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.
Check yourself
1.An investor buys a share on 31 Jul 2011 for ₹150, receives dividends of ₹5, ₹6 and ₹4 on three different October dates, and sells on 15 Jan 2014 for ₹165. How should the CAGR of this investment be computed?
- a)By applying the direct CAGR formula to the purchase and sale prices only
- b)By using the XIRR function in Excel, with dates in one column and matching cash flows alongside
- c)By adding the dividends to the sale price and then annualising simply
- d)By computing the arithmetic average of the annual dividend yields
Show the answer
Answer: (b) By using the XIRR function in Excel, with dates in one column and matching cash flows alongside
The workbook is explicit about this case: "This problem cannot be solved using the direct CAGR formula. The underlying CAGR for these multiple flows has to be calculated by using XIRR function in Excel." The procedure is to create separate columns for the dates and the matching cash flows. The answer for this example is 8.06%.
Option A fails because the direct formula handles only one amount in and one amount out — it cannot place the three dividends at their actual dates. Option C ignores the timing of each dividend, which is the entire reason XIRR exists; money received in 2011 is worth more than money received in 2013. Option D is not a return calculation at all.
Remember that the test centre workstation has Excel or LibreOffice Calc. When a question puts irregular dates in front of you, that is an instruction to use XIRR, not a trick.
Where this is taught
- Series V-B · Chapter 7: Performance of Mutual Fundsintroduced here
- 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 XVII · Chapter 5: Evaluating Fund Performance & Fund Selectionintroduced here
- Series XIX-C · Chapter 9: 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.
- 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.