Momentum Crashes. The Q -GROUP: FALL SEMINAR. 17 October Kent Daniel & Tobias Moskowitz. Columbia Business School & Chicago-Booth

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1 Momentum Crashes Kent Daniel & Tobias Moskowitz Columbia Business School & Chicago-Booth The Q -GROUP: FALL SEMINAR 17 October 2012

2 Momentum Introduction This paper does a deep-dive into one particular factor/anomaly: price momentum. It is employed by many (most?) quantitative managers. Grinblatt and Titman (1989, 1993), Carhart (1997), and subsequent work argue that mutual funds also employ momentum. Historically, momentum strategies deliver high premia. Over the post WWII period, through 2008, the long-short 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 Momentum is pervasive: US Equities: Jegadeesh and Titman (1993, 2001). Developed Equities: Rouwenhorst (1998) Emerging Equities: Rouwenhorst (1999) 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 (2008), Moskowitz, Ooi, and Pedersen (2012).

4 Momentum Introduction However, momentum strategy returns exhibit significant negative skewness: e.g., in March-May 2009, equity 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 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: Grundy and Martin (2001) show that the market beta of momentum strategies is highly dependent on the lagged market return. They 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: Cooper, Gutierrez, and Hameed (2004) demonstrate the state dependence of momentum strategy returns They don t control for conditional variations in risk. Optionality in momentum returns: Rouwenhorst (1998), Chan (1988), DeBondt and Thaler Daniel (1987). & Moskowitz, Momentum Crashes

6 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: 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)

7 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:

8 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).

9 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns

10 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns

11 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns

12 Literature Review Portfolio Construction Crash Characterization Long-Only Investment Strategy Returns

13 Literature Review Portfolio Construction Crash Characterization Momentum Performance

14 Literature Review Portfolio Construction Crash Characterization Momentum in the Great Depression

15 Cumulative Momentum Returns Literature Review Portfolio Construction Crash Characterization

16 Literature Review Portfolio Construction Crash Characterization Momentum Portfolio Characteristics: Momentum Decile Portfolios wml Mkt µ σ α t(α) (-5.8) (-3.5) (-3.2) (-1.5) (-1.1) (-0.1) (1.9) (4.4) (4.4) (5.4) (6.5) (0) β SR sk(m) sk(d) Note that the skewness is less pronounced for the daily returns than for the monthly.

17 Literature Review Portfolio Construction Crash Characterization 10 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.

18 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%.

19 Momentum Beta Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes 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

20 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Market Beta and Momentum

21 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Market Beta and Momentum

22 Hedging market risk Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Consistent with Grundy and Martin (2001), this evidence suggests hedging out market risk could be beneficial. We estimate rolling 42-day (2-month) betas We regress r WML,t on contemporaneous Market, and 10 lags of the market return. This is particularly important in the early period, and for the low momentum portfolios, because of non-trading/illiquidity biases. We then construct a hedged WML portfolio: r h WML,t = r WML,t β t r e m,t, where β t is the forward-looking rolling-beta estimate. This closely follows the procedure of Grundy and Martin (2001).

23 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Hedged Momentum Portfolio Performance

24 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Grundy and Martin (2001) perform their analysis using ex-post betas becuase: The dynamics of beta are complicated. They had only monthly data. Also, as long as the realized beta is uncorrelatted with the contemporaneous market return, there procedure should introduce a bias in the efficacy of the hedge...

25 Estimating Beta Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes 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 + t Estimated Coefficients (t-statistics in parentheses) Coeff. Variable (1) (2) (3) (4) ˆα (7.1) (6.8) (6.9) (7.5) ˆα B I B (-3.4) (0.9) ˆβ 0 Re m,t (-12.6) (0.7) (0.7) (0.7) ˆβ B I B R m,t e (-15.5) (-6.1) (-7.4) ˆβ B,U I B ĨU R m,t e (-5.0) (-6.0) Radj I B = 1 when the past 2-year market return is non-positive there are 177 Bear-market months. Ĩ U = 1 when R m,t > 0. This is not an ex-ante variable.

26 Where is the Option? Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes 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.

27 WML Option Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes

28 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes The regression results show that the up-beta of the WML portfolio is much more negative than the down-beta. This means, if you use a forward looking beta estimate: You hedge more (i.e., buy more market) when then market is going to rise. This imparts a large positve bias to the estimate of the hedged portfolio returns.

29 Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes Hedged Momentum Portfolio Performance

30 Forecasting Crashes Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes 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 is also consistent with behavioral motivations for the premium Based on this we investigate whether other variables associated with perceived risk affect the payoff to momentum strategies. Specifically we look at a realized volatility related to the VIX.

31 Forecasting Momentum Returns Market Beta Performance of Hedged Portfolios WML Option Forecasting Crashes 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 + t γ 0 γ B γ σ 2 m γ int (5.59) (-4.51) (6.78) (-6.07) (6.98) (-2.04) (-4.54) (6.06) (-7.17) (4.87) (0.36) (-0.53) (-3.30)

32 Momentum in Other Markets International Equity Markets Other Asset Class Momentum We now 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 (2008). 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. VW for equities, EW for other asset classes.

33 Data International Equity Markets Other Asset Class Momentum 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 27 commodities from 8 exchanges. Oil and Gas, Metals, Agricultural. Currencies 9 Currencies. Australia, Canada, Germany (spliced with the Euro), Japan, New Zealand, Norway, Sweden, Switzerland, and U.K. Bonds 10 Government Bonds. Australia, Canada, Denmark, Germany, Japan, Norway, Sweden, Switzerland, U.K., and U.S. Equities Daniel & Moskowitz, 18 Equity Momentum Indices Crashes

34 International Equity Markets Other Asset Class Momentum International Equity Market Momentum

35 International Equity Markets Other Asset Class Momentum 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 + 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)

36 Optionality in Bear Markets International Equity Markets Other Asset Class Momentum 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 + 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)

37 Other Asset Class Momentum International Equity Markets Other Asset Class Momentum

38 International Equity Markets Other Asset Class Momentum 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 + 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)

39 Optionality in Bear Markets International Equity Markets Other Asset Class Momentum 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 + 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)

40 Conclusions & Future Work International Equity Markets Other Asset Class Momentum 1 In normal environments, the market appears to underreact to public information, resulting in consistent price momentum. 2 However, in extreme market enviroments, 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 premia earned by momentum.

41 Possible Behavioral Explanations International Equity Markets Other Asset Class Momentum Recent behavioral work suggests that when an event has strong affective content, the price that individuals are willing to pay to avoid bad outcomes is not closely related to the probabilities of the event. Rottenstreich and Hsee (2001) attempts to explore people s willingness to pay to avoid bad outcomes One outcome an electric shock was described as short, painful, but not dangerous. In contrast, a second control group, was told that there was a chance that they could lose $20 of their payment. Probabilties were either stated to be 1% or 99%.

42 Rottenstreich and Hsee (2001) International Equity Markets Other Asset Class Momentum Subjects were willing to pay $1 to avoid a 1% chance, and $18 to avoid a 99% chance of losing the $20. For the electric shock, in contrast, the difference in probability made little difference to median willingness to pay: $7 to avoid a 1% chance, and $10 to avoid a 99% chance.

43 References I International Equity Markets Other Asset Class Momentum 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 Moskowitz, and Lasse Pedersen, 2008, Value and momentum everywhere, University of Chicago working paper. Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment, Journal of Financial Economics 49, 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, Chan, K.C., 1988, On the contrarian investment strategy, Journal of Business 61, 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,

44 References II International Equity Markets Other Asset Class Momentum 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, 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, Merton, Robert C., 1974, On the pricing of corporate debt: The risk structure of interest rates, The Journal of Finance 29,

45 References III International Equity Markets Other Asset Class Momentum 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, University of Chicago Working Paper. 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, , 1999, Local return factors and turnover in emerging stock markets, Journal of Finance 54,