4.3 Evidence: momentum, reversal and crashes

Motivation

The swing frameworks claim that strength persists. Academic finance has tested that claim more thoroughly than almost any other. The answer is: yes on 3–12 month horizons, across many markets and asset classes; no on one-week to one-month horizons, where returns reverse; and the persistence has crashes that are predictable in timing but not in size.

Reading guide

The evidence in 4.3.1–4.3.6 is for every reader: it is the empirical basis of the swing frameworks in 4.2 and of Playbooks 15.1–15.2. The decompositions and proofs (the Lo–MacKinlay decomposition of momentum profits and the momentum-beta argument behind crashes) are advanced and can be skipped on a first reading; keep their conclusions.

4.3.1Cross-sectional momentum#

Jegadeesh and Titman (1993) formed "J/K" portfolios. Each month, rank all stocks by their past $J$ -month return ( $J=3,6,9,12$ ). Buy the top decile (winners) and sell the bottom decile (losers). Hold for $K$ months ( $K=3,6,9,12$ ), with overlapping portfolios so that each month's position is the average of the last $K$ formation cohorts. Later work skips the most recent month between formation and holding to avoid the one-month reversal (4.3.3). Their abstract reports that strategies buying past winners and selling past losers "generate significant positive returns over 3- to 12-month holding periods", that the profits are not due to systematic risk or delayed reactions to common factors, and that part of the abnormal return in the first year dissipates over the following two years.

The longest-sample summary is in Daniel and Moskowitz's NBER working paper (w20439, 2014; published in the Journal of Financial Economics in 2016). For US stocks over 1927:01–2013:03, using top-minus-bottom deciles of past 12-month return, they report: winner-decile excess return 15.3% a year, loser-decile −2.5%, market 7.6%; Sharpe ratio of the winner-minus-loser (WML) portfolio 0.71 against 0.40 for the market; WML beta −0.58 and CAPM alpha 22.3% a year ( $t=8.5$ ).

Why can sorting on past returns earn money? The next result separates the sources.

Proposition 4.6Lo–MacKinlay decomposition

Let $N$ assets have returns $r_t\in\mathbb R^N$ with mean vector $\mu$ and lag-1 autocovariance matrix $\Gamma_1=\mathbb E[(r_{t-1}-\mu)(r_t-\mu)^\top]$ . Let $\bar r_t=\frac1N\mathbf 1^\top r_t$ and use the relative-strength weights $w_{i,t}=\frac1N(r_{i,t-1}-\bar r_{t-1})$ , which sum to zero (a dollar-neutral long–short portfolio). Its profit $\pi_t=\sum_i w_{i,t}r_{i,t}$ has

\mathbb E[\pi_t]=\underbrace{\frac{N-1}{N^2}\operatorname{tr}\Gamma_1}_{\text{own autocovariance}}\;-\;\underbrace{\frac1{N^2}\big(\mathbf 1^\top\Gamma_1\mathbf 1-\operatorname{tr}\Gamma_1\big)}_{\text{cross-autocovariance}}\;+\;\underbrace{\sigma^2_\mu}_{\text{dispersion of means}}, \tag{4.6}

where $\sigma^2_\mu=\frac1N\sum_i(\mu_i-\bar\mu)^2$ .

Proof

$\pi_t=\frac1N\sum_i r_{i,t-1}r_{i,t}-\bar r_{t-1}\bar r_t$ , since $\sum_i\bar r_{t-1}r_{i,t}/N=\bar r_{t-1}\bar r_t$ . Take expectations: $\mathbb E[r_{i,t-1}r_{i,t}]=(\Gamma_1)_{ii}+\mu_i^2$ and $\mathbb E[\bar r_{t-1}\bar r_t]=\frac1{N^2}\mathbf 1^\top\Gamma_1\mathbf 1+\bar\mu^2$ . So $\mathbb E[\pi_t]=\frac1N\operatorname{tr}\Gamma_1-\frac1{N^2}\mathbf 1^\top\Gamma_1\mathbf 1+\frac1N\sum_i\mu_i^2-\bar\mu^2$ . The last two terms are $\sigma^2_\mu$ . Write $\frac1N\operatorname{tr}\Gamma_1-\frac1{N^2}\mathbf 1^\top\Gamma_1\mathbf 1=\frac{N-1}{N^2}\operatorname{tr}\Gamma_1-\frac1{N^2}(\mathbf 1^\top\Gamma_1\mathbf 1-\operatorname{tr}\Gamma_1)$ .∎

Three distinct stories hide in (4.6). Positive own-autocovariance (each stock trends) helps. Positive cross-autocovariance (one stock's return predicts another's, a lead–lag effect) hurts a relative-strength strategy. And even with no predictability at all ( $\Gamma_1=0$ ), the strategy earns $\sigma^2_\mu$ : past winners tend to be stocks with higher unconditional means. That third term is risk premium, not timing, and it does not vanish with publication. Problem 4.6 applies (4.6) to a two-stock example.

4.3.2Time-series momentum#

Moskowitz, Ooi and Pedersen (2012) studied each asset against its own past instead of against other assets. For 58 liquid futures and forwards (equity indices, currencies, commodities, bonds) over 1985–2009, the sign of an asset's past 12-month excess return predicts its return over the next 1 to 12 months, with partial reversal at longer horizons, and the strategy does best in extreme markets. Their trading rule takes position $\operatorname{sign}(R_{t-12,t})\cdot 40\%/\hat\sigma_t$ in each asset, where $\hat\sigma_t$ is an ex-ante (lagged, exponentially weighted) volatility estimate, so each asset contributes similar risk. The AQR website posts their original data.

Time-series momentum is Proposition 4.2 with $w_i=1$ for $i<12$ months and a sign nonlinearity. Its profit has a drift part ( $\mu^2$ terms) and an autocovariance part. Unlike cross-sectional momentum it can be net long or net short the whole market, which is why it tends to profit in prolonged bear markets such as 2008.

4.3.3Short-term reversal#

On horizons of a week to a month, individual stock returns reverse: last month's losers outperform last month's winners next month (Jegadeesh 1990; Lehmann 1990). The usual interpretation is liquidity provision. Investors who need to trade fast push prices away from value, and whoever takes the other side is paid to absorb the order flow. Two consequences for this module:

Momentum strategies skip the most recent month, otherwise the reversal partly cancels the momentum.
Reversal profits are concentrated in small, illiquid stocks and are largely consumed by bid–ask spreads and impact. "RSI below 30, buy" in small caps is a reversal trade whose gross edge must beat the costs of 4.4.4 and M05.

4.3.4Momentum crashes#

Momentum's return distribution is negatively skewed, and its worst months cluster. Daniel and Moskowitz's working paper lists the worst WML months over 1927–2013. The two worst were consecutive: July 1932 (−60.98%) and August 1932 (−74.36%). Three of the ten worst came from 2009: March (−42.28%), April (−45.52%) and August (−30.54%). In every case the market had fallen hard over the prior two years and then rose sharply in the crash month. Over July–August 1932 the market rose 82%, the winner decile 32% and the loser decile 232%. Over March–May 2009 the market rose 26%, winners 8% and losers 163%. The crash is the short side "crashing up".

Proposition 4.7momentum's beta has the sign of the past market return

Over a formation window let each stock's cumulative return be $R_i=\beta_iR_m+e_i$ , where across stocks $\beta_i$ has mean $\bar\beta$ and variance $\sigma^2_\beta$ , $e_i$ has mean 0 and variance $\sigma_e^2$ , and $\beta_i$ , $e_i$ are uncorrelated given the market path. Then the cross-sectional linear projection of beta on past return is

\hat{\mathbb E}[\beta_i\mid R_i]=\bar\beta+\frac{\sigma^2_\beta R_m}{\sigma^2_\beta R_m^2+\sigma^2_e}\,(R_i-\bar\beta R_m), \tag{4.7}

so winners (high $R_i$ ) have above-average beta when $R_m>0$ and below-average beta when $R_m<0$ . After a bear market the WML portfolio has beta $\beta_W-\beta_L<0$ : it is short the market.

Proof

Across stocks, $\operatorname{Cov}(\beta_i,R_i)=\operatorname{Cov}(\beta_i,\beta_iR_m+e_i)=\sigma_\beta^2R_m$ and $\operatorname{Var}(R_i)=\sigma_\beta^2R_m^2+\sigma_e^2$ . The linear projection is $\bar\beta+\frac{\operatorname{Cov}}{\operatorname{Var}}(R_i-\mathbb E R_i)$ with $\mathbb E R_i=\bar\beta R_m$ . The slope has the sign of $R_m$ . Winners have $R_i$ above the mean, so their projected beta exceeds $\bar\beta$ iff $R_m>0$ . Losers are the reverse.∎

In early 2009 the loser decile held stocks that had fallen 84% on average from their peaks (Citigroup, Bank of America, Ford, GM and International Paper are named in the paper). Those were the highest-beta, most levered firms. When the market turned, WML lost not only its negative beta times the market's 26% rise, but much more. A levered firm's equity is a call option on its assets (Merton's model; see M08), so losers' upside beta exceeds their downside beta. Daniel and Moskowitz describe the short side in panic states as "similar to shorting call options". Their remedy is to forecast WML's mean and variance from bear-market indicators and ex-ante volatility, and scale exposure accordingly. They report that this dynamic strategy approximately doubles the alpha and Sharpe ratio of static momentum, and that across all their markets and asset classes it delivers an annualised Sharpe ratio of 1.18. Barroso and Santa-Clara (2015) propose the simpler constant-volatility scaling.

4.3.5Evidence for India#

IIMA factor library. The Indian Institute of Management Ahmedabad publishes Indian Fama–French–momentum factors (market, size SMB, value HML, momentum WML) built from CMIE Prowess data, in survivorship-bias-adjusted daily, monthly and yearly files (Agarwalla, Jacob and Varma, IIMA working paper 2013-09-05). The 2025-12 release covers October 1993 to December 2025. Its page reports the annualised geometric mean return of WML since 1 January 1994 as 10.65%, and −5.53% for calendar year 2025 to date at that release (fetched 6 Nov 2026). This is the natural dataset for replicating 4.3.1 on Indian stocks (Problem 4.15).
NSE momentum indices. NSE Indices publishes momentum strategy indices, for example the Nifty200 Momentum 30, which select stocks by a volatility-adjusted momentum score. I could not reach niftyindices.com to verify the current methodology document, so read it there before using the index as a benchmark.
A simple Indian implementation. Rank a universe such as the BSE 500 by trailing 12-month return, hold the top 10–12 equally weighted, rebalance monthly after the close on the last trading day.

4.3.6Practitioner notes#

Momentum is well documented, but it is crowded and it crashes. A swing trader running breakout systems on Indian mid-caps is long the same factor and should expect losses at the turns of bear markets, exactly when the stop-loss discipline is tested.
The skip month matters in India too. Large one-month moves in small caps often reverse.
After costs, the edge is in holding periods of weeks to months, not days. That matches the swing horizon.