Research Findings
Insights
Lump Sum vs. Dollar-Cost Averaging: What 24,747 Starting Days Say
July 13, 2026Tested every possible starting day in the S&P 500 since 1927: invest a lump sum all at once, or spread it out over a fixed window. Investing all at once wins about 6 times out of 10 over a year, more often over longer windows, but spreading it out gives a measurably smoother ride, and wins more often right after the market has run up a long way. Includes an interactive calculator.
What 517 Series Tell You: Fat Tails Are Universal, and So Are Data Artifacts
July 12, 2026Running the same statistical tests across 502 stocks, 5 indices, and 10 Treasury/credit series confirms fat tails everywhere, but also surfaces a quieter finding: the most "extreme" stocks by the numbers usually aren't extreme at all, they're data artifacts from mergers and spinoffs.
Nearly a Century of S&P 500 Returns: The Normal Distribution Doesn't Fit
July 12, 2026Daily S&P 500 returns since 1927 are far from normally distributed, with heavier tails, negative skew, and a return profile shaped disproportionately by a handful of extreme days. What that means for anyone modeling market risk.