2.3 Predicting Momentum Crashes
2.3.2 Isolation of Crash Periods
momentum-specific risk, only one month shows an annualized volatility of slightly below the average (0.18), while still exceeding the median annualized volatility of 0.14.
if a rebound takes place and momentum beta is negative.
IC,τ =
1 ifMarket2Y ,t−1<0 &Market1M,τ>0 &βMOM,t−1<0,
0 otherwise
(2.3)
Table 2.2 presents average momentum returns with respect to the state of the indicators. Most importantly, each indicator features significantly lower returns in periods defined as a crash. Considering ex-ante mea-sures,IC,t−1 displays the highest and most significant absolute difference in means (−5.12%). In months depicted as ‘no crash’, average returns increase from the full sample mean of 1.15% to 1.49%, while dropping to
−3.63% in crash periods. For the rebound indicator,IR,t−1, the absolute difference in means decreases (−3.84%) and significance reduces to the 5%-level. While average returns in non-crash periods are similar to those ofIC,t−1(1.47%), returns in crash periods increase to−2.38%. For the bear market indicator,IB,t−1, the difference remains significant at the 5%-level, although the absolute spread shrinks to 2.63%. The crash period aver-age increases to roughly−1.04%, whereas the non-crash mean amounts to 1.59%.16 Considering ex-post indicators, differences and absolute t-values strongly increase. However,IC,t still displays the highest and most significant difference (10.40%).
While these results suggest thatIC is a meaningful crash indicator, it seems reasonable to ask how an investor could have known this in 1930.
Note that bear markets are often initiated by a market crash. In these
16The latter result is driven by the fact thatIR,t−1andIC,t−1occasionally miss the first month of momentum crashes, whereasIB,t−1covers the whole period of market stress.
As bear markets also include positive returns prior to momentum crashes, the crash
Table 2.2:Comparison of Mean Returns
Indicator (Ij) Ij= 0 Ij= 1 Diff. t-value Implementation IB,t−1 1.59% −1.04% −2.63% −2.49** ex-ante IR,t−1 1.47% −2.38% −3.84% −2.53** ex-ante IC,t−1 1.49% −3.63% −5.12% −2.83*** ex-ante IR,t 1.95% −6.66% −8.61% −5.65*** ex-post IC,t 1.94% −8.47% −10.40% −5.94*** ex-post
Table 2.2 presents average momentum returns with respect to indicator j, where B denotes the bear-market indicator,Ris the rebound indicator andCis the crash indicator.
To calculate means, we apply the full sample period from September 1928 to May 2020. Ex-ante (ex-post) implementation indicates that lagged (contemporaneous) market returns are used. Stars indicate significance at the 10% (*), 5% (**) and 1% (***) level.
particular periods, momentum winners (losers) are those stocks with the smallest (largest) losses. In line with Shleifer and Vishny (1997), losers are more likely to be undervalued than winners and their expected returns increase.17 By construction, losers also exhibit a higher beta than winners, resulting in a negative beta of the momentum portfolio.18 When the market starts to recover, contemporaneous returns are positive, but the overall market condition is still considered to be a bear market.19 Finally, as losers move back to their fair value, they display higher returns and the return of the momentum portfolio is negative.
To investigate whether a combination of the crash indicators and momentum-specific risk further improves momentum predictability, we employ predictive regressions of monthly momentum returns on the
17According to Shleifer and Vishny (1997), professional traders (arbitrageurs) apply the capital of less sophisticated (potentially irrational) retail investors who are unaware of fair values and focus on past performance. Therefore, larger losses in the recent past likely entail more withdrawals, resulting in an undervaluation of loser stocks.
18See Barroso and Santa-Clara (2015) and Daniel and Moskowitz (2016).
19See Daniel and Moskowitz (2016).
interaction of crash indicators and annualized momentum volatility. The regression framework is set up as follows
rMOM,t=α+γ·Ij,t−1+δ·Ij,t−1·σMOM,t−1+η·σMOM,t−1+λ·X~t−1+t, whererMOM,t andσMOM,t−1 denote monthly momentum returns and the annualized momentum volatility of the preceding 126 daily momentum returns, respectively. Ex-ante crash indicators are depicted byIj,t−1. In addition to that,X~t−1andt denote a vector of lagged Fama and French (1993) risk factors and the monthly residuals.
Table 2.3 presents results for the full sample period from September 1928 to May 2020. The first three models simply regress momentum returns on indicator dummies. By construction, coefficients correspond to the difference in means presented in Table 2.2 andt-statistics are lowest for IC,t−1 (well below−5). In Model (4), momentum returns are solely regressed on the preceding momentum volatility. Consistent with Stivers and Sun (2010) and Barroso and Santa-Clara (2015), we find that momen-tum volatility has a significantly negative impact on subsequent returns.
Models (5) to (7) present results for the interaction of crash indicators and momentum volatility, where we obtain four important results. First, significance increases for each of the indicators. Second, in absolute terms, coefficients,t-values, and R2’s exceed those of Models (1) to (4), suggesting that a combination of market risk and momentum-specific risk improves crash predictability. Third,IC,t−1 remains the most significant indicator, both statistically and economically. Fourth, as explained
vari-Table 2.3:Predictive Regressions
Dependent variable:
rMOM,t
(1) (2) (3) (4) (5) (6) (7) (8) (9)
IB,t−1 −0.026***
(−4.18)
IR,t−1 −0.038***
(−4.47)
IC,t−1 −0.051***
(−5.43)
σMOM,t−1 −0.078***
(−4.14)
IB,t−1·σMOM,t−1 −0.083***
(−5.06)
IR,t−1·σMOM,t−1 −0.123*** −0.103***
(−5.63) (−4.47)
IC,t−1·σMOM,t−1 −0.144*** −0.125***
(−6.30) (−5.23)
FF3 included? No No No No No No No Yes Yes
Adj.R2 0.016 0.018 0.026 0.014 0.022 0.027 0.034 0.040 0.046
Table 2.3 presents OLS-regressions of monthly momentum returns on the interaction of several combinations of lagged crash indicators and lagged annualized momentum volatility over the full sample period from September 1928 to May 2020. In addition to that, model (8) and (9) include Fama and French (1993) risk-factors. The regression framework is set up as follows:
rMOM,t=α+γ·Ij,t−1+δ·Ij,t−1·σMOM,t−1+η·σMOM,t−1+λ·X~t−1+t
rMOM,tandσMOM,t−1denote monthly momentum returns and the annualized momen-tum volatility of the preceding 126 daily momenmomen-tum returns, respectively. Ex-ante crash indicatorsjare depicted byIj,t−1. In addition to that,X~t−1andtstate a vector of lagged Fama and French (1993) risk-factors and the monthly residuals. Stars indicate significance at the 10% (*), 5% (**) and 1% (***) level,t-values are stated in parentheses.
high.20 To examine whether these findings are robust to common risk factors, the last two models add Fama and French (1993) factors. For both indicators,IR,t−1andIC,t−1, coefficients andt-values only slightly decrease (in absolute terms) andIC,t−1 continues to exhibit the highest predictive
20See Campbell and Thompson (2008). Even in-sample regressions do not exceed R2= 1.35% (their Table 2).
power. We thus findIC,t−1 to effectively isolate momentum crashes from momentum bull markets.
To illustrate why beta adds information, Panel A of Fig. 2.4 plots cu-mulative momentum returns in contrast to 2-year market returns. High-lighted areas of both panels begin when momentum starts to recover and end when the 2-year market return (or beta) recognizes that the momentum crash is over (i.e. changes sign). A closer look at the years 2008 to 2010 reveals highly positive returns prior to momentum crashes.
According to the bear-market indicator (which is solely based on 2-year market returns), the crash period would not only include the crash but also a large proportion of preceding positive returns. Moreover, the 2-year market return remains negative until September 2010, whereas momen-tum already starts to recover in October 2009. In contrast, the rebound indicator (IR,t−1) additionally incorporates 1-month market returns and is thus capable of separating crashes from the preceding rise. However, IR,t−1 still fails to isolate momentum crashes from the beginning recovery (as 2-year-market returns remain negative until late 2010). In Panel B, the market return is replaced by momentum beta, which recognizes the recovery in March 2010, six months earlier than the 2-year market return.
The reasoning is simple. In contrast to the 2-year market return, beta estimates are based on the previous six months and therefore show a faster response to market changes.
To examine the information content of beta in more detail, we perform a simple regression of momentum volatility on the contemporaneous and
Fig. 2.4:Isolation of Crash Periods
−0.5 0.0 0.5 1.0 1.5 2.0 2.5
2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Value
Mkt2Y Raw Momentum
Panel A: Momentum Returns and Bear Markets (2000:01−2020:05)
−2.0
−1.5
−1.0
−0.5 0.0 0.5 1.0 1.5 2.0 2.5
2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Value
Momentum Beta Raw Momentum
Panel B: Momentum Returns and Beta (2000:01−2020:05)
Fig. 2.4 opposes cumulative momentum returns over the period from January 2000 to May 2020 to 2-year market returns (Panel A) and momentum beta (Panel B). Highlighted areas mark the period from the beginning of momentum recovery to the point when 2-year market returns and beta change signs. At the beginning of each month, beta is estimated by a simple regression of the 126 preceding daily momentum returns on the CAPM.
lagged beta, respectively
σMOM,τ =α+γ·βMOM,t+t,
whereτis eithertort+ 1. Table 2.4 shows that both the contemporaneous and the lagged beta add information, suggesting that beta predicts future momentum volatility. More precisely, a decrease of beta by one unit in-creases contemporaneous (future) momentum volatility by economically and statistically significant 7.6 (7.2) percentage points.
Table 2.4:The Information Content of Beta
Dependent Variable Independent Variables
α βMOM,t R2
σMOM,t 0.190 −0.076*** 0.157
(t-value) (54.14) (−14.34)
σMOM,t+1 0.190 −0.072*** 0.143
(t-value) (53.54) (−13.57)
Table 2.4 presents results for OLS-regressions of momentum volatility on the contempo-raneous and lagged momentum beta over the full sample period from September 1928 to May 2020, respectively:
σMOM,τ=α+γ·βMOM,t+t,
whereτis eithertort+ 1. At the beginning of each month, beta is estimated by a simple rolling regression of the 126 preceding daily momentum returns on the standard market model. Momentum volatility is calculated as the realized volatility of the 126 daily momentum returns preceding the start of the current month. Stars indicate significance at the 10% (*), 5% (**) and 1% (***) level,t-values are stated in parentheses.