Definition
CAGR
CAGR is the compound annual growth rate — the constant yearly rate that links a starting value to an ending one. Definition, formula, and what it hides.
CAGR, the compound annual growth rate, is the constant annual rate that would take a starting value to an ending value over a given period. It is a geometric mean, which is why it differs from a simple average of yearly returns: a +50% year followed by a −50% year averages 0% arithmetically but produces a CAGR of −13.4%, and the second figure is the one the account actually experienced.
- Also known as
- compound annual growth rate · annualised return
How it is calculated
CAGR = (Ending value ÷ Beginning value)^(1 ÷ Years) − 1
Geometric mean, not arithmetic: a +50% year followed by a −50% year
is an arithmetic mean of 0% and a CAGR of −13.4%.
Worked example: $10,000 growing to $26,533 over 10 years → (26,533 ÷ 10,000)^(1/10) − 1 = 10.3% CAGR.
Geometric, because losses compound too
Arithmetic averages describe a set of numbers; geometric means describe a path through them. Since each year’s return applies to the balance the previous year left behind, a large loss permanently shrinks the base that everything after it compounds on. CAGR captures that; an average of annual percentages does not.
It says nothing about the ride
Two strategies with an identical 20% CAGR can differ by a factor of three in maximum drawdown and by years in time-to-recovery. CAGR is a summary of endpoints and is blind to everything between them, which is exactly the part that determines whether a strategy is holdable.
How it gets misread
CAGR is frequently quoted for accounts that received deposits during the period, which silently counts savings as investment return. Growth from contributions and growth from performance are different claims, and combining them inflates the figure by however much was paid in.
Sources
- Geometric or Arithmetic Mean: A Reconsideration — Financial Analysts Journal (author copy, Boston University)
- Global Investment Performance Standards (GIPS) for Firms 2020 — CFA Institute
- COBS 4.6 Past, simulated past and future performance (non-MiFID provisions) — Financial Conduct Authority (FCA Handbook)
Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.
Definitions are the easy part
Knowing what drawdown means is not the same as having a system that halts on it. QANTERION applies these limits while a strategy runs.