CAGR
Also written Compounded Annual Growth Rate · Compound annual growth rate
The single smoothed annual rate at which a starting value would have to grow, compounding each year, to reach the ending value over a given period.
In plain language
Real growth is lumpy — 40% one year, −10% the next, 18% the year after. CAGR replaces that with the one steady rate that would have produced the same final result.
It is the honest way to compare two investments held for different lengths of time, because it converts every result to a per-year basis with compounding included.
How it works
The key word is compounding. Growth in year two is earned on the year-one result, not on the original amount, so CAGR is always lower than the simple average of the annual returns whenever those returns vary.
That gap widens with volatility. A pair of years returning +50% and −50% averages zero but compounds to −13.4% — Rs 100 becomes Rs 150, then Rs 75. This is why a fund advertising "average annual return" is telling you something less useful than CAGR.
The formula
CAGR = (Ending value ÷ Beginning value)^(1 ÷ n) − 1
where n is the number of years, not the number of data points. Five year-end figures span four years.
A worked example
An investor puts Rs 5,00,000 into an equity fund in April 2019 and redeems Rs 11,20,000 in April 2026 — 7 years.
CAGR = (11,20,000 ÷ 5,00,000)^(1/7) − 1
= (2.24)^0.142857 − 1
= 1.1226 − 1
= 12.26% a year
The money grew 124% in total, which sounds far better than 12.26%. Both are true; only the second can be compared with a fixed deposit.
Had the same Rs 5,00,000 reached Rs 11,20,000 in 4 years instead, the CAGR would be 22.3% — the same total gain, a very different investment.
Why NISM asks about it
Chapter 12 covers return measurement. CAGR appears in numerical questions on portfolio and company growth, and in Chapter 8 when analysing multi-year revenue or profit trends.
Common exam traps
- Count years, not observations. March 2020 to March 2025 is 5 years, from 6 year-end figures.
- CAGR is not the average of the annual returns, and is always lower when returns vary.
- It says nothing about the path. Two investments with the same CAGR can have had wildly different drawdowns — that is what standard deviation is for.
- CAGR cannot be computed where the beginning value is negative or zero.
- For periods under a year, annualising a short run produces a number that is arithmetically correct and practically meaningless.
Where this is taught
- Series XIX-B · Chapter 6: Fees Structure, Fund Performance and Benchmarkingintroduced here
- Series XV · Chapter 12: Fundamentals of Risk and Returnintroduced here
- Series X-A · Chapter 2: Time Value of Moneyintroduced here
- Series XIX-C · Chapter 9: Fee Structure and Fund Performanceintroduced here
- Series XVII · Chapter 5: Evaluating Fund Performance & Fund Selectionintroduced here
- Series V-B · Chapter 7: Performance of Mutual Fundsintroduced here
- Series XIX-E · Chapter 7: Fee Structure and Fund Performanceintroduced here
Related terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Sharpe ratioReturn earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Entry loadThe former mark-up of a mutual fund's sale price over NAV, charged when an investor bought units. SEBI has banned it, so units are now sold at NAV, subject only to stamp duty.
- Price Return IndexThe variant of a market index that captures only the price movement — the capital gains — of its constituents, leaving out dividends and interest. Mutual funds were benchmarked to it until 1 February 2018.
- Annualised returnA return scaled up or down to a one-year basis so that investments held for different lengths of time can be compared — a simple scaling that, unlike CAGR, ignores compounding.
- Geometric Mean ReturnThe single constant yearly rate that would turn the starting value into the ending value — found by chain-linking period returns and taking the nth root.
- Rolling returnsThe average annualised return over many consecutive holding periods inside an evaluation period — say every one-year return in three years — used to remove the distortion of an unusually high or low start or end point.
- Compounded returnThe single yearly rate at which an investment's starting value would have to grow, each year's growth earned on the year before, to reach its ending value over a stated number of years.
- Holding period returnThe total of coupons, income earned on reinvesting them and any capital gain, expressed as a percentage of the purchase price — a crude return for the period actually held, with no compounding in it.
- PEG ratioThe price to earnings ratio divided by the expected earnings growth rate — Peter Lynch's way of asking whether a high P/E is justified by the growth behind it.
- Composite CAGRThe blended CAGR SEBI requires for benchmark comparison when Total Return Index data is not available for the whole period — Price Return Index CAGR up to the date TRI began, spliced with TRI CAGR after it.
- Net returnThe return on an AIF's NAV after fund expenses, costs and management fees — measured before incentive fees (pre-incentives) or after them (post-incentives, what the investor actually keeps).
- Compound interestInterest earned on the original amount and also on the interest already earned. Rs 1,000 at 9% grows to Rs 31,409 in 40 years compounded, against Rs 4,600 with simple interest.
- Simple returnThe plain percentage change in the value of an investment over a period — (ending value minus beginning value) divided by beginning value — with no adjustment for time or compounding.
- Absolute returnThe plain rupee gain or loss from an investment relative to what was invested — simple to compute, but it ignores both the amount invested and the time taken to earn it.
- Percentage returnReturn expressed as a percentage of the amount invested rather than in rupees, which puts every investment on a base of Rs 100 and makes holdings of different sizes comparable.
- Time Weighted Rate of ReturnA compounded return that neutralises client deposits and withdrawals by linking sub-period returns, so it measures the manager’s decisions. Mandatory for PMS investment approach performance.
- XIRRExtended Internal Rate of Return: the annualised return on an investment with irregular cash flows, found by assigning a date to each flow. PMS reports it for each investor’s own experience.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.