Rolling Returns vs CAGR

Monday morning. A friend forwards a fund brochure with the headline "18 percent CAGR since 2018". Same fund. Same NAV today. Start the clock in 2018 and you get one number. Start in 2020, off the COVID base, and the CAGR roughly doubles. Start in 2021, after the post-pandemic rally had already done most of the lifting, and the same fund quotes a CAGR that is barely half the headline. All three numbers are arithmetically correct. The brochure prints the one that flatters the line.

That is what a point-to-point CAGR actually is. A chosen story. Start date plus end date plus the number that falls out. Change the start date by a year and the story changes by hundreds of basis points.

Rolling returns is the same fund evaluated across every Monday you could have started on. Not one window. Hundreds of overlapping ones. NIFTY 50 TRI, monthly start dates from 2002 to today, rolling 5Y CAGR. Around 230 windows. The worst 5Y window came in at minus 1.2 percent CAGR. The 5th percentile at 3.6. The median sits at 12.8. The 75th percentile at 16.9. The best 5Y window at 22.4. Same index, 23 percentage points of spread depending on which Monday a real person walked in. The brochure shows you the 14 percent long-run number. The rolling distribution shows you the regime risk the brochure is averaging over.

So three questions I now run before I trust a CAGR. Which window did you pick and why this one. What does the rolling 5Y distribution look like, particularly the worst window, because that is what a bad Monday actually felt like. And does the fund beat its benchmark in more than half of all rolling windows, not the one window that ended up on the marketing pdf.

A CAGR is a sentence. A rolling distribution is the paragraph. Read the paragraph before you sign the cheque