Glossary & References

Definitions of technical terms used throughout this study, plus academic citations and data sources.

Statistical Terms

TermDefinitionIn Plain English
Beta coefficient (β) The estimated effect size from a regression — how much daily return changes (in percentage points) when a given condition is present vs. absent. The size of the effect we're measuring. For example, β = +0.10% means the market goes up an extra 0.10% per day when the condition holds.
βrun (Run-up coefficient) The regression coefficient on the 'run-up' dummy variable, measuring excess return in the 5 trading days before a payday, after controlling for known calendar effects. How much extra (or less) the market moves in the 5 days leading up to a payday, compared to normal days.
Block bootstrap A resampling method (Politis & Romano 1994) that preserves the time-series structure of the data by resampling in blocks rather than individual observations. A way to check our results by reshuffling the data in chunks (not individual days), which preserves the realistic pattern of calm and stormy market periods.
FDR (False Discovery Rate) Benjamini-Hochberg (1995) procedure that controls the expected proportion of false positives when running many statistical tests simultaneously. When you run 100 tests, about 5 will look significant by pure luck. FDR adjusts for this, so findings that survive are less likely to be flukes.
GARCH Generalized Autoregressive Conditional Heteroskedasticity. A model that explicitly captures the tendency of stock market volatility to cluster — periods of high volatility follow high volatility, and calm follows calm (Engle 1982, Bollerslev 1986). A statistical model that handles the fact that the stock market has calm weeks and stormy weeks, rather than pretending volatility is constant.
HAC Heteroskedasticity and Autocorrelation Consistent. A statistical method that adjusts standard errors to account for the fact that stock returns have changing volatility and are slightly correlated from day to day. A correction that makes our tests more honest by accounting for the messiness of real market data.
Monte Carlo permutation test A distribution-free significance test that shuffles the dates randomly thousands of times and checks whether the real pattern is more extreme than what random dates produce. We scramble the calendar dates randomly 500+ times and check: does the real payday calendar produce a stronger pattern than random dates? If yes, it's probably not coincidence.
Newey-West Standard Errors A specific HAC estimator (Newey & West, 1987) that uses a weighted average of lagged covariances to produce robust standard errors. A way to calculate how confident we can be in our numbers, designed specifically for financial data that doesn't behave like textbook examples.
OLS (Ordinary Least Squares) The most common regression method. Finds the line of best fit by minimizing the sum of squared errors between predicted and actual values. The standard way to draw a 'best fit line' through data points and measure how much each factor matters.
p-value The probability of seeing results at least this extreme if there were no real effect (null hypothesis is true). Conventionally, p < 0.05 is considered statistically significant. How likely it is that the pattern we found is just random noise. Lower = more likely to be real. Below 0.05 (5%) is the standard bar.
Parkinson volatility A range-based volatility estimator using the daily high and low prices: sqrt((1/4ln2) · ln(H/L)²). More efficient than close-to-close volatility (Parkinson 1980). A measure of how wild the market swings within a single day, calculated from the high and low price.
q-value (FDR-adjusted p-value) The smallest FDR level at which a test would be deemed significant. A q-value of 0.10 means at most 10% of findings at this threshold are expected to be false. A stricter version of the p-value that accounts for running many tests at once.
Welch t-test A two-sample t-test that does not assume equal variances. Compares the mean of one group to the mean of another. A basic statistical test that asks: is the average return on 'payday window' days meaningfully different from the average on other days?

Market & Finance Terms

TermDefinitionIn Plain English
401(k) plan A tax-advantaged retirement savings plan offered by employers, where employees contribute a percentage of each paycheck. Created by the Revenue Act of 1978, first plans appeared in 1980. Current assets exceed $7 trillion. The retirement savings account where a portion of each paycheck automatically goes into stock/bond investments. The money flows from millions of paychecks into the stock market on a predictable schedule.
Clearing lag The delay between when a paycheck is issued and when the 401(k) contribution from that paycheck is actually invested in the stock market. Typically 3–7 business days due to ERISA processing, recordkeeper settlement, and mutual fund NAV pricing. Your 401(k) money doesn't hit the market the day you get paid. It takes about a week to travel from your paycheck through your employer, to Fidelity/Vanguard, and into actual stock purchases.
Close-to-High ratio (C2H) (Close − Low) / (High − Low). Measures where the closing price sits within the day's range. C2H = 1 means close at the high; C2H = 0 means close at the low. Did the market close near the top or bottom of its daily range? A high ratio means buying pressure pushed prices up by end of day.
Directional ratio (DR) (Close − Open) / (High − Low). Measures the net intraday direction relative to the day's total range. Positive = bullish intraday drift. Did the market go up or down during the trading day? Positive means it opened low and closed high (buyers were winning).
FOMC Federal Open Market Committee. The Federal Reserve committee that sets interest rate policy. Meets ~8 times per year. Lucca & Moench (2015) documented a +25–50bp drift in stocks in the 24 hours before announcements. The group at the Federal Reserve that decides interest rates. The stock market tends to go up slightly right before their announcements.
OpEx (Options Expiration) The third Friday of each month when standard monthly options contracts expire. Creates predictable hedging flow as market makers unwind delta and gamma positions. The day each month when stock options expire. This forces specific buying/selling by the firms that sell options, creating predictable market activity.
Semi-monthly pay schedule A payroll schedule with two paydays per month, typically the 15th and the last day of the month. Used by approximately 19% of US private-sector workers, predominantly salaried/white-collar employees. Getting paid twice a month, on the 15th and the last day. Common for salaried office workers.
TSP (Thrift Savings Plan) The federal government's equivalent of a 401(k), available to military and civilian federal employees. Managed by a single recordkeeper, making contribution flow highly concentrated and predictable. ~$800B in assets. The military and government version of a 401(k). Because it all goes through one system, the money flow is even more predictable than private-sector 401(k)s.
Turn-of-month effect A documented market anomaly where stock returns are disproportionately concentrated in the last trading day of the month and first three trading days of the next month (Ariel 1987, Lakonishok & Smidt 1988). Stocks tend to go up slightly more at the turn of each month. Researchers have known about this since the 1980s.

Academic References

  1. Ariel, R. A. (1987). A monthly effect in stock returns. Journal of Financial Economics, 18(1), 161–174. DOI
  2. Lakonishok, J. & Smidt, S. (1988). Are seasonal anomalies real? A ninety-year perspective. Review of Financial Studies, 1(4), 403–425. DOI
  3. Ogden, J. P. (1990). Turn-of-month evaluations of liquid profits and stock returns: A common explanation for the monthly and January effects. Journal of Finance, 45(4), 1259–1272. JSTOR
  4. French, K. R. (1980). Stock returns and the weekend effect. Journal of Financial Economics, 8(1), 55–69. DOI
  5. Cross, F. (1973). The behavior of stock prices on Fridays and Mondays. Financial Analysts Journal, 29(6), 67–69. DOI
  6. Rozeff, M. S. & Kinney, W. R. (1976). Capital market seasonality: The case of stock returns. Journal of Financial Economics, 3(4), 379–402. DOI
  7. Ariel, R. A. (1990). High stock returns before holidays: Existence and evidence on possible causes. Journal of Finance, 45(5), 1611–1626. DOI
  8. Lucca, D. O. & Moench, E. (2015). The Pre-FOMC Announcement Drift. Journal of Finance, 70(1), 329–371. DOI
  9. Newey, W. K. & West, K. D. (1987, 1994). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix (1987); Automatic lag selection in covariance matrix estimation (1994). Econometrica, 55(3), 703–708; Review of Economic Studies, 61(4), 631–653. DOI (1987) DOI (1994)
  10. Benjamini, Y. & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, 57(1), 289–300. DOI
  11. Politis, D. N. & Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association, 89(428), 1303–1313. DOI
  12. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. DOI
  13. McLean, R. D. & Pontiff, J. (2016). Does Academic Research Destroy Stock Return Predictability? Journal of Finance, 71(1), 5–32. DOI
  14. Carhart, M. M., Kaniel, R., Musto, D. K. & Reed, A. V. (2002). Leaning for the tape: Evidence of gaming behavior in equity mutual funds. Journal of Finance, 57(2), 661–693. DOI
  15. Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987–1007. DOI
  16. Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press. ISBN 978-0691043012. Publisher

Data Sources

SourceDataUsage
Yahoo Finance ^GSPC (S&P 500), BTC-USD (Bitcoin) Daily OHLCV price data, 1960–2026. Primary dataset for all return calculations, volatility measures, and calendar-effect regressions.
BLS Current Employment Statistics Pay frequency distribution by industry Payroll schedule breakdowns (weekly, biweekly, semi-monthly, monthly) used to model when 401(k) contributions enter the market.
ERISA regulations 401(k) contribution timing rules Legal framework governing the maximum delay between payroll deduction and plan investment, used to calibrate the clearing-lag window.
Payday-Effect Research Study Data: S&P 500 (^GSPC) via Yahoo Finance, 1960–2026