In this article
Three years of returns: +50 percent, −20 percent, +30 percent. Add them up and divide by three, and you get 20 percent a year. It sounds great. Put ₹1 lakh in at the start and you finish with ₹1.56 lakh, not ₹1.73 lakh. What you actually earned, each year, was about 16 percent.
That 16 is the CAGR, the compound annual growth rate. It is the single yearly rate that, applied every year, would have taken you from your starting amount to your ending amount. Once you know the difference between it and a simple average, a lot of return claims become easier to read.
Walk through the three years
Each year’s percentage is taken from the previous year’s balance, not from the original ₹1 lakh. The −20 percent year takes away more rupees than the +30 percent year gives back.
Step by step: ₹1,00,000 × 1.5 = ₹1,50,000. Then × 0.8 = ₹1,20,000. Then × 1.3 = ₹1,56,000. If the true average was 20 percent every year, you would have ₹1,00,000 × 1.2 × 1.2 × 1.2 = ₹1,72,800.
The CAGR formula
Why the simple average is always too flattering
Whenever returns jump around, the simple average is higher than the CAGR. The rougher the ride, the bigger the gap. This is sometimes called volatility drag. A loss hurts more than an equal gain helps, because you are then investing a smaller base. The earlier article on percentages shows why: a 50 percent fall needs a 100 percent rise to repair.
Both paths have an average return of exactly 20 percent. The smooth one ends with ₹1.73 lakh and the bumpy one with ₹1.56 lakh. The average hid ₹17,000.
Read return claims with this in mind
- Add the yearly figures, divide by three
- Ignores the order and size of swings
- Always flatters a bumpy path
- The one steady rate that gives the same result
- Uses only start, end and years
- What your bank balance actually did
If you only get one number, ask for the CAGR, or the actual start and end values so you can work it out.
- “Averaged 18 percent a year” with no start and end figures is worth a second look. Ask what the CAGR was.
- Different time windows change the story. A fund’s CAGR over five years can differ a lot from its CAGR over ten. Picking a flattering start date is common.
- Check fees and tax. CAGR on the numbers the fund reports may be before costs. What lands in your account is what matters.
Where CAGR is the right tool, and where it is not
Use CAGR when you put in one lump sum and took it out at the end: a house, a single investment, a company’s revenue over years. It is also good for comparing two investments over the same period, because it reduces each to one steady rate.
Do not use it directly for a monthly SIP or any plan where you add money over time. Each deposit has been invested for a different length, so a single start value is misleading. For those, a return method that accounts for the timing of every deposit, like XIRR, is the right one.
Questions people ask
What is CAGR?
Compound annual growth rate: the single steady yearly rate that would take an amount from its starting value to its ending value over a given number of years.
How do I calculate CAGR?
Divide the ending value by the starting value, raise the result to the power of one over the number of years, and subtract 1. Multiply by 100 for a percentage.
Why is average return higher than CAGR?
Because losses shrink the base you earn on next. When yearly returns vary, the simple average overstates growth, and the more they vary, the bigger the gap.
Is CAGR the same as the return I got each year?
No. It is a smoothed figure. Your actual yearly returns may have been far higher or lower in individual years.
Can I use CAGR for SIP investments?
Not directly, because each monthly deposit is invested for a different length of time. Use a measure like XIRR that takes the date of every deposit into account.