Who this is for — Readers comparing results over different durations who need an equivalent annual growth rate without mistaking it for an average return or a forecast.
The compound annual growth rate (CAGR) is the constant annual rate linking an opening and closing value through compounding. It asks which identical annual growth rate would have produced the observed final ratio. The actual path may contain gains, losses and flat periods; CAGR replaces it with one uniform mathematical equivalent.
For positive opening value Vᵢ, positive closing value
V_f and duration Y in years:
CAGR = (V_f / Vᵢ)^(1 / Y) − 1The ratio must represent a coherent growth process. Two account balances are not sufficient when contributions or withdrawals occurred between them; capital flows are not return. A cash-flow-aware or unitised series must first be constructed.
Compounding: returns multiply
For simple periodic returns r₁, r₂, …, rₙ:
cumulative return = ∏ₜ (1 + rₜ) − 1When intervals are complete, homogeneous years, CAGR is the geometric mean of
gross factors 1+rₜ minus one. With a positive endpoint ratio:
CAGR = exp[ln(V_f / Vᵢ) / Y] − 1These identities show why compounded growth is not the sum or arithmetic mean of percentage returns. A loss reduces the base on which the next return acts.
CAGR is not the arithmetic mean
Suppose a portfolio gains 20% in year one and loses 20% in year two. The arithmetic mean is zero, but 100 becomes 120 and then 96:
100 × 1.20 × 0.80 = 96Cumulative return is −4% and CAGR is approximately −2.02%, not zero. The difference comes from the changing compounding base. Arithmetic mean can still be relevant to other statistical questions, such as a one-period expected return under stated assumptions; it is not realised multi-period growth. Likewise, multiplying an average monthly return by twelve does not generally produce annual compounded return.
Duration, calendar and annualisation
Duration Y is part of the result. Between non-anniversary dates it
may use actual days divided by a disclosed basis or another consistent
convention. Valuation dates, time zone, calendar and leap years can create
small differences; early rounding can magnify them.
Annualisation converts an interval measure into an annual equivalent. For
a compounded return over D days, one convention is:
annual return = (1 + period return)^(annual basis / D) − 1The basis might use calendar days or trading periods, but must be stated. The operation is mathematical, not evidence that the result is repeatable. Annualising a few positive weeks can create an economically unrepresentative number. Within its scope, GIPS requires returns for periods shorter than one year not to be annualised; this illustrates the extrapolation risk but should not be misrepresented as a universal rule outside that framework.
Volatility, Sharpe ratio and other statistics follow different annualisation
rules. Factors such as √12 or √252 require temporal-
dependence assumptions and do not come from the CAGR formula.
External flows: when endpoints are insufficient
When capital enters or leaves during the period, V_f/Vᵢ mixes flows
and performance. A balance moving from €100,000 to €160,000 after a €50,000
contribution is not 60% growth. An interpretable CAGR may be derived from a
unitised or time-weighted series that neutralises
external flows.
If the question concerns the experience of capital and its flow timing, money-weighted return is more direct. Converting an irregular-flow MWR to an annual rate follows IRR/XIRR time conventions, not simple profit divided by years.
Standard CAGR also assumes positive endpoints. With zero opening value the ratio does not exist; with a negative ratio the root may have no economically meaningful real solution; with zero ending value it yields −100% but the constant reversible-rate interpretation is degenerate. These cases should be reported, not “fixed” by adding arbitrary constants.
Price return, total return, cost and currency
Two CAGRs are comparable only when the underlying objects are comparable. Price return excludes distributions; total return includes dividends, coupons or other distributions under a reinvestment rule. Index gross- and net-total- return variants may differ by assumed withholding tax. Provider, exact variant and currency are material.
A portfolio series must state whether it is gross or net and which trading, spread, impact, custody, management, performance and tax charges are included. Base currency also changes growth; a euro CAGR and a dollar CAGR contain different FX paths, while hedging adds its own rules and cost.
A benchmark comparison needs the same dates, calendar, compatible return variant, currency and flow treatment.
What CAGR shows and hides
CAGR shows the equivalent compounded speed between endpoints. It does not show volatility, order of returns, maximum loss, recovery time, tail risk, leverage, liquidity, concentration, flow timing or uncertainty. Two portfolios with the same CAGR can have radically different paths. Moving the start or end date by a few days can materially alter short or volatile samples.
CAGR belongs beside portfolio return, drawdown and other risk measures. No CAGR is universally “good”: objective, benchmark, inflation, cost, risk and horizon determine its economic meaning. It is descriptive, not predictive.
Minimum reproducible record
Publish the opening and closing dates and values; exact duration and calendar convention; source series and cash-flow treatment; whether simple returns, log returns or a unitised index were used upstream; price/total-return and reinvestment policy; base currency and hedge; gross/net basis and included costs; formula, precision and rounding; comparable benchmark; and path-risk metrics shown alongside CAGR.
Common error — Presenting an annualised return from a short favourable period as though it were earned for a full year. Annual equivalence does not create a longer observation history.
Sources
- CFA Institute, 2020 GIPS Standards for Firms — calculation, linking and presentation of returns, including periods shorter than one year.
- CFA Institute, GIPS Standards Handbook for Firms — official interpretations on returns, cash flows, valuation and annualised presentations.
- CFA Institute, Portfolio Performance Evaluation — professional framework for measuring and comparing portfolio performance.
- U.S. Securities and Exchange Commission, Investment Adviser Marketing, Final Rule IA-5653 — primary regulatory source on performance presentation within its scope.
- S&P Dow Jones Indices, Index Mathematics Methodology — index calculation, chaining and return variants.
- MSCI, Index Calculation Methodology — price, gross and net total returns, corporate actions, currencies and continuity.