfolio Construction Crash Characterization Momentum Performance 6 5 risk-free market past losers past winners Cumulative Gains from Investments, Mar 09, Mar 28, 2013 ($ value of investment) Aug 2009 Feb 2010 Aug 2010 Feb 2011 Aug 2011 Feb 2012 Aug 2012 Feb 2013 date

21 Literature Review Portfolio Construction Crash Characterization Momentum in the Great Depression Cumulative Gains from Investments, Jun 01, Dec 30, ($ value of investment) date risk-free market past losers past winners

22 Cumulative Momentum Returns 10 7 Literature Review Portfolio Construction Crash Characterization Cumulative Momentum Strategy Returns, Jan 1927-Mar Portfolio Value date

23 Literature Review Portfolio Construction Crash Characterization 15 Worst Monthly Momentum Returns RANK MONTH MOM t MKT-2Y MKT t MKT-2Y is the lagged 2-year market return MKT t is the contemporaneous (1-month) market return.

24 Literature Review Portfolio Construction Crash Characterization Bear Market Momentum Performance The preceding table shows that the momentum strategy suffers its worst performance at turning points, following large 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%.

25 Literature Review Portfolio Construction Crash Characterization Bear Market Momentum Performance The preceding table shows that the momentum strategy suffers its worst performance at turning points, following large 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%.

26 Literature Review Portfolio Construction Crash Characterization Bear Market Momentum Performance The preceding table shows that the momentum strategy suffers its worst performance at turning points, following large 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%.

27 Momentum Beta Market Beta WML Option Dynamic Strategy Performance As of March 2009, many the firms in the Loser portfolio had 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 of defensive 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-money option on the firm value (à là (Merton 1974)) This suggests that there were potentially large differences in the market betas of the winner and loser portfolios

28 Momentum Beta Market Beta WML Option Dynamic Strategy Performance As of March 2009, many the firms in the Loser portfolio had 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 of defensive 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-money option on the firm value (à là (Merton 1974)) This suggests that there were potentially large differences in the market betas of the winner and loser portfolios

29 Momentum Beta Market Beta WML Option Dynamic Strategy Performance As of March 2009, many the firms in the Loser portfolio had 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 of defensive 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-money option on the firm value (à là (Merton 1974)) This suggests that there were potentially large differences in the market betas of the winner and loser portfolios

30 Market Beta WML Option Dynamic Strategy Performance Market Beta and Momentum Rolling 126-day betas, 1927: : day (rolling) beta date

31 Market Beta WML Option Dynamic Strategy Performance Market Beta and Momentum Rolling 126-day betas, 1999: : day (rolling) beta date

32 Estimating Beta Market Beta WML Option Dynamic Strategy Performance There is a strong Up- and Down-β differential in bear markets: R WML,t = [α 0 + α B I B] + [ β 0 + β B I B + β B,U(I B Ĩ U) ] Re m,t + ɛ t Estimated Coefficients (t-statistics in parentheses) Coeff. Variable (1) (2) (3) (4) ˆα (7.3) (7.7) (7.8) (8.4) ˆα B I B (-3.5) (0.6) ˆβ 0 Re m,t (-12.5) (-0.5) (-0.5) (-0.6) ˆβ B I B R m,t e (-13.4) (-5.0) (-6.2) ˆβ B,U I B I U R m,t e (-4.5) (-5.7) R 2 _adj I B = 1 when the past 2-year market return is non-positive there are 186 Bear-market months. Ĩ U = 1 when R m,t > 0. This is not an ex-ante variable.

33 Estimating Beta Market Beta WML Option Dynamic Strategy Performance There is a strong Up- and Down-β differential in bear markets: R WML,t = [α 0 + α B I B] + [ β 0 + β B I B + β B,U(I B Ĩ U) ] Re m,t + ɛ t Estimated Coefficients (t-statistics in parentheses) Coeff. Variable (1) (2) (3) (4) ˆα (7.3) (7.7) (7.8) (8.4) ˆα B I B (-3.5) (0.6) ˆβ 0 Re m,t (-12.5) (-0.5) (-0.5) (-0.6) ˆβ B I B R m,t e (-13.4) (-5.0) (-6.2) ˆβ B,U I B I U R m,t e (-4.5) (-5.7) R 2 _adj I B = 1 when the past 2-year market return is non-positive there are 186 Bear-market months. Ĩ U = 1 when R m,t > 0. This is not an ex-ante variable.

34 Estimating Beta Market Beta WML Option Dynamic Strategy Performance There is a strong Up- and Down-β differential in bear markets: R WML,t = [α 0 + α B I B] + [ β 0 + β B I B + β B,U(I B Ĩ U) ] Re m,t + ɛ t Estimated Coefficients (t-statistics in parentheses) Coeff. Variable (1) (2) (3) (4) ˆα (7.3) (7.7) (7.8) (8.4) ˆα B I B (-3.5) (0.6) ˆβ 0 Re m,t (-12.5) (-0.5) (-0.5) (-0.6) ˆβ B I B R m,t e (-13.4) (-5.0) (-6.2) ˆβ B,U I B I U R m,t e (-4.5) (-5.7) R 2 _adj I B = 1 when the past 2-year market return is non-positive there are 186 Bear-market months. Ĩ U = 1 when R m,t > 0. This is not an ex-ante variable.

35 Estimating Beta Market Beta WML Option Dynamic Strategy Performance There is a strong Up- and Down-β differential in bear markets: R WML,t = [α 0 + α B I B] + [ β 0 + β B I B + β B,U(I B Ĩ U) ] Re m,t + ɛ t Estimated Coefficients (t-statistics in parentheses) Coeff. Variable (1) (2) (3) (4) ˆα (7.3) (7.7) (7.8) (8.4) ˆα B I B (-3.5) (0.6) ˆβ 0 Re m,t (-12.5) (-0.5) (-0.5) (-0.6) ˆβ B I B R m,t e (-13.4) (-5.0) (-6.2) ˆβ B,U I B I U R m,t e (-4.5) (-5.7) R 2 _adj I B = 1 when the past 2-year market return is non-positive there are 186 Bear-market months. Ĩ U = 1 when R m,t > 0. This is not an ex-ante variable.

36 Where is the Option? Market Beta WML Option Dynamic Strategy Performance This optionality is mostly in the loser portfolio: For the past-loser portfolio, ˆβ B,U = For the past-winner portfolio, ˆβ B,U = The optionality is not present in BulL markets: For past-loser portfolio, ˆβ L,U = 0.02.

37 WML Option Momentum in Investment Strategies Market Beta WML Option Dynamic Strategy Performance Winner Return 0 Loser Return -10% 0 +10% Market Return 0 WML Return -10% 0 +10% Market Return 0-10% 0 +10% Market Return

38 Forecasting Crashes Market Beta WML Option Dynamic Strategy Performance We have seen that the payoff associated with the WML portfolio has short-option-like characteristics. It seems likely this this option will be more costly when market variance is higher This would also be consistent with a behavioral motivation for our forecasting variable. Based on this we investigate whether other variables associated with perceived risk affect the payoff to momentum strategies. Specifically we look at market volatility related to the VIX.

39 Forecasting Crashes Market Beta WML Option Dynamic Strategy Performance We have seen that the payoff associated with the WML portfolio has short-option-like characteristics. It seems likely this this option will be more costly when market variance is higher This would also be consistent with a behavioral motivation for our forecasting variable. Based on this we investigate whether other variables associated with perceived risk affect the payoff to momentum strategies. Specifically we look at market volatility related to the VIX.

40 Forecasting Crashes Market Beta WML Option Dynamic Strategy Performance We have seen that the payoff associated with the WML portfolio has short-option-like characteristics. It seems likely this this option will be more costly when market variance is higher This would also be consistent with a behavioral motivation for our forecasting variable. Based on this we investigate whether other variables associated with perceived risk affect the payoff to momentum strategies. Specifically we look at market volatility related to the VIX.

41 Forecasting Momentum Returns Market Beta WML Option Dynamic Strategy Performance r WML,t = γ 0 + γ B I B,t 1 + γ σ 2 m ˆσ 2 m,t 1 + γ int I B,t 1 ˆσ 2 m,t 1 + ɛ t (1) (2) (3) (4) (5) ˆγ (6.6) (6.6) (6.0) (7.1) (3.3) ˆγ B (-3.8) (-1.8) (1.5) ˆγ σ 2 m (-4.4) (-2.9) (-0.5) ˆγ int (-5.2) (-2.8)

42 Exposure to variance risk Market Beta WML Option Dynamic Strategy Performance RHS Vars. (1) (2) (3) α (4.7) (4.8) (4.9) I Bσ (-5.2) (-4.8) (-5.3) r m e (4.5) (3.3) I Bσ 2 r m,t e (-28.4) (-24.7) r vs,t (-0.2) I Bσ 2 r vs,t (-4.8) Daily Regressions, January 2, 1990 to March 28, r vs,t is the return to a variance-swap on the S&P 500. ˆα and I Bσ 2 coeffficients are (i.e., in %/year)

43 Exposure to variance risk Market Beta WML Option Dynamic Strategy Performance RHS Vars. (1) (2) (3) α (4.7) (4.8) (4.9) I Bσ (-5.2) (-4.8) (-5.3) r m e (4.5) (3.3) I Bσ 2 r m,t e (-28.4) (-24.7) r vs,t (-0.2) I Bσ 2 r vs,t (-4.8) Daily Regressions, January 2, 1990 to March 28, r vs,t is the return to a variance-swap on the S&P 500. ˆα and I Bσ 2 coeffficients are (i.e., in %/year)

44 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance We next evalulate the performance of a strategy which dynamically adjusts the weight on the basic wml strategy based on the forecast return and volatility of the wml strategy. E t 1 [r wml,t ] is forecast using the interaction on the preceding slide (regression 4) ˆσ 2 wml,t 1 is forecast using a GARCH-like procedure applied to daily wml returns: The weight on wml at at the start of period t is: w wml,t 1 = κ Et 1[r wml,t ] ˆσ 2 wml,t 1 Each strategy is scaled to give an unconditional volatility of 19% equal to σ mkt over the full sample.

45 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance We next evalulate the performance of a strategy which dynamically adjusts the weight on the basic wml strategy based on the forecast return and volatility of the wml strategy. E t 1 [r wml,t ] is forecast using the interaction on the preceding slide (regression 4) ˆσ 2 wml,t 1 is forecast using a GARCH-like procedure applied to daily wml returns: The weight on wml at at the start of period t is: w wml,t 1 = κ Et 1[r wml,t ] ˆσ 2 wml,t 1 Each strategy is scaled to give an unconditional volatility of 19% equal to σ mkt over the full sample.

46 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance We next evalulate the performance of a strategy which dynamically adjusts the weight on the basic wml strategy based on the forecast return and volatility of the wml strategy. E t 1 [r wml,t ] is forecast using the interaction on the preceding slide (regression 4) ˆσ 2 wml,t 1 is forecast using a GARCH-like procedure applied to daily wml returns: The weight on wml at at the start of period t is: w wml,t 1 = κ Et 1[r wml,t ] ˆσ 2 wml,t 1 Each strategy is scaled to give an unconditional volatility of 19% equal to σ mkt over the full sample.

47 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance We next evalulate the performance of a strategy which dynamically adjusts the weight on the basic wml strategy based on the forecast return and volatility of the wml strategy. E t 1 [r wml,t ] is forecast using the interaction on the preceding slide (regression 4) ˆσ 2 wml,t 1 is forecast using a GARCH-like procedure applied to daily wml returns: The weight on wml at at the start of period t is: w wml,t 1 = κ Et 1[r wml,t ] ˆσ 2 wml,t 1 Each strategy is scaled to give an unconditional volatility of 19% equal to σ mkt over the full sample.

48 WML & Dynamic Strategy Returns Portfolio Value ($) Market Beta WML Option Dynamic Strategy Performance Cumulative Normalized Strategy Returns (19% ann. vol.) : :03 wml dynamic c_vol date

49 Market Beta WML Option Dynamic Strategy Performance WML & Dynamic Strategy Returns - Subsamples wml dynamic wml dynamic wml dynamic wml dynamic

50 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance Strategy S.R. Subperiod WML const. σ dynamic 1927: : : : : : : : : : The dynamic strategy almost doubles the Sharpe Ratio of the static momentum strategy. Moreover, the improvement is strong in each subperiod. A constant volatility strategy provides a substantial improvement over standard momentum. See Barroso and Santa-Clara (2012). However, exploiting the strong forecastability of the mean gets you still superior performance.

51 Dynamic Strategy Returns Market Beta WML Option Dynamic Strategy Performance Strategy S.R. Subperiod WML const. σ dynamic 1927: : : : : : : : : : The dynamic strategy almost doubles the Sharpe Ratio of the static momentum strategy. Moreover, the improvement is strong in each subperiod. A constant volatility strategy provides a substantial improvement over standard momentum. See Barroso and Santa-Clara (2012). However, exploiting the strong forecastability of the mean gets you still superior performance.

52 Market Beta WML Option Dynamic Strategy Performance Dynamic Strategy Returns Skewness Strategy S.R./(skewness) Subperiod WML const. σ dynamic 1927: : (-4.70) (-0.76) (0.09) 1927: : (-3.38) (-1.25) (-0.99) 1950: : (-1.16) (-0.54) (-0.05) 1975: : (-0.78) (-0.41) (0.18) 2000: : (-1.50) (-0.68) (0.14) The dynamic strategy also exhibits considerably less negative skewness.

53 Momentum in Other Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work The remarkably strong results for predictability in US equity markets is consistent across the four quarter-century subsamples. To further assesss the robustness of the phenonmena we document, we also investigate whether the predictability and optionality patterns are also present in other markets We examine 3 other equity markets, and 4 other asset classes. Data is similar to that in Asness, Moskowitz, and Pedersen (2013). Our momentum measure is 12-2 in each market momentum portfolio is long top third, short bottom third. We use a market return that corresponds to the asset universe in which the momentum strategy is constructed. Portfolios are VW for equities, EW for other asset classes.

54 Momentum in Other Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work The remarkably strong results for predictability in US equity markets is consistent across the four quarter-century subsamples. To further assesss the robustness of the phenonmena we document, we also investigate whether the predictability and optionality patterns are also present in other markets We examine 3 other equity markets, and 4 other asset classes. Data is similar to that in Asness, Moskowitz, and Pedersen (2013). Our momentum measure is 12-2 in each market momentum portfolio is long top third, short bottom third. We use a market return that corresponds to the asset universe in which the momentum strategy is constructed. Portfolios are VW for equities, EW for other asset classes.

55 Momentum in Other Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work The remarkably strong results for predictability in US equity markets is consistent across the four quarter-century subsamples. To further assesss the robustness of the phenonmena we document, we also investigate whether the predictability and optionality patterns are also present in other markets We examine 3 other equity markets, and 4 other asset classes. Data is similar to that in Asness, Moskowitz, and Pedersen (2013). Our momentum measure is 12-2 in each market momentum portfolio is long top third, short bottom third. We use a market return that corresponds to the asset universe in which the momentum strategy is constructed. Portfolios are VW for equities, EW for other asset classes.

56 Momentum in Other Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work The remarkably strong results for predictability in US equity markets is consistent across the four quarter-century subsamples. To further assesss the robustness of the phenonmena we document, we also investigate whether the predictability and optionality patterns are also present in other markets We examine 3 other equity markets, and 4 other asset classes. Data is similar to that in Asness, Moskowitz, and Pedersen (2013). Our momentum measure is 12-2 in each market momentum portfolio is long top third, short bottom third. We use a market return that corresponds to the asset universe in which the momentum strategy is constructed. Portfolios are VW for equities, EW for other asset classes.

57 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities Currencies Bonds Equities

58 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities US, UK, Continental Europe, and Japan In each market, universe is largest market capitalization firms, such that we include 90% of the total market cap. comprises 15-20% of names in each market. Other Asset Classes Commodities Currencies Bonds Equities

59 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities Currencies Bonds Equities

60 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities 27 commodities from 8 exchanges. Oil and Gas, Metals, Agricultural. Currencies Bonds Equities

61 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities Currencies 9 Currencies. Australia, Canada, Germany (spliced with the Euro), Japan, New Zealand, Norway, Sweden, Switzerland, and U.K. Bonds Equities

62 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities Currencies Bonds 10 Government Bonds. Australia, Canada, Denmark, Germany, Japan, Norway, Sweden, Switzerland, U.K., and U.S. Equities

63 Data Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equities Other Asset Classes Commodities Currencies Bonds Equities 18 Equity Indices Australia, Austria, Belgium, Canada, Denmark, France, Germany, Hong Kong, Italy, Japan, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, U.K., and U.S.

64 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work International Equity Market Momentum

65 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Past Market Returns and Market Variance R mom t = [α 0 + α B I B + α V ˆσ 2 m] + [β 0 + β B I B + β V ˆσ 2 m] R e m,t + ɛ t. Europe Japan UK US global ˆα (4.2) (1.4) (3.5) (3.2) (4.7) ˆα B (0.5) (0.4) (-0.1) (1.2) (0.4) ˆα V (-2.7) (-2.3) (-2.3) (-3.3) (-3.1) ˆβ (2.4) (4.4) (1.6) (3.6) (1.4) ˆβ B (-4.3) (-6.8) (-1.2) (-5.0) (-2.8) ˆβ V (-3.0) (0.5) (-2.9) (-2.1) (-1.9)

66 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Past Market Returns and Market Variance R mom t = [α 0 + α B I B + α V ˆσ 2 m] + [β 0 + β B I B + β V ˆσ 2 m] R e m,t + ɛ t. Europe Japan UK US global ˆα (4.2) (1.4) (3.5) (3.2) (4.7) ˆα B (0.5) (0.4) (-0.1) (1.2) (0.4) ˆα V (-2.7) (-2.3) (-2.3) (-3.3) (-3.1) ˆβ (2.4) (4.4) (1.6) (3.6) (1.4) ˆβ B (-4.3) (-6.8) (-1.2) (-5.0) (-2.8) ˆβ V (-3.0) (0.5) (-2.9) (-2.1) (-1.9)

67 Optionality in Bear Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work R mom t = [α 0 + α B I B ] + [ β 0 + β B I B + β B,U (I B Ĩ U ) ] Re m,t + ɛ t Europe Japan UK US global ˆα (3.0) (-0.3) (2.6) (1.2) (3.2) ˆα B (1.8) (1.8) (0.6) (0.5) (1.0) ˆβ (1.7) (4.7) (0.6) (2.9) (0.8) ˆβ B (-2.6) (-2.0) (0.1) (-3.2) (-0.9) ˆβ B,U (-2.5) (-2.1) (-2.2) (-0.3) (-2.2)

68 Other Asset Class Momentum International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work

69 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Past Market Returns and Market Variance R mom t = [α 0 + α B I B + α V ˆσ 2 m] + [β 0 + β B I B + β V ˆσ 2 m] R e m,t + ɛ t Bonds Commod s Currencies Equities all all+stock ˆα (1.2) (3.2) (2.8) (3.8) (4.4) (5.5) ˆα B (-0.0) (-1.0) (-3.0) (-0.2) (-0.4) (0.0) ˆα V (-1.4) (-0.7) (-0.4) (-0.5) (-1.2) (-2.3) ˆβ (3.7) (2.7) (2.9) (6.2) (2.7) (2.3) ˆβ B (-2.9) (-4.1) (-7.3) (-7.0) (-2.6) (-2.4) ˆβ V (-0.8) (0.5) (0.2) (-1.4) (-1.5) (-1.9)

70 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Past Market Returns and Market Variance R mom t = [α 0 + α B I B + α V ˆσ 2 m] + [β 0 + β B I B + β V ˆσ 2 m] R e m,t + ɛ t Bonds Commod s Currencies Equities all all+stock ˆα (1.2) (3.2) (2.8) (3.8) (4.4) (5.5) ˆα B (-0.0) (-1.0) (-3.0) (-0.2) (-0.4) (0.0) ˆα V (-1.4) (-0.7) (-0.4) (-0.5) (-1.2) (-2.3) ˆβ (3.7) (2.7) (2.9) (6.2) (2.7) (2.3) ˆβ B (-2.9) (-4.1) (-7.3) (-7.0) (-2.6) (-2.4) ˆβ V (-0.8) (0.5) (0.2) (-1.4) (-1.5) (-1.9)

71 Optionality in Bear Markets International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work R mom t = [α 0 + α B I B ] + [ β 0 + β B I B + β B,U (I B Ĩ U ) ] Re m,t + ɛ t Bonds Commod s Currencies Equities all all+stock ˆα (-1.5) (2.4) (1.7) (2.4) (2.3) (3.4) ˆα B (1.5) (1.8) (2.0) (2.1) (2.7) (2.3) ˆβ (4.5) (3.7) (3.4) (6.1) (2.8) (2.1) ˆβ B (-0.9) (0.1) (-1.8) (-4.2) (0.8) (-0.2) ˆβ B,U (-0.4) (-2.6) (-2.4) (-1.9) (-2.7) (-3.2)

72 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance: Equity Strategies Annualized Strategy SR (skewness) by Region EU JP UK US GE start 06/90 06/90 06/90 07/72 07/72 end 05/13 05/13 05/13 05/13 05/13 Static WML (-0.34) (0.02) (-0.62) (-0.04) (-0.34) Const. σ (0.55) (-0.13) (-0.02) (-0.09) (0.13) Dynamic (0.97) (1.41) (0.36) (0.08) (0.33) Full-dynamic WML (1.11)

73 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance: Equity Strategies Annualized Strategy SR (skewness) by Region EU JP UK US GE start 06/90 06/90 06/90 07/72 07/72 end 05/13 05/13 05/13 05/13 05/13 Static WML (-0.34) (0.02) (-0.62) (-0.04) (-0.34) Const. σ (0.55) (-0.13) (-0.02) (-0.09) (0.13) Dynamic (0.97) (1.41) (0.36) (0.08) (0.33) Full-dynamic WML (1.11)

74 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance: Equity Strategies Annualized Strategy SR (skewness) by Region EU JP UK US GE start 06/90 06/90 06/90 07/72 07/72 end 05/13 05/13 05/13 05/13 05/13 Static WML (-0.34) (0.02) (-0.62) (-0.04) (-0.34) Const. σ (0.55) (-0.13) (-0.02) (-0.09) (0.13) Dynamic (0.97) (1.41) (0.36) (0.08) (0.33) Full-dynamic WML (1.11)

75 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance: Equity Strategies Annualized Strategy SR (skewness) by Region EU JP UK US GE start 06/90 06/90 06/90 07/72 07/72 end 05/13 05/13 05/13 05/13 05/13 Static WML (-0.34) (0.02) (-0.62) (-0.04) (-0.34) Const. σ (0.55) (-0.13) (-0.02) (-0.09) (0.13) Dynamic (0.97) (1.41) (0.36) (0.08) (0.33) Full-dynamic WML (1.11)

76 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance in Other Asset Classes Annualized Strategy SR (skewness) by Asset Class: FI CM FX EQ GA GAll start 06/83 02/73 02/80 02/79 02/73 02/73 end 05/13 05/13 05/13 05/13 05/13 05/13 Static WML (-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33) Const. σ WML (-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18) Dynamic WML (0.06) (0.39) (-0.20) (0.25) (0.11) (0.20) Full-dynamic WML (-0.19) (0.44)

77 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance in Other Asset Classes Annualized Strategy SR (skewness) by Asset Class: FI CM FX EQ GA GAll start 06/83 02/73 02/80 02/79 02/73 02/73 end 05/13 05/13 05/13 05/13 05/13 05/13 Static WML (-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33) Const. σ WML (-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18) Dynamic WML (0.06) (0.39) (-0.20) (0.25) (0.11) (0.20) Full-dynamic WML (-0.19) (0.44)

78 International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Dynamic Strategy Performance in Other Asset Classes Annualized Strategy SR (skewness) by Asset Class: FI CM FX EQ GA GAll start 06/83 02/73 02/80 02/79 02/73 02/73 end 05/13 05/13 05/13 05/13 05/13 05/13 Static WML (-0.24) (0.01) (-0.54) (-0.18) (-0.48) (-0.33) Const. σ WML (-0.45) (-0.07) (-0.47) (0.05) (-0.31) (-0.18) Dynamic WML (0.06) (0.39) (-0.20) (0.25) (0.11) (0.20) Full-dynamic WML (-0.19) (0.44)

79 Conclusions & Future Work International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work 1 In normal environments, the market appears to underreact to public information, resulting in consistent price momentum. 2 However, in panic states, the market prices of severe past losers embody a very high premium. When market conditions ameliorate, these losers experience strong gains, resulting in a momentum crash. The expected gains from the loser portfolio are related to both past market losses, and lagged market volatility. 3 Market risk of momentum portfolios varies dramatically, but does not appear to explain the variation in the premium earned by momentum.

80 Conclusions & Future Work International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work 1 In normal environments, the market appears to underreact to public information, resulting in consistent price momentum. 2 However, in panic states, the market prices of severe past losers embody a very high premium. When market conditions ameliorate, these losers experience strong gains, resulting in a momentum crash. The expected gains from the loser portfolio are related to both past market losses, and lagged market volatility. 3 Market risk of momentum portfolios varies dramatically, but does not appear to explain the variation in the premium earned by momentum.

81 Conclusions & Future Work International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work 1 In normal environments, the market appears to underreact to public information, resulting in consistent price momentum. 2 However, in panic states, the market prices of severe past losers embody a very high premium. When market conditions ameliorate, these losers experience strong gains, resulting in a momentum crash. The expected gains from the loser portfolio are related to both past market losses, and lagged market volatility. 3 Market risk of momentum portfolios varies dramatically, but does not appear to explain the variation in the premium earned by momentum.

82 References I Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Asness, Clifford S., John M. Liew, and Ross L. Stevens, 1997, Parallels between the cross-sectional predictability of stock and country returns, Journal of Portfolio Management 23, Asness, Clifford S., Toby J. Moskowitz, and Lasse Heje Pedersen, 2013, Value and momentum everywhere, The Journal of Finance 58, Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment, Journal of Financial Economics 49, Barroso, Pedro, and Pedro Santa-Clara, 2012, Managing the risk of momentum, Nova School of Business and Economics working paper. Boguth, Oliver, Murray Carlson, Adalai Fisher, and Mikhail Simutin, 2010, Conditional risk and performance evaluation: Volatility timing, overconditioning, and new estimates of momentum alphas, Journal of Financial Economics, forthcoming. Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen, 2008, Carry trades and currency crashes, NBER Macroeconomics Annual. Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 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,

83 References II Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Cooper, Michael J., Roberto C. Gutierrez, and Allaudeen Hameed, 2004, Market states and momentum, Journal of Finance 59, Daniel, Kent D., David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psychology and security market under- and over-reactions, Journal of Finance 53, DeBondt, Werner F. M., and Richard H. Thaler, 1987, Further evidence on investor overreaction and stock market seasonality, Journal of Finance 42, Erb, Claude B., and Campbell R. Harvey, 2006, The strategic and tactical value of commodity futures, Financial Analysts Journal 62, George, Thomas J., and Chuan-Yang Hwang, 2004, The 52-week high and momentum investing, The Journal of Finance 59, Grinblatt, Mark, and Bing Han, 2005, Prospect theory, mental accounting and momentum, Journal of Financial Economics 78, Grundy, Bruce, and J. Spencer Martin, 2001, Understanding the nature of the risks and the source of the rewards to momentum investing, Review of Financial Studies 14, Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, momentum trading and overreaction in asset markets, Journal of Finance 54,

84 References III Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 48, , 2001, Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance 56, Kothari, S.P., and Jay Shanken, 1992, Stock return variation and expected dividends, Journal of Financial Economics 31, Merton, Robert C., 1974, On the pricing of corporate debt: The risk structure of interest rates, The Journal of Finance 29, Moskowitz, Tobias J., and Mark Grinblatt, 1999, Do industries explain momentum?, The Journal of Finance 54, Moskowitz, Tobias J., Yoa Hua Ooi, and Lasse H. Pedersen, 2012, Time series momentum, Journal of Financial Economics 104, Okunev, John, and Derek White, 2003, Do momentum-based strategies still work in foreign currency markets?, Journal of Financial and Quantitative Analysis 38, Rottenstreich, Yuval, and Chris K. Hsee, 2001, Money, kisses, and electric shocks: On the affective psychology of risk, Psychological Science 12, Rouwenhorst, K. Geert, 1998, International momentum strategies, Journal of Finance 53,

85 References IV Momentum in Investment Strategies International Equity Markets Other Asset Class Momentum Dynamic Strategy in Other Asset Classes Conclusions & Future Work, 1999, Local return factors and turnover in emerging stock markets, Journal of Finance 54, Swaminathan, Bhaskaran, 2010, Qunatitative money management: A practical application of behavioral finance, Working Paper.