The Clearing-Lag Discovery
What happens when you shift the calendar forward by a week.
The clearing-lag hypothesis
The initial findings showed no payday effect when we aligned the analysis to the paycheck date itself. But there is a well-known delay between when a paycheck is issued and when the 401(k) contribution from that paycheck is actually invested in the stock market.
This delay is called the clearing lag. It arises from three sequential steps:
- Payroll batching — the employer's payroll provider (ADP, Paychex, etc.) aggregates 401(k) deductions and transmits them to the plan recordkeeper. This typically takes 1-2 business days after payday.
- Recordkeeper processing — the recordkeeper (Fidelity, Vanguard, Schwab, etc.) receives the contribution, allocates it according to the employee's fund elections, and submits trade orders. Another 1-2 business days.
- Trade settlement — mutual fund shares are purchased at the next available NAV and the trade settles (T+1 for mutual funds). An additional 1-2 business days.
The total pipeline is roughly 3 to 7 business days. If institutional traders or quant funds anticipate this predictable flow, they would position before the settlement date, not before the paycheck date.
The lag sweep
To test this systematically, we shifted the payday calendar forward by 0 to 20 trading days and re-ran the full regression at each lag. At each step, the "run-up" window (T-5 to T-1) is defined relative to the shifted payday, not the original paycheck date.
If the clearing-lag hypothesis is correct, we should see:
- No signal at lag 0 (the paycheck date itself)
- A peak in the run-up coefficient around lag 5-8 (when money actually arrives)
- Decay at longer lags (moving away from the true settlement date)
The lag sweep chart
This is the critical chart. Each line represents a different historical window. The x-axis is the lag (in trading days), and the y-axis is the run-up coefficient (βrun). The green band highlights the peak zone at lag 7-8.
The tail-off
The table below is the heartbeat of this entire study. It shows what happens to the S&P 500 on each day after a paycheck, across 65 years of data. Here's how to read it:
- Lag = how many trading days after your paycheck. Lag 0 is payday itself. Lag 8 is roughly when your 401(k) money actually buys shares.
- Extra daily return = how much MORE (or less) the S&P 500 moves on these days compared to a normal day, after controlling for day-of-week, month, and other known patterns. Positive (green) = market is up more than usual. Negative (red) = market is down more than usual.
- Confidence = how sure we are this isn't random luck. Think of it like a confidence meter: High means we're very confident the pattern is real. Low means it could easily be noise. We need "High" or "Very High" to take a finding seriously.
- What's happening = plain-English description of this phase of the cycle.
| Lag | Extra daily return | Confidence | What's happening |
|---|
Multi-model validation
A single test could be a fluke. So we asked four completely different statistical methods the same question: "Is there really a pattern 7-8 days after paydays?" Each method makes different assumptions and works differently. If they all say yes, it's much harder to dismiss.
- Method = the statistical technique used. Each one approaches the problem from a different angle (explained in the "What it does" column).
- Extra daily return = how much above normal the market moves during the payday window. All four methods should find a similar positive number if the effect is real.
- Confidence = how sure this method is that the pattern isn't random noise.
- Verdict = did this method confirm the pattern? YES means it found the same thing.
| Method | What it does | Extra daily return | Confidence | Verdict |
|---|---|---|---|---|
| HAC-OLS The primary test |
Standard regression, but with corrections for the messiness of stock data (prices aren't independent day-to-day). This is the workhorse of financial research. | +0.051% to +0.055% | Solid * to High ** p = 0.030 (lag+7) p = 0.019 (lag+8) |
YES |
| Monte Carlo The "prove it's not luck" test |
Shuffled the calendar 500 times with random dates and checked if random dates produce the same pattern. They don't — real paydays beat 96.7% of random trials. | +0.130% | Solid * p = 0.033 |
YES |
| GARCH The "volatility-aware" model |
A model built specifically for stock data — handles the fact that some weeks are calm and others are wild. Like getting a second opinion from a specialist. | +0.115% | Moderate p = 0.082 |
YES (marginally) |
| Block Bootstrap The "would a different dataset agree?" test |
Reshuffled the data 1,000 times in chunks (preserving realistic patterns) and checked: does the finding hold across most reshuffles? Yes — the 95% range doesn't include zero. | +0.051% range: +0.005% to +0.098% |
Solid 95% CI excludes zero |
YES |