Time beats amount
Over 40 years, $104k put in became about $475k at the typical start, 4.6x the money. Ten more years roughly doubled the 30 year result of $237k.
Quant study · 100 year backtest
Waiting for the trend line versus buying every paycheck.
Two people earn the same paycheck every two weeks for 100 years. One buys the S&P 500 automatically at whatever the price is. The other holds the cash and buys only when the index is at or below its long run trend line. Same money in, no hindsight. Who ends up with more?
Contributed$260,000$100 × 26 paychecks a year
Bi-weekly buying$34.3M131.8x the money in
Trend line buying$34.6M133.1x the money in
Gain after inflation$34.0MBi-weekly: 7.04% a year after inflation, 10.6% before
Longest wait in cash22 yrs 11 moTrend rule, never bought
01 / Thesis
Small amounts, invested automatically, become large because time does the work.
$100 a paycheck is about 5% of a $2,000 paycheck. Bought every time, at whatever the price, this is what it became after inflation, from every start month since 1871.
What $100 a paycheck became, after inflation
Even the worst start grew
No 30 or 40 year stretch ended below the money put in. The worst 40 year start still finished at $169k. Short horizons are riskier: 12% of 10 year stretches ended below what went in.
Automatic is enough
Buying every paycheck needed no forecast and still matched a rule that waited for cheap prices. Real growth was 7.04% a year after inflation; inflation itself averaged 2.9%.
02 / The two rules
Same paycheck, same market, different trigger.
July 1923 to June 2023, 1,200 months. All figures are in June 2023 dollars, so a dollar in 1923 and a dollar in 2023 buy the same amount.
Bi-weekly automatic buying
Every paycheck is invested the month it arrives, at that month's price. No decisions, never holds cash.
Buy at the trend line
Paychecks pile up as cash. In any month the index is at or below its trend line, all of the cash is invested. Above the line, it waits.
Kept equal
Both get the same $100 paychecks on the same dates, dividends reinvested, no fees or taxes. Leftover cash counts at the end, so nothing is thrown away.
03 / The trend line
The line only knows the past.
The trend is a straight line through the log of the inflation adjusted total return index, so it is the index's long run growth path. It is refitted every month using data from 1871 up to that month only, so the rule never sees the future. Shaded months are buy months.
Jun 2023 (end)S&P 500, real total return (start = 100): 126,608.4Trend line, as known that month: 109,591
The index sat at or below the line in 40% of months. The longest gap between buy months ran 22 years and 11 months, during which rule B kept every paycheck in cash and the pile reached about 422 paychecks.
04 / Growth of each account
Two accounts, same paychecks, one race.
Account value in June 2023 dollars, replayed month by month from July 1923. Teal is bi-weekly buying, gold is trend line buying (cash at 0%), the dashed line is money put in, and the shaded band is the largest fall so far. The axis grows with the accounts while it plays; switch to Log to compare the whole century on one fixed scale. Pause and hover any month to read it.
Jun 2023Bi-weekly: $34,270,058Trend line: $34,612,307Put in: $260,000Gain after inflation: $34,010,058 bi-weeklyTrend line ahead by $342,249
05 / Who is ahead, month by month
The gap is the story, not the totals.
Trend account divided by bi-weekly account. Above 1.00 the trend rule is ahead, below 1.00 it is behind. The gold line gives the waiting cash the 10 year Treasury yield instead of 0%.
Jun 2023 (end)Trend ÷ bi-weekly, cash at 0%: 1.010Trend ÷ bi-weekly, cash at 10y yield: 1.058
Nearly all of the trend rule's lead comes from one episode. It fell to 0.87 in September 1929, after holding every paycheck as cash from late 1926 while the market rose into the 1929 peak, then jumped to 1.15 by September 1931 after buying through the crash. For the next four decades the lead shrank, and after the 1970s the line barely moves because each new paycheck is tiny next to the account. Start the same test in January 1933 instead and the trend rule finishes 9% behind with cash at 0%, and still 3% behind with cash earning the 10 year yield.
06 / Results
What the cash earns decides it.
The trend rule holds cash, so its result depends on what that cash earns. Two bounds: cash in a 0% account, which loses value to inflation, and cash earning the 10 year Treasury yield, which is generous.
Ending value after 100 years
Trend rule versus bi-weekly, by start date
Largest fall in account value
07 / Is it luck of the start date?
Start in a different month and the answer changes.
One 100 year run is a single sample. This repeats the test from every possible start month since the end of 1890 (the first month with 20 years of history behind the line) for each horizon and counts how often the trend rule finished ahead. Below the 50% line, bi-weekly buying won more often.
Share of start dates where the trend rule finished ahead
Holding plain cash, the trend rule finished ahead in only 28% to 41% of start dates, and its worst 20 year window ended with 33% of what bi-weekly buying had. Only when the waiting cash earns the 10 year yield does it win more often than not, and then the typical edge is under 2%.
08 / What it means and what it leaves out
The paycheck rule is hard to beat by waiting.
TakeawayBuying every paycheck matched the trend rule over a century with no decisions, never sat out for two decades, and avoided the start date lottery. Waiting for a cheaper price mostly trades time in the market for a better entry, and over most horizons time won.
Monthly dataShiller's series is monthly averages, so bi-weekly pay is modeled as 26 paychecks a year spread evenly across 12 months, bought at the month's average price.
Data ends June 2023Dividends and inflation in the dataset stop there, so the test stops there rather than mixing in price only data.
One trend definitionA straight line through log prices since 1871. Other lines (moving averages, shorter windows) would trigger differently and are not tested here.
No costs or taxesNo trading costs, taxes, or account limits. These would affect both rules, the trend rule slightly less because it trades less often.