Annualized Return (CAGR)
A way to restate returns earned over different holding periods on a common one-year basis. CAGR is the most common form, expressing that annualized figure as a compound growth rate.
Formula
CAGR = (ending value / starting value) ^ (1 / years) − 1 // LDBD's primary metric annualizes the directional log return, then averages it a = g / holding_years (g = directional log return) rate = Σa / (n + 100) × 100 (n = resolved predictions, K=100 is the smoothing prior)
Which is better: making 5% in a month, or 20% spread over three years? You cannot tell from the raw percentages, because the time spans differ. Annualizing solves this by translating every return into "what it would have been over a full year."
CAGR (Compound Annual Growth Rate) is the version of annualizing that assumes compounding. It answers what steady yearly rate would have produced the same end result. Unlike a simple arithmetic average, which just adds up the yearly returns and divides by their count, CAGR folds all the ups and downs into one smooth growth rate.
One caveat: annualizing a short window can inflate the number dramatically. A 5% monthly gain compounded for a full year works out to nearly 80%, but that pace rarely holds. So treat any annualized figure as sitting on top of an "if this rate continued" assumption.
Example
Say you made +5% in a single month (about 1/12 of a year). Annualized, that is (1.05)^12 − 1 ≈ +79.6%. A +20% return spread over three years is (1.2)^(1/3) − 1 ≈ +6.3% — which makes clear the monthly gain was on a far steeper trajectory.
How LDBD uses it
LDBD's headline leaderboard metric (rate) rests on exactly this idea. To rank a one-day call against a one-year call on the same scale, each prediction's return has to be put on an annual basis. LDBD annualizes the directional log return rather than using plain CAGR, averages it across a predictor's history, and applies Bayesian smoothing (K=100) so a small sample cannot spike the score. You can see how the ranking shakes out on the leaderboard.
FAQ
How is CAGR different from a simple (arithmetic) average return?
An arithmetic average just adds up yearly returns and divides, which overstates real performance for volatile assets. CAGR reflects compounding — it works back from "what you actually ended up with" to an annual growth rate — so it is more honest for comparing multi-year results.
Why does annualizing a short period make the number so large?
Annualizing assumes the rate keeps compounding for a full year. A 5% monthly gain compounded twelve times approaches 80%, but that pace rarely persists, so read it as an illustrative figure rather than a promise.