Definition — what CAGR is
– CAGR stands for compound annual growth rate. It is the single annual growth rate that would take a beginning value to an ending value over a specified number of years, assuming all gains are reinvested and the growth compounds each year.
– In plain terms: CAGR smooths a multi‑year sequence of returns into one steady annual rate that produces the same total change.
Formula and how to
calculate it
Formula (basic)
– CAGR = (Ending value / Beginning value)^(1 / number of years) − 1
– In symbols: CAGR = (V_end / V_begin)^(1/n) − 1
– Assumptions: no external cash flows (no deposits/withdrawals), dividends or distributions are reinvested, and compounding occurs at the stated periodicity.
Worked examples (step‑by‑step)
Example 1 — positive growth
– Beginning value: $10,000
– Ending value after 3 years: $16,000
– n = 3
– Calculation: CAGR = (
= (16,000 / 10,000)^(1/3) − 1
= (1.6)^(0.333333) − 1
≈ 1.166529 − 1
≈ 0.16653, or about 16.65% per year.
Interpretation: a steady 16.65% annual rate compounded each year would grow $10,000 to $16,000 in three years.
Example 2 — volatile returns (same beginning value, different path)
– Beginning value: $10,000
– Year 1 return: −10% → value = 10,000 × 0.90 = $9,000
– Year 2 return: +20% → value = 9,000 × 1.20 = $10,800
– Year 3 return: +5% → value = 10,800 × 1.05 = $11,340
– Ending value after 3 years: $11,340
– n = 3
Calculation:
CAGR = (11,340 / 10,000)^(1/3) − 1
= (1.134)^(0.333333) − 1
≈ 1.0429 − 1
≈ 0.0429, or about 4.29% per year.
Note the contrast: the arithmetic average of the three annual returns (−10% +20% +5%) / 3 = +5% is higher than the CAGR (≈4.29%). That’s because volatility reduces compounded growth; CAGR is a geometric measure that accounts for that compounding effect.
Common variations and quick formulas
– Monthly to annual (when you have a total growth factor over m months): Annualized return = (Ending / Beginning)^(12 / m) − 1.
– From periodic returns r1, r2, …, rn (expressed as decimals): CAGR = (∏(1 + ri))^(1/n) − 1. This is the geometric mean of the period returns.
– If there are external cash flows (deposits/withdrawals), use IRR (internal rate of return) or XIRR in Excel rather than simple CAGR.
How to calculate in spreadsheets and code
– Excel / Google Sheets:
– Direct formula: =POWER(EndValue/StartValue, 1/Periods) – 1
– If you have dated cash flows, use XIRR(values, dates) for a proper time-weighted IRR equivalent.
– Python (simple example):
– import math
– cagr = (end_value / start_value) ** (1.0 / periods) – 1
– R:
– cagr <- (end_value/start_value)^(1/periods) – 1
Checklist before you use CAGR
– Confirm there are no external cash flows; if there are, switch to IRR/XIRR.
– Make sure dividends or distributions are reinvested in the values used.
– Check the period length (years, months); convert consistently.
– Remember CAGR hides intra-period volatility and path dependence.
Limitations and cautions
– Path blind: CAGR uses only start and end points; it ignores how returns were distributed within the period.
– Sensitive to endpoints: small differences in start or end valuations (timing, one-off events) can materially change CAGR.
– Not a predictive rate: CAGR describes past compounded growth; it does not forecast future returns.
– Not appropriate for series with intermittent cash flows—use time-weighted or money-weighted return measures instead.
Practical example you can reuse
– To compare two funds over 5 years: compute each fund’s CAGR using the same start and end dates and equivalent assumptions about reinvestment. Use CAGR as a summary statistic, but review volatility metrics (standard deviation, max drawdown) and fees for a fuller comparison.
Further reading
– Investopedia — Compound Annual Growth Rate (CAGR): https://www.investopedia.com/terms/c/cagr.asp
– U.S. Securities and Exchange Commission — Compound interest calculator / investor tools: https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
– Khan Academy — Compound interest and geometric mean topics: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial
Educational disclaimer
This explanation is educational only and not individualized investment advice. It explains how CAGR is calculated and interpreted; it does not recommend specific
investments or give trading advice. Consult a qualified financial professional before making decisions that depend on your personal circumstances.
Quick how-to checklist (when you want a simple average annual growth rate)
– Confirm the period: choose the exact start and end dates and measure total beginning and ending values on those dates.
– Ensure comparable assumptions: include dividends/interest if you want total return; exclude if you want price-only return. Adjust for fees or taxes if you want net-of-costs results.
– No interim cash flows: use CAGR only when there are no contributions/withdrawals. If there are, use a money-weighted (internal rate of return) or time-weighted return instead.
– Apply the formula: CAGR = (Ending Value / Starting Value)^(1 / N) − 1, where N is the number of years (can be fractional).
– Report precision: show CAGR as a percentage with an appropriate number of decimals and state the period covered.
Worked numeric example
– Problem: You invested $10,000 and after 5 years the account value is $16,500. Compute CAGR.
– Step 1: Ending/Starting = 16,500 / 10,000 = 1.65
– Step 2: Raise to 1/5: 1.65^(0.2) ≈ 1.1053
– Step 3: Subtract 1 → CAGR ≈ 0.1053 or 10.53% per year.
– Checks: Total return = (1 + CAGR)^5 − 1 = 1.1053^5 − 1 ≈ 0.65 → 65% total gain (matches 16,500/10,000 − 1). Monthly equivalent rate ≈ (1.1053)^(1/12) − 1 ≈ 0.837% per month.
Common limitations (keep these in mind)
– No path information: CAGR ignores volatility and intra-period drawdowns; two investments can share the same CAGR with very different risk profiles.
– Cash-flow blind spot: contributions and withdrawals break the CAGR assumption. Use IRR or TWR when cash flows matter.
– Survivorship and selection bias: reported CAGRs for funds or strategies may exclude failures or be net-of- or pre-fees—check the basis.
– Short periods are misleading: annualizing very short-term moves can exaggerate expected long-term performance.
Practical comparison checklist for two funds
1. Use identical calendar start/end dates.
2. Make sure both are total-return (or both price-only).
3. Adjust for expense ratios and known one-time fees.
4. Complement CAGR with volatility (standard deviation), maximum drawdown, and Sharpe ratio.
5. If you or the fund made cash flows, compare money-weighted returns (IRR) or time-weighted returns as appropriate.
Further reading (reputable resources)
– Investopedia — Compound Annual Growth Rate (CAGR): https://www.investopedia.com/terms/c/cagr.asp
– U.S. Securities and Exchange Commission — Investor.gov (compound interest and calculators): https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
– Khan Academy — Compound interest and geometric mean: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial
– Morningstar — Articles and guides on fund returns and performance metrics: https://www.morningstar.com
Educational disclaimer: This explanation is educational only and not individualized investment advice. It describes how to calculate and interpret CAGR and highlights its limitations; it does not endorse specific securities, funds, or trading strategies. Consult a licensed financial advisor for advice tailored to your situation.