TBI Momentum Portfolio Calculator — Jegadeesh & Titman (1993)

Upload Stock Data

▶ What data do I need?

Monthly stock returns expressed as percentages. A return of 1.52 means +1.52% that month.

Wide format (recommended): First column = date (YYYY-MM), remaining columns = one per stock ticker. Each cell = that stock's return in that month.

\[ r_{i,t} = \frac{P_{i,t} - P_{i,t-1}}{P_{i,t-1}} \times 100 \]

Minimum: 10 tickers & 15 months. Ideal: 30+ tickers & 60+ months for robust decile sorts.

If you only have prices, tick the price checkbox below and the app will auto-compute returns. — Jegadeesh & Titman (1993), CRSP monthly return data.

CSV Format

My data is in prices (auto-convert to returns)

Click or drag & drop a CSV file

Wide format: Date | STK1 | STK2 | … (monthly returns in %)

Or Use Sample Data

Load 40 synthetic stocks × 120 months with a built-in momentum factor — explore all features without uploading data.

Risk Factor Data (optional — for CAPM/FF3/Carhart alpha)

▶ What are risk factors & why do I need them?

Risk-adjusted alpha tests whether momentum profits survive controlling for known risk factors. Three models:

CAPM: \(\alpha = \bar{R}_{WML} - \hat{\beta}\cdot\overline{MktRF}\)
Fama-French 3F: adds SMB + HML factors
Carhart 4F: +MOM factor. Significant alpha here = strategy beats priced momentum.

\[ \alpha = \bar{R}_{WML,t} - (\hat{\beta}_1 MktRF_t + \hat{\beta}_2 SMB_t + \hat{\beta}_3 HML_t + \hat{\beta}_4 MOM_t) \]

Ideal: Alpha still significantly > 0 after Carhart = unexplained excess return from the momentum strategy.

Kenneth French Data Library — Fama & French (1993); Carhart (1997).

Upload a monthly factor CSV with columns: date, mktrf, smb, hml, mom (Kenneth French Data Library format accepted). Dates must overlap with your stock data.

Click to upload factor CSV

Download from Kenneth French Data Library — use the "Fama/French 3 Factors" file. For Carhart add the "Momentum Factor (Mom)" column.

Data Requirements

Minimum 10 stocks (for decile sort)
Minimum 15 months of data
Monthly frequency (returns in %)
First column = date (YYYY-MM or YYYY-MM-DD)
Remaining columns = stock tickers
Missing values (blank cells) are handled — stock excluded for that month
Longer series → more J-K cells with sufficient observations

Wide format example:

Date,AAPL,MSFT,AMZN,…
2020-01,1.52,-0.83,3.27,…
2020-02,-2.10,1.44,-0.91,…

Portfolio Construction Options

▶ How does the JT momentum strategy work?

At each month s, rank all stocks by their cumulative return over the past \(J\) months. Buy the top decile (Winners), short the bottom decile (Losers), skip 1 month, hold for \(K\) months. Repeat for every month, creating overlapping cohorts.

\[ WML_t = \bar{R}_{W,t} - \bar{R}_{L,t} \]

where \(\bar{R}_{W,t}\) = equal-weighted return of winner portfolio in month \(t\).

Key insight: 16 strategy variants (J∈{3,6,9,12} × K∈{3,6,9,12}) are computed simultaneously. The 6-6 and 12-3 strategies typically show the strongest momentum in developed markets.

Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers. Journal of Finance, 48(1), 65–91.

Skip-month between formation and holding

▶ Why skip a month?

Without skip, the holding period immediately follows formation. Stocks tend to reverse in the immediate next month due to bid-ask bounce — not real momentum, just microstructure noise.

Standard: Skip = 1 (JT recommendation). Set to 0 only if deliberately studying short-term effects.

Jegadeesh (1990). Evidence of predictable behavior of security returns. Journal of Finance, 45(3).

Portfolio cutoff (ranking groups)

▶ Decile vs Quintile

Decile (top/bottom 10%) replicates the original JT methodology. Quintile (top/bottom 20%) is better for small universes where a decile would contain only 1–2 stocks per cohort.

When to use quintile: fewer than ~30 stocks per period. When to use decile: 30+ stocks — this is the academic standard from JT (1993).

Note: All 16 J-K strategies (J ∈ {3,6,9,12} × K ∈ {3,6,9,12}) are computed simultaneously. Formation = lookback ranking period. Holding = months to hold the portfolio. Overlapping portfolios use the exact Jegadeesh & Titman (1993) approach.

Advanced Options (Phase 4)

Exclude January Effect
Removes January months from the reported WML statistics (but not from formation ranking). Tests whether momentum is driven by January seasonality.

▶ Why does January matter?

The January effect: abnormal January returns, especially for loser stocks (tax-loss selling in Dec, buying back in Jan). If WML is large with January but collapses without it, momentum is partly a seasonal artifact.

If WML stays significant after removing January: momentum is real. If it collapses: January is driving your results.

Jegadeesh & Titman (1993), Table VI; Roll (1983) on the January effect.

Round-Trip Transaction Cost (basis points)

▶ What is a basis point and how is TC applied?

1 basis point (bps) = 0.01%. A round-trip cost of 50bps = 0.5% for buying + selling each rebalancing.

Applied as \(TC/K\) drag per held month (since overlapping portfolios share rebalancing costs across K months):

\[ WML_{\text{net}} = WML_{\text{gross}} - \frac{TC_{\text{bps}}}{100 \times K} \text{ (per month)} \]

Typical realistic TC: 20–50bps round-trip for institutional equity. At 50bps with K=6 → 0.083%/month drag. Momentum becomes less profitable at very high TC.

0bps (0.00%)

Applied as TC ÷ K drag per holding month (overlapping rebalancing). E.g. 50bps round-trip with K=6 → 0.083%/month WML drag.

Sub-Period Analysis

Split the sample at a year to test whether momentum persists across sub-periods. Both halves must have enough data (≥48 months each).

Split year

Phase 5 — Advanced Robustness

Fama-MacBeth Cross-Sectional Regression

Each month, regress individual stock returns on their past J-month momentum signal. The average slope (γ) tests whether past performance cross-sectionally predicts future returns — independent of portfolio grouping. t-statistics use Newey-West correction.

Bootstrap / Permutation Significance Test

Shuffles the time order of monthly returns N times (destroying autocorrelation while preserving cross-sectional co-movement). Reports the empirical fraction of shuffled WML means that exceed the actual WML — a non-parametric p-value that doesn't assume normality.

No. of Bootstrap Iterations

Sector-Neutralised Momentum

Ranks stocks within each sector separately (top/bottom quintile per sector), then combines the sector-relative winner and loser pools. Controls for the possibility that momentum is simply due to sector-level performance differences.

Upload sector mapping CSV

Columns: ticker, sector

Phase 6 — Behavioural Adjustments

Alternative Momentum Signal

Replace the raw formation-period return with a behaviourally-motivated signal, then re-run the full 4×4 portfolio engine on that signal.

Signal Type

MAX / Lottery filter (Bali et al. 2011)

Exclude if max monthly return > %

Market-State Conditioning

Splits WML results by UP vs DOWN market (prior 36-month equal-weighted market return). Momentum is typically much stronger in UP markets (Cooper et al. 2004).

Crash Risk Statistics

Computes skewness, excess kurtosis, max monthly loss, max gain, and crash months (WML < mean − 2σ) for all 16 J-K strategies. Momentum strategies are known to have strong negative skewness (Daniel & Moskowitz 2016).

Sentiment Conditioning

Splits WML by high vs low investor sentiment months (above/below median). Momentum is typically stronger in high-sentiment periods when overreaction is largest (Baker & Wurgler 2006).

Upload sentiment index CSV

Columns: date (YYYY-MM), sentiment

Methodology Summary

Sort stocks at each month s by their cumulative return over the past J months (formation period).
Assign deciles — top 10% = Winner portfolio (W), bottom 10% = Loser portfolio (L) for that cohort.
Skip 1 month (optional) to avoid short-term reversal from bid-ask bounce.
Hold for K months — track equal-weighted return of each cohort's W and L portfolios for the next K months.
Overlap — at each month t, the portfolio simultaneously holds 1/K portions from the K most recent formation cohorts.
WML = Winner − Loser (zero-cost long-short). Monthly time series then tested with Newey-West HAC t-statistics (up to K lags).

Reference: Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.

J-K Portfolio Return Matrix

Show t-statistics

▶ How to read this table

Rows = J (formation period), Columns = K (holding period). Each cell shows the average monthly WML return for that J-K strategy.

\[ WML_{t} = \bar{R}_{\text{Winner},t} - \bar{R}_{\text{Loser},t} \]

Stars indicate Newey-West significance: *** p<0.01 ** p<0.05 * p<0.10. The t-stat below each value uses HAC standard errors with up to K lags to correct for autocorrelation from overlapping portfolios.

What to look for: Positive WML (blue) + significant stars = momentum strategy profitable in that period. The 6-6, 9-3, 12-3 cells are typically the strongest. Negative WML (red) = return reversal.

Jegadeesh & Titman (1993); Newey & West (1987) for HAC standard errors.

View:

*** p<0.01 ** p<0.05 * p<0.10 · Newey-West HAC t-statistics · Values = % per month

Run the analysis first (Strategy tab → Run).

Sub-Period Comparison

▶ Why split the sample?

Robustness check: if momentum is genuine, it should appear in both halves of the sample independently. If it only holds in one sub-period, results may be sample-specific.

Good result: WML positive and significant in both sub-periods. Weak result: momentum only in pre-split half → may have disappeared post-crisis.

WML mean return (%) per sub-period. Significant cells (p<0.05) are blue. Compare with full-sample results above.

Factor Alpha — All J-K Strategies

▶ What is factor alpha & why does it matter?

Alpha (α) = the intercept from regressing WML returns on risk factor returns. It is the portion of WML that cannot be explained by loading on known risk factors.

\[ \alpha = \mathbb{E}[WML_t] - \hat{\beta}_1 \mathbb{E}[MktRF_t] - \hat{\beta}_2 \mathbb{E}[SMB_t] - \hat{\beta}_3 \mathbb{E}[HML_t] \]

CAPM α significant: momentum not explained by market beta. Carhart α significant: momentum exceeds even the priced momentum factor — strongest evidence of genuine alpha.

Fama & French (1993); Carhart (1997); Newey & West (1987).

Alpha = intercept from OLS regression of WML on risk factors. Newey-West t-stats displayed.

Fama-MacBeth Cross-Sectional Regression Results

▶ What is a Fama-MacBeth regression?

Each month, run a cross-sectional OLS of next-period returns on momentum signals (and controls). Average the monthly slope coefficients γ over time.

\[ r_{i,t+1} = \gamma_{0,t} + \gamma_{1,t} \cdot \text{Mom}_{i,t} + \varepsilon_{i,t+1} \]

Test \(\bar{\gamma}_1 = 0\) using the time-series standard deviation of \(\hat{\gamma}_{1,t}\). This is cross-sectional confirmation that stocks with higher past returns earn higher future returns.

Positive, significant γ₁ = strong cross-sectional momentum. Compare magnitude across J values (3m, 6m, 9m, 12m).

Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium. Journal of Political Economy, 81(3), 607–636.

γ = average cross-sectional slope of next-month return on J-month momentum signal. Positive and significant γ confirms momentum cross-sectionally.

Bootstrap Permutation p-values — WML

▶ What is bootstrap / permutation testing?

A non-parametric significance test. Instead of assuming normal returns, the time stamps of the return matrix are randomly shuffled many times (≥500). If the actual WML is larger than 95% of shuffled WMLs, p < 0.05 — no normality needed.

\[ p_{\text{perm}} = \frac{\#\{|WML_{\text{shuffle}}| \geq |WML_{\text{actual}}|\}}{B} \]

Bootstrap p < 0.05 AND NW t-stat significant = double confirmation momentum is not noise. Especially useful for non-normal return distributions.

Empirical (non-parametric) p-values from 500 permutations. Fraction of |shuffled WML| ≥ |actual WML| — no normality assumed.

Sector-Neutralised WML Returns

▶ What is sector-neutral momentum?

Standard momentum may simply reflect sector rotation (e.g., buying tech winners and shorting energy losers). Sector-neutral momentum ranks stocks within each sector — so winners and losers come from the same sector, eliminating cross-sector bets.

If sector-neutral WML is still significantly positive: momentum is a genuine within-sector anomaly, not just sector rotation. If it collapses: most of the gross momentum was cross-sector.

Grundy & Martin (2001). Understanding the nature of risks and the source of rewards to momentum investing. Review of Financial Studies, 14(1).

Stocks ranked within each sector (top/bottom quintile). Tests if momentum is driven by cross-sector effects.

Behavioural Signal: WML Returns

▶ What are behavioural momentum signals?

Instead of raw past return, an alternative behavioural signal is used for portfolio sorting. This tests which bias drives momentum:

Volatility-scaled: \(\text{Signal} = R_J / \sigma_J\) — loss aversion makes investors avoid high-vol stocks.
52-week high: \(P_t / \max(P_{t-12m:t})\) — anchoring to past peaks causes under-reaction.
CGO: \((P_t - \bar{P}_{t-36m})/\bar{P}_{t-36m}\) — disposition effect causes delayed selling of winners.

If behavioural signal WML > raw WML: that bias is amplifying momentum. Compare the 4×4 tables side-by-side to spot differences across J-K cells.

Alternative signal 4×4 WML table. Compare with the main raw-return results to isolate the behavioural component.

Market-State Conditioning — WML in UP vs DOWN Markets

▶ What is market-state conditioning?

This splits results by whether the prior 36-month equal-weighted market return was positive (UP) or negative (DOWN) at each formation date.

Cooper et al. (2004): momentum WML is strongly positive in UP markets (herding amplified) and near zero or negative in DOWN markets (trend-chasers exit, momentum crashes). Significant difference = state-dependent momentum.

Cooper, M., Gutierrez, R., & Hameed, A. (2004). Market states and momentum. Journal of Finance, 59(3), 1345–1365.

WML means and NW t-stats split by preceding 36-month market return. Cooper et al. (2004) find momentum significantly positive in UP markets, near zero or negative in DOWN markets.

Crash Risk Statistics

▶ Understanding skewness and kurtosis

Skewness measures asymmetry. A skewness of −1 means the distribution has a fat left tail — occasional large losses are more likely than large gains of equal size.

\[ \text{Skew} = \frac{n}{(n-1)(n-2)} \sum_t \left(\frac{WML_t - \bar{WML}}{\hat{\sigma}}\right)^3 \]

Excess kurtosis > 0 = fatter tails than a normal distribution. Crash months = months where WML < mean − 2σ.

Daniel & Moskowitz (2016): momentum has the most negative skewness of all common factors (−2 to −3). This means momentum strategies can "crash" violently when markets reverse. A good strategy should have skewness close to 0.

Daniel, K., & Moskowitz, T. (2016). Momentum crashes. Journal of Financial Economics, 122(2), 221–247.

Skewness < 0 = left tail; Kurtosis > 0 = fat tails. Crash months = months where WML < mean − 2σ.

Sentiment Conditioning — High vs Low Sentiment Periods

▶ What is investor sentiment?

Investor sentiment = aggregate optimism/pessimism in the market, measured by indices such as the Baker-Wurgler (2006) index (IPO activity, closed-end fund discounts, NYSE turnover, dividend premium).

In high-sentiment periods, investors extrapolate trends more aggressively → winners keep winning longer. Short-selling constraints also prevent correction of overpriced losers.

Expected finding (Baker & Wurgler 2006): WML stronger in high-sentiment periods. Low-sentiment WML may be near zero or negative (investors are already cautious; less trend-chasing).

Baker, M., & Wurgler, J. (2006). Investor sentiment and the cross-section of stock returns. Journal of Finance, 61(4), 1645–1680.

WML split by investor sentiment (above/below median). Baker & Wurgler (2006): momentum tends to be stronger in high-sentiment environments.

Colour intensity = magnitude of WML return. Blue = positive momentum, red = reversal.

J-K	WML%	Ann.%	t-stat	p-val	Sharpe	Max DD	Win%	N
Run analysis to see results.

How to Use

Upload Stock Returns (Data Tab) — Wide CSV: rows = months (YYYY-MM), columns = tickers, values = % monthly return. Min 10 tickers & 15 months. Or click Load Sample Dataset. Supports wide or long format.
Configure Strategy (Strategy Tab) — Choose skip-month (1 recommended), cutoff (decile for >30 stocks; quintile for smaller datasets). Expand Advanced Options for January effect, TC drag, sub-period split, and Phase 5 tools. Click ▶ Run.
View Risk-Adjusted Alpha — Upload Fama-French factor data (Data Tab), then switch View in Results: CAPM α / FF3 α / Carhart α. Computes OLS regression with Newey-West t-stats.
Read Results (Results Tab) — WML, Winner, Loser 4×4 tables. Blue cells = p<0.05. Hover cells for full stats. Also shows sub-period, bootstrap, FM, and sector-neutral result cards when triggered.
Explore Charts (Tab 4) — Bar chart, Winner-Loser comparison, cumulative return (select strategies), WML distribution, 12-month rolling WML.
Export (Tab 5) — CSV full results, LaTeX table, Word document (.doc), ready-made APA methods paragraph. All client-side; no data sent anywhere.

Phase 5 Features Explained

Fama-MacBeth Cross-Sectional Regression

Each month, run a cross-sectional OLS of all stocks' next-month return on their past J-month return signal. Average the monthly slope γ over time. A positive, significant γ (Newey-West t-stat) confirms momentum at the individual stock level — not just in sorted portfolio groups. This avoids arbitrary decile cut-offs. Output: γ, t, p, avg R², N months.

Bootstrap / Permutation Significance

Randomly shuffles the time order of monthly returns (destroying autocorrelation, preserving cross-sectional co-movement) N times. Each shuffle re-runs the full momentum engine. The empirical p-value = fraction of |shuffled WML means| ≥ |actual WML mean|. Makes no normality assumption; robust to fat tails and non-stationarity. Choose N = 200 (fast), 500 (recommended), or 1000 (precise).

Sector-Neutral Momentum

Winners and losers are ranked within each sector (top/bottom quintile per sector) then pooled across sectors. Momentum that persists after sector-neutralisation cannot be explained by sector rotation alone. Upload a ticker, sector CSV (or use Load Sample Sectors). Requires ≥6 stocks per sector per period.

Interpreting Results

What does a positive WML mean?

A positive WML return means momentum is present — past winners continue to outperform past losers over the holding period. According to Jegadeesh & Titman (1993), this is evidence of medium-term momentum (3–12 months). Values of 0.5–1.5% per month are typical in developed markets.

Why does WML vary across J-K?

Short formation periods (J=3) may capture noise, while long holding periods (K=12) can dilute the signal. The classic finding is that 6-6 and 12-3 tend to have the strongest, most significant WML in U.S. data. Reversal (negative WML) at very short horizons is due to bid-ask bounce.

Why Newey-West t-statistics?

Overlapping portfolios introduce autocorrelation in the WML time series (K adjacent portfolios share observations). Standard OLS t-statistics are too large in this case. Newey-West HAC (Heteroskedasticity and Autocorrelation Consistent) standard errors correct for this, using up to K lags in the Bartlett kernel — exactly as done in the original JT paper.

Skip-month — why does it matter?

Without skip-month, the holding period immediately follows formation, which captures the short-term reversal documented by Jegadeesh (1990) — a known anomaly driven by microstructure effects (bid-ask bounce, infrequent trading). Skipping 1 month ensures the strategy measures genuine medium-term momentum, not microstructure.

Key References

Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.

Jegadeesh, N. (1990). Evidence of predictable behavior of security returns. The Journal of Finance, 45(3), 881–898.

Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57–82.

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.

Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708.

Typical Results (Literature)

Strategy	Typical WML%/m	Notes
3-3	0.6–1.0%	Short-term
6-6	0.9–1.3%	Classic JT
12-3	1.0–1.5%	Strong signal
12-12	0.7–1.1%	Dilutes later

Source: Jegadeesh & Titman (1993), U.S. stock data 1965–1989.