Ch 5.3 — Reader’s Guide: Jegadeesh & Titman (1993)

Paper. Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance, 48(1), 65–91.¹

Yesterday’s two Reader’s Guides put a price on risk. Fama–French (1992) said the cross-section of average returns lines up with size and book-to-market, not with CAPM beta; Fama–French (1993) turned those patterns into tradable factor portfolios. Both papers are, at heart, efficient-markets papers: returns differ across stocks because the stocks carry different bundles of priced risk. Today’s paper is the one that broke that story open. Jegadeesh and Titman take a strategy a 16-year-old day-trader would invent on a napkin — buy the stocks that went up, short the ones that went down — and show it makes money, robustly, for decades, in a way the risk factors of the day could not explain. Sam, our markets-and-momentum student, has been waiting all week for this one.

This is the paper that named momentum. It matters not because the strategy is exotic — it is almost insultingly simple — but because of what its success implies. If a rule this dumb beats the market after you adjust for known risk, then either there is a risk factor nobody had written down, or prices are not impounding information the way the efficient-markets hypothesis says they do. Thirty years later we still argue about which. That unresolved argument is exactly why this paper is on the syllabus: it is a clean, replicable anomaly that forces you to take a side and defend it with evidence.

We read it the professional way — tables first, in a deliberate order, hunting for where the result could break before we let ourselves believe it. The fixed Reader’s-Guide anatomy from the Week 5 reading pack drives the sections below.

1. Research question

The plain-English question: do past winners keep winning? Take a stock’s return over the past few months — say the past six. Sort all stocks by that past return. Do the ones near the top (the winners) go on to earn higher returns over the next few months than the ones near the bottom (the losers)? If yes, then past returns predict future returns at intermediate horizons, and a strategy of buying winners and shorting losers should be profitable.

The horizon is the whole game. Jegadeesh and Titman are precise about it: they study 3-to-12-month formation and holding periods. This is deliberately wedged between two horizons where the opposite pattern was already known. At very short horizons (a week, a month) returns tend to reverse — last week’s losers bounce back — a pattern attributable partly to bid-ask bounce and short-run overreaction. At long horizons (3–5 years) De Bondt and Thaler had documented long-run reversal: past long-term losers outperform past long-term winners.² Momentum lives in the medium-horizon gap between these two reversals: continuation for a few months to a year, then eventual reversal. Pinning the result to that specific window is part of why the paper is credible — it is not “stocks trend forever,” it is “stocks trend for 3–12 months and then unwind.”

The implication is the title’s second half: implications for stock market efficiency. Recall the weak-form efficient-markets hypothesis (EMH) from Week 1’s framing of “what is a finding”: prices already reflect all information in past prices, so past returns should carry no usable signal about future returns. A profitable rule built only from past returns is a direct strike at weak-form efficiency. So the paper has a methodological burden it cannot dodge: it must show the profits are not just compensation for risk. If buying winners is really just loading up on some risk factor, then there is no anomaly — you are being paid for bearing danger, exactly as efficiency predicts. The authors therefore spend much of the paper trying to kill their own result with risk adjustment, and reporting that it survives.

2. Identification strategy

There is no instrument and no natural experiment here. The “identification” is the portfolio construction, and reading the paper means understanding that construction cold.

The J/K sort. Fix two numbers: a formation (or ranking) period of J months and a holding period of K months. At the end of each month t:

Compute each stock’s cumulative return over the past J months (months t-J+1 through t).
Sort all stocks on that past return and split into ten deciles. The top decile is the winner portfolio W; the bottom decile is the loser portfolio L.
Hold an equal-weighted position in each decile for the next K months, then re-sort.

The headline trade is the zero-cost winner-minus-loser portfolio: go long the winners and short the losers in equal dollar amounts. Long and short legs cancel in cost, so the net investment is (notionally) zero and the return is a pure spread, r^{W} - r^{L}. A positive average spread is the momentum profit. The paper reports a grid of these spreads over a J \times K menu — formation periods of 3, 6, 9, 12 months crossed with holding periods of 3, 6, 9, 12 months — sixteen strategies in one table. The classic, the one everyone quotes, is 6/6: rank on six months, hold six months.

The overlapping-holding-period trick — and why it complicates inference. Here is the move that makes the methodology efficient and also makes the statistics subtle. If you held a 6-month portfolio and only re-balanced every six months, you would get one fresh, non-overlapping return observation every half-year — throwing away five-sixths of your months. Instead, Jegadeesh and Titman form a new winner-minus-loser portfolio every month and hold each for K months. So in any given month you hold K overlapping cohorts at once — the one formed this month, last month, … back K-1 months — and your reported monthly return is the equal-weighted average across those overlapping cohorts. This is sometimes called the overlapping-portfolio or calendar-time construction. It uses every month of data and smooths the estimate.

The price you pay is serial correlation in the return series you then test. Because consecutive monthly returns share K-1 of their K component cohorts, adjacent observations are mechanically correlated even if the true underlying signal were i.i.d. This is exactly the overlapping-observations problem we built in Week 2. When you regress an overlapping series on a constant to test whether its mean differs from zero, the usual OLS / i.i.d. standard error is too small: it assumes independent observations you do not have, so it overstates your effective sample size and inflates the t-statistic. The fix is the one from Ch 2.4: a heteroskedasticity-and-autocorrelation-consistent (HAC) standard error — Newey–West — with the lag truncation set to at least K-1 to absorb the induced autocorrelation. When you read this paper’s t-statistics, the first question a referee asks is: did they correct the standard errors for the overlap, or are these naive t-stats on overlapping data? (The paper’s own returns are computed as averages across cohorts, which dampens but does not eliminate the issue; modern replications report Newey–West t-stats as a matter of course.)

A second design choice worth flagging: many momentum implementations skip the most recent week or month between formation and holding — rank on months t-6 through t-1, say, and start holding at t+1 — to dodge the short-horizon reversal and bid-ask bounce that would otherwise contaminate the winner/loser definitions. [CHECK] the exact skip convention used in JT93’s main tables versus later momentum papers; the one-month skip is more strongly associated with later work, so attribute carefully.

3. Data

The dataset is CRSP monthly returns — the Center for Research in Security Prices file, the same return tape Fama–French use, restricted in the paper to NYSE and AMEX common stocks. (Nasdaq’s broad coverage on CRSP arrives later, which is one reason early momentum work leans on NYSE/AMEX.)

The sample period is 1965–1989 — twenty-five years of monthly data. That gives roughly 300 monthly formation dates, each spawning a decile sort over hundreds to a couple thousand eligible stocks.

The J/K grid is the data object you will spend the most time on: J \in \{3,6,9,12\} formation months crossed with K \in \{3,6,9,12\} holding months. Equal-weighted decile portfolios (each stock counts the same, not value-weighted), with the overlapping monthly re-formation described above. For our notebook we will swap in modern CRSP and extend the sample forward — and you should expect the magnitudes to shift, because the post-1990 period (especially the 2009 “momentum crash”) is unkind to the strategy.

4. Table-by-table reading order

A professional does not read this paper top to bottom. Here is the order that gets you to the truth fastest.

First: the J \times K returns matrix. This is the heart of the paper — a single table of average monthly winner-minus-loser spreads across the sixteen formation/holding combinations, with t-statistics. Read it as a surface. Three things to check before anything else:

Sign and significance of the diagonal. Are the spreads positive and significant across the grid, especially at 6/6, 9/9, 12/3? The qualitative finding is that medium-horizon momentum profits are positive and on the order of roughly 1% per month for the classic 6/6 strategy — a big number, annualized. Describe it as order-of-magnitude ~1%/month; do not quote a specific decimal from memory. [CHECK] the exact 6/6 figure against the table.
Where it strengthens and weakens. Longer formation periods paired with longer holding periods start to show the profit decaying — the seed of the long-run reversal story.
Are these t-stats overlap-corrected? Hold this question; it governs how much of the significance you believe (see §2).

Second: the risk-adjustment table. Having shown raw spreads are positive, the authors ask whether risk explains them. They adjust returns for market exposure (CAPM beta) and report that winners are not meaningfully riskier than losers — if anything the beta and size differences run the wrong way to rescue efficiency. The momentum alpha survives the risk controls available in 1993. Read this table asking: what risk model is being used, and what is left unexplained? (The honest answer, from later work, is that the standard factor models of the era cannot price momentum — which is why a dedicated momentum factor, UMD/WML, eventually gets bolted onto the Fama–French machinery you saw in Ch 5.2.³)

Third: the sub-period and seasonality robustness. Two checks here. (a) Sub-periods: split the sample in half and confirm the profit is not driven by one lucky decade. (b) Seasonality — the crucial one: break the profits out by calendar month, because the size/value anomalies of the era were famously concentrated in January. Momentum has the opposite January problem: the strategy tends to lose money in January (losers — often beaten-down small caps — bounce hard in January) while earning its keep in the other eleven months. Reading this table tells you the profit is not a January artifact; it is an anti-January effect, which is harder to dismiss.

Last (optional): the longer-horizon / post-holding behavior. Evidence that the medium-horizon profits eventually reverse if you hold long enough — reconciling momentum with De Bondt–Thaler long-run reversal and hinting at the overreaction interpretation.

5. What’s clever

The strategy design is brutally simple and that is the point. There is no parameter to tune beyond J and K, no firm characteristic to construct, no accounting data to clean. You need only past returns — the one input the weak-form EMH swears is useless. A simple rule that works is far more damaging to a theory than a complicated one, because there is nowhere to hide a degree of freedom. Sam should sit with this: the elegance is the evidence.

The overlapping-portfolio trick squeezes the data. Re-forming every month and averaging across K overlapping cohorts turns a data-poor design (one independent 6-month return every six months) into a data-rich monthly series, and the cohort-averaging itself smooths idiosyncratic noise. It is a genuinely good idea — provided you then respect the serial dependence it creates when you do inference. The cleverness and the vulnerability are the same coin.

Framing momentum as an efficiency anomaly, not just a trading tip. The authors could have stopped at “here is a strategy that makes money.” Instead they pre-empt the obvious rebuttal — you are just being paid for risk — by running the risk adjustment themselves and showing the profit is not beta in disguise. By doing the skeptic’s work first, they shift the burden: now the defender of efficiency has to name the missing risk factor. That rhetorical move, doing your critic’s job before they can, is the mark of a paper built to survive.

6. What’s vulnerable

This is where a referee earns their keep. Five live threats:

Transaction costs — does the profit survive trading? This is the first and biggest. Momentum is a high-turnover strategy: every month you re-rank and trade a fresh slice of the portfolio, and the losers you short are disproportionately small, illiquid, low-priced stocks with wide bid-ask spreads — the most expensive names to trade. A gross spread of ~1%/month can be eaten alive by round-trip costs, the short-sale costs of borrowing hard-to-borrow losers, and price impact. The paper engages this, but the honest verdict from later work is contested: net profitability shrinks substantially and, by some accounts of the short leg in small caps, can vanish. Any claim of momentum profits must be quoted net of a credible cost model — which is precisely the exercise PS 5.3 forces.

Data-snooping (Week 1’s multiple testing). Sixteen J \times K cells is sixteen strategies. If you stare at a 4 \times 4 grid and crown the most significant cell, you have run sixteen tests and reported the winner — a textbook multiple-comparisons problem (Ch 1.5; revisited under FDR in Ch 8.2 and the pre-analysis-plan discussion in Ch 7.3). A single t = 2.5 means much less when it is the maximum over sixteen correlated tries. The mitigating facts here are real and worth crediting: the result is not one isolated cell but a broad region of the grid, it was predicted ex ante by the overreaction literature, and it has since replicated out of sample — other countries, asset classes, and the decades after 1989. Out-of-sample survival is the strongest answer to a snooping charge, and momentum has it. Still, the reader should mentally Bonferroni-discount any single starred cell.

The January / seasonality effect. Even though momentum is an anti-January phenomenon, the seasonality cuts both ways as a vulnerability: a strategy whose entire annual profit depends on eleven months minus a January loss is exposed to anything that shifts that seasonal pattern (tax-loss selling rule changes, the rise of index investing). The seasonal structure is a clue to mechanism, not a clean robustness check you can wave away.

Risk-based vs. behavioral interpretation — genuinely unresolved. Even granting the profits are real and net-positive, why do they exist? The behavioral camp says investors underreact to news (prices drift toward fundamentals slowly) and later overreact (the eventual long-run reversal). The risk-based camp says momentum loads on some priced, time-varying macro risk — and the spectacular 2009 momentum crash (when beaten-down losers rocketed in the recovery and the short leg blew up) is exhibited as evidence that momentum carries crash risk you are compensated for. JT93 cannot adjudicate this; it predates the evidence on both sides. A careful reader reports the anomaly and labels the interpretation as open.

Overlapping-portfolio inference (Week 2, again). If the paper’s t-statistics do not correct for the K-1 induced autocorrelation, they are overstated. This does not erase a t of, say, 6, but it can sink a marginal one. The first thing to recompute in replication is Newey–West t-stats with lag \geq K-1.

7. Three replication exercises

These point at nb5.3 (the momentum backtest) and feed PS 5.3. Pin your CRSP snapshot date per the conventions and keep licensed data on GMU infrastructure.

Exercise 1 — Rebuild the J \times K grid and report it honestly. On CRSP monthly NYSE/AMEX (then optionally add Nasdaq), construct equal-weighted decile winner-minus-loser portfolios for all sixteen J,K \in \{3,6,9,12\} combinations using the overlapping monthly-reformation method. Report the average monthly spread for each cell with two standard errors side by side: naive i.i.d. and Newey–West with lag = K-1. The deliverable is a table that makes the §2 inference point visible — show how much the t-statistics shrink once you respect the overlap. Confirm 6/6 is positive and ~1%/month order of magnitude over a window near the original sample; do not expect to match a textbook decimal.

Exercise 2 — The transaction-cost critique (the PS 5.3 core). Take your 6/6 gross series and layer on a cost model: a per-side bid-ask + commission charge applied to the turnover each month (the fraction of the portfolio that actually trades on re-ranking), plus a separate, larger cost on the short leg to proxy borrow fees, and a sensitivity dial for the small-cap losers. Plot net momentum profit as a function of round-trip cost in basis points, and find the break-even cost at which the strategy’s net alpha hits zero. Write the one-paragraph verdict: at realistic costs, does momentum survive — and which leg kills it? This is the exercise that turns “anomaly” into “tradable or not.”

Exercise 3 — Out-of-sample and the snooping defense. Re-estimate the 6/6 strategy in rolling, non-overlapping sub-periods across the full modern sample (e.g., 1965–1989 in-sample versus 1990–present out-of-sample), explicitly including the 2009 crash window. Report the spread, the worst drawdown, and the January-versus-rest-of-year decomposition in each era. The point is to let Sam see both the multiple-testing rebuttal (does the effect persist outside the original grid and sample?) and the crash-risk story (how brutal is the tail?) in one figure. Tie the write-up back to the risk-vs-behavioral debate of §6.

Referee questions

If this manuscript landed on your desk, you would write back:

Are the reported t-statistics corrected for the serial correlation induced by overlapping holding periods? Please report Newey–West standard errors with lag length at least K-1 alongside the originals, and tell us how much the inference changes.
What is the strategy’s profit net of realistic transaction and short-sale costs, separately for the long and short legs? Given that the losers are disproportionately small, illiquid, low-priced stocks, a gross-return result is not yet an efficiency violation.
How do you rule out data-snooping across the sixteen J \times K cells, and can you commit to an out-of-sample test? A predicted, broad-region effect that survives in post-sample data and other markets is far more convincing than the single most-starred cell of the grid.

Next: open nb5.3 and rebuild the grid. The moment your Newey–West t-stats print next to the naive ones, you will understand why Week 2 came before Week 5.

Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Journal of Finance, 48(1), 65–91.↩︎
De Bondt, W. F. M., & Thaler, R. (1985). Does the Stock Market Overreact? Journal of Finance, 40(3), 793–805.↩︎
Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. Journal of Finance, 52(1), 57–82.↩︎

# Ch 5.3 — Reader's Guide: Jegadeesh & Titman (1993) > **Paper.** Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. *Journal of Finance*, 48(1), 65–91.[^jt93] [^jt93]: Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. *Journal of Finance*, 48(1), 65–91. Yesterday's two Reader's Guides put a price on *risk*. Fama–French (1992) said the cross-section of average returns lines up with size and book-to-market, not with CAPM beta; Fama–French (1993) turned those patterns into tradable factor portfolios. Both papers are, at heart, *efficient-markets* papers: returns differ across stocks because the stocks carry different bundles of priced risk. Today's paper is the one that broke that story open. Jegadeesh and Titman take a strategy a 16-year-old day-trader would invent on a napkin — *buy the stocks that went up, short the ones that went down* — and show it makes money, robustly, for decades, in a way the risk factors of the day could not explain. Sam, our markets-and-momentum student, has been waiting all week for this one. This is the paper that named **momentum**. It matters not because the strategy is exotic — it is almost insultingly simple — but because of *what its success implies*. If a rule this dumb beats the market after you adjust for known risk, then either there is a risk factor nobody had written down, or prices are not impounding information the way the efficient-markets hypothesis says they do. Thirty years later we still argue about which. That unresolved argument is exactly why this paper is on the syllabus: it is a clean, replicable anomaly that forces you to take a side and defend it with evidence. We read it the professional way — tables first, in a deliberate order, hunting for where the result could break before we let ourselves believe it. The fixed Reader's-Guide anatomy from the Week 5 reading pack drives the sections below. --- ## 1. Research question The plain-English question: **do past winners keep winning?** Take a stock's return over the past few months — say the past six. Sort all stocks by that past return. Do the ones near the top (the *winners*) go on to earn higher returns over the *next* few months than the ones near the bottom (the *losers*)? If yes, then past returns predict future returns at intermediate horizons, and a strategy of buying winners and shorting losers should be profitable. The horizon is the whole game. Jegadeesh and Titman are precise about it: they study **3-to-12-month** formation and holding periods. This is deliberately wedged between two horizons where the *opposite* pattern was already known. At very short horizons (a week, a month) returns tend to *reverse* — last week's losers bounce back — a pattern attributable partly to bid-ask bounce and short-run overreaction. At long horizons (3–5 years) De Bondt and Thaler had documented *long-run reversal*: past long-term losers outperform past long-term winners.[^dbt] Momentum lives in the medium-horizon gap between these two reversals: continuation for a few months to a year, then eventual reversal. Pinning the result to that specific window is part of why the paper is credible — it is not "stocks trend forever," it is "stocks trend for 3–12 months and then unwind." [^dbt]: De Bondt, W. F. M., & Thaler, R. (1985). Does the Stock Market Overreact? *Journal of Finance*, 40(3), 793–805. The *implication* is the title's second half: **implications for stock market efficiency.** Recall the weak-form efficient-markets hypothesis (EMH) from Week 1's framing of "what is a finding": prices already reflect all information in *past prices*, so past returns should carry no usable signal about future returns. A profitable rule built only from past returns is a direct strike at weak-form efficiency. So the paper has a methodological burden it cannot dodge: it must show the profits are *not* just compensation for risk. If buying winners is really just loading up on some risk factor, then there is no anomaly — you are being paid for bearing danger, exactly as efficiency predicts. The authors therefore spend much of the paper trying to *kill their own result* with risk adjustment, and reporting that it survives. --- ## 2. Identification strategy There is no instrument and no natural experiment here. The "identification" is the *portfolio construction*, and reading the paper means understanding that construction cold. **The J/K sort.** Fix two numbers: a **formation** (or *ranking*) period of $J$ months and a **holding** period of $K$ months. At the end of each month $t$: 1. Compute each stock's cumulative return over the past $J$ months (months $t-J+1$ through $t$). 2. Sort all stocks on that past return and split into ten deciles. The top decile is the **winner** portfolio $W$; the bottom decile is the **loser** portfolio $L$. 3. Hold an equal-weighted position in each decile for the next $K$ months, then re-sort. The headline trade is the **zero-cost winner-minus-loser portfolio**: go long the winners and short the losers in equal dollar amounts. Long and short legs cancel in cost, so the net investment is (notionally) zero and the return is a pure spread, $r^{W} - r^{L}$. A positive average spread is the momentum profit. The paper reports a grid of these spreads over a $J \times K$ menu — formation periods of 3, 6, 9, 12 months crossed with holding periods of 3, 6, 9, 12 months — sixteen strategies in one table. The classic, the one everyone quotes, is **6/6**: rank on six months, hold six months. **The overlapping-holding-period trick — and why it complicates inference.** Here is the move that makes the methodology efficient and also makes the statistics subtle. If you held a 6-month portfolio and only re-balanced every six months, you would get one fresh, non-overlapping return observation every half-year — throwing away five-sixths of your months. Instead, Jegadeesh and Titman form a *new* winner-minus-loser portfolio **every month** and hold each for $K$ months. So in any given month you hold $K$ overlapping cohorts at once — the one formed this month, last month, … back $K-1$ months — and your reported monthly return is the *equal-weighted average across those overlapping cohorts*. This is sometimes called the *overlapping-portfolio* or *calendar-time* construction. It uses every month of data and smooths the estimate. The price you pay is **serial correlation in the return series you then test.** Because consecutive monthly returns share $K-1$ of their $K$ component cohorts, adjacent observations are mechanically correlated even if the true underlying signal were i.i.d. This is *exactly* the overlapping-observations problem we built in Week 2. When you regress an overlapping series on a constant to test whether its mean differs from zero, the usual OLS / i.i.d. standard error is **too small**: it assumes independent observations you do not have, so it overstates your effective sample size and inflates the $t$-statistic. The fix is the one from **Ch 2.4**: a **heteroskedasticity-and-autocorrelation-consistent (HAC)** standard error — **Newey–West** — with the lag truncation set to at least $K-1$ to absorb the induced autocorrelation. When you read this paper's $t$-statistics, the first question a referee asks is: *did they correct the standard errors for the overlap, or are these naive $t$-stats on overlapping data?* (The paper's own returns are computed as averages across cohorts, which dampens but does not eliminate the issue; modern replications report Newey–West $t$-stats as a matter of course.) A second design choice worth flagging: many momentum implementations **skip the most recent week or month** between formation and holding — rank on months $t-6$ through $t-1$, say, and start holding at $t+1$ — to dodge the short-horizon *reversal* and bid-ask bounce that would otherwise contaminate the winner/loser definitions. [CHECK] the exact skip convention used in JT93's main tables versus later momentum papers; the one-month skip is more strongly associated with later work, so attribute carefully. --- ## 3. Data The dataset is **CRSP** monthly returns — the Center for Research in Security Prices file, the same return tape Fama–French use, restricted in the paper to **NYSE and AMEX** common stocks. (Nasdaq's broad coverage on CRSP arrives later, which is one reason early momentum work leans on NYSE/AMEX.) The **sample period is 1965–1989** — twenty-five years of monthly data. That gives roughly 300 monthly formation dates, each spawning a decile sort over hundreds to a couple thousand eligible stocks. The **J/K grid** is the data object you will spend the most time on: $J \in \{3,6,9,12\}$ formation months crossed with $K \in \{3,6,9,12\}$ holding months. Equal-weighted decile portfolios (each stock counts the same, not value-weighted), with the overlapping monthly re-formation described above. For our notebook we will swap in modern CRSP and extend the sample forward — and you should expect the magnitudes to shift, because the post-1990 period (especially the 2009 "momentum crash") is unkind to the strategy. --- ## 4. Table-by-table reading order A professional does not read this paper top to bottom. Here is the order that gets you to the truth fastest. **First: the $J \times K$ returns matrix.** This is the heart of the paper — a single table of average monthly winner-minus-loser spreads across the sixteen formation/holding combinations, with $t$-statistics. Read it as a *surface*. Three things to check before anything else: - *Sign and significance of the diagonal.* Are the spreads positive and significant across the grid, especially at 6/6, 9/9, 12/3? The qualitative finding is that medium-horizon momentum profits are **positive and on the order of roughly 1% per month** for the classic 6/6 strategy — a big number, annualized. Describe it as *order-of-magnitude ~1%/month*; do **not** quote a specific decimal from memory. [CHECK] the exact 6/6 figure against the table. - *Where it strengthens and weakens.* Longer formation periods paired with longer holding periods start to show the profit decaying — the seed of the long-run reversal story. - *Are these $t$-stats overlap-corrected?* Hold this question; it governs how much of the significance you believe (see §2). **Second: the risk-adjustment table.** Having shown raw spreads are positive, the authors ask whether *risk* explains them. They adjust returns for market exposure (CAPM beta) and report that winners are **not** meaningfully riskier than losers — if anything the beta and size differences run the *wrong way* to rescue efficiency. The momentum alpha survives the risk controls available in 1993. Read this table asking: *what risk model is being used, and what is left unexplained?* (The honest answer, from later work, is that the standard factor models of the era cannot price momentum — which is why a dedicated momentum factor, UMD/WML, eventually gets bolted onto the Fama–French machinery you saw in Ch 5.2.[^carhart]) [^carhart]: Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. *Journal of Finance*, 52(1), 57–82. **Third: the sub-period and seasonality robustness.** Two checks here. (a) *Sub-periods*: split the sample in half and confirm the profit is not driven by one lucky decade. (b) *Seasonality* — the crucial one: break the profits out **by calendar month**, because the size/value anomalies of the era were famously concentrated in **January**. Momentum has the *opposite* January problem: the strategy tends to **lose money in January** (losers — often beaten-down small caps — bounce hard in January) while earning its keep in the other eleven months. Reading this table tells you the profit is not a January artifact; it is an *anti*-January effect, which is harder to dismiss. **Last (optional): the longer-horizon / post-holding behavior.** Evidence that the medium-horizon profits eventually *reverse* if you hold long enough — reconciling momentum with De Bondt–Thaler long-run reversal and hinting at the *overreaction* interpretation. --- ## 5. What's clever **The strategy design is brutally simple and that is the point.** There is no parameter to tune beyond $J$ and $K$, no firm characteristic to construct, no accounting data to clean. You need *only past returns* — the one input the weak-form EMH swears is useless. A simple rule that works is far more damaging to a theory than a complicated one, because there is nowhere to hide a degree of freedom. Sam should sit with this: the *elegance* is the evidence. **The overlapping-portfolio trick squeezes the data.** Re-forming every month and averaging across $K$ overlapping cohorts turns a data-poor design (one independent 6-month return every six months) into a data-rich monthly series, and the cohort-averaging itself smooths idiosyncratic noise. It is a genuinely good idea — *provided* you then respect the serial dependence it creates when you do inference. The cleverness and the vulnerability are the same coin. **Framing momentum as an efficiency anomaly, not just a trading tip.** The authors could have stopped at "here is a strategy that makes money." Instead they pre-empt the obvious rebuttal — *you are just being paid for risk* — by running the risk adjustment themselves and showing the profit is not beta in disguise. By doing the skeptic's work first, they shift the burden: now the *defender* of efficiency has to name the missing risk factor. That rhetorical move, doing your critic's job before they can, is the mark of a paper built to survive. --- ## 6. What's vulnerable This is where a referee earns their keep. Five live threats: **Transaction costs — does the profit survive trading?** This is the first and biggest. Momentum is a *high-turnover* strategy: every month you re-rank and trade a fresh slice of the portfolio, and the losers you short are disproportionately small, illiquid, low-priced stocks with wide bid-ask spreads — the *most* expensive names to trade. A gross spread of ~1%/month can be eaten alive by round-trip costs, the short-sale costs of borrowing hard-to-borrow losers, and price impact. The paper engages this, but the honest verdict from later work is contested: net profitability shrinks substantially and, by some accounts of the short leg in small caps, can vanish. **Any claim of momentum profits must be quoted net of a credible cost model** — which is precisely the exercise PS 5.3 forces. **Data-snooping (Week 1's multiple testing).** Sixteen $J \times K$ cells is sixteen strategies. If you stare at a $4 \times 4$ grid and crown the most significant cell, you have run sixteen tests and reported the winner — a textbook multiple-comparisons problem (Ch 1.5; revisited under FDR in Ch 8.2 and the pre-analysis-plan discussion in Ch 7.3). A single $t = 2.5$ means much less when it is the maximum over sixteen correlated tries. The mitigating facts here are real and worth crediting: the result is *not* one isolated cell but a broad region of the grid, it was *predicted ex ante* by the overreaction literature, and it has since replicated **out of sample** — other countries, asset classes, and the decades *after* 1989. Out-of-sample survival is the strongest answer to a snooping charge, and momentum has it. Still, the reader should mentally Bonferroni-discount any single starred cell. **The January / seasonality effect.** Even though momentum is an *anti*-January phenomenon, the seasonality cuts both ways as a vulnerability: a strategy whose entire annual profit depends on eleven months *minus* a January loss is exposed to anything that shifts that seasonal pattern (tax-loss selling rule changes, the rise of index investing). The seasonal structure is a clue to *mechanism*, not a clean robustness check you can wave away. **Risk-based vs. behavioral interpretation — genuinely unresolved.** Even granting the profits are real and net-positive, *why* do they exist? The **behavioral** camp says investors *underreact* to news (prices drift toward fundamentals slowly) and later *overreact* (the eventual long-run reversal). The **risk-based** camp says momentum loads on some priced, time-varying macro risk — and the spectacular **2009 momentum crash** (when beaten-down losers rocketed in the recovery and the short leg blew up) is exhibited as evidence that momentum carries crash risk you are compensated for. JT93 cannot adjudicate this; it predates the evidence on both sides. A careful reader reports the anomaly and labels the interpretation as open. **Overlapping-portfolio inference (Week 2, again).** If the paper's $t$-statistics do not correct for the $K-1$ induced autocorrelation, they are overstated. This does not erase a $t$ of, say, 6, but it can sink a marginal one. The first thing to recompute in replication is Newey–West $t$-stats with lag $\geq K-1$. --- ## 7. Three replication exercises These point at **nb5.3** (the momentum backtest) and feed **PS 5.3**. Pin your CRSP snapshot date per the conventions and keep licensed data on GMU infrastructure. **Exercise 1 — Rebuild the $J \times K$ grid and report it honestly.** On CRSP monthly NYSE/AMEX (then optionally add Nasdaq), construct equal-weighted decile winner-minus-loser portfolios for all sixteen $J,K \in \{3,6,9,12\}$ combinations using the overlapping monthly-reformation method. Report the average monthly spread for each cell **with two standard errors side by side**: naive i.i.d. and **Newey–West** with lag $= K-1$. The deliverable is a table that makes the §2 inference point visible — show how much the $t$-statistics shrink once you respect the overlap. Confirm 6/6 is positive and ~1%/month order of magnitude over a window near the original sample; do not expect to match a textbook decimal. **Exercise 2 — The transaction-cost critique (the PS 5.3 core).** Take your 6/6 gross series and layer on a cost model: a per-side bid-ask + commission charge applied to the *turnover* each month (the fraction of the portfolio that actually trades on re-ranking), plus a separate, larger cost on the short leg to proxy borrow fees, and a sensitivity dial for the small-cap losers. Plot net momentum profit as a function of round-trip cost in basis points, and find the **break-even cost** at which the strategy's net alpha hits zero. Write the one-paragraph verdict: at realistic costs, does momentum survive — and *which leg* kills it? This is the exercise that turns "anomaly" into "tradable or not." **Exercise 3 — Out-of-sample and the snooping defense.** Re-estimate the 6/6 strategy in **rolling, non-overlapping sub-periods** across the full modern sample (e.g., 1965–1989 *in-sample* versus 1990–present *out-of-sample*), explicitly including the 2009 crash window. Report the spread, the worst drawdown, and the January-versus-rest-of-year decomposition in each era. The point is to let Sam *see* both the multiple-testing rebuttal (does the effect persist outside the original grid and sample?) and the crash-risk story (how brutal is the tail?) in one figure. Tie the write-up back to the risk-vs-behavioral debate of §6. --- ### Referee questions If this manuscript landed on your desk, you would write back: 1. **Are the reported $t$-statistics corrected for the serial correlation induced by overlapping holding periods?** Please report Newey–West standard errors with lag length at least $K-1$ alongside the originals, and tell us how much the inference changes. 2. **What is the strategy's profit net of realistic transaction and short-sale costs, separately for the long and short legs?** Given that the losers are disproportionately small, illiquid, low-priced stocks, a gross-return result is not yet an efficiency violation. 3. **How do you rule out data-snooping across the sixteen $J \times K$ cells, and can you commit to an out-of-sample test?** A predicted, broad-region effect that survives in post-sample data and other markets is far more convincing than the single most-starred cell of the grid. > **Next:** open **nb5.3** and rebuild the grid. The moment your Newey–West $t$-stats print next to the naive ones, you will understand why Week 2 came before Week 5.