CAGR vs Average Return

Suppose an investment rises 50 percent one year and falls 50 percent the next. The average return is (50 - 50) / 2 = 0 percent. Did you break even? No.

• Start with 100 rupees.
• After +50 percent: 150 rupees.
• After -50 percent: 75 rupees.

You lost 25 percent. The simple average hides this.

Compound annual growth rate

The compound annual growth rate, or CAGR, is the steady yearly rate that would take you from the starting value to the ending value:

CAGR = (Ending value / Starting value)^(1 / years) - 1

In the example: (75 / 100)^(1/2) - 1 = about -13.4 percent a year.

A positive example

An investment grows from 1 lakh to 2 lakh rupees in 6 years:

CAGR = (2)^(1/6) - 1 = about 12.2 percent a year.

This matches the rule of 72: at 12 percent, money doubles in about 72 / 12 = 6 years.

Why averages overstate returns

The simple (arithmetic) average is always equal to or higher than the CAGR (geometric average). The more volatile the returns, the bigger the gap. This is sometimes called volatility drag: big losses need even bigger gains to recover. A 50 percent loss needs a 100 percent gain to get back to where you started.

Where you see it

• Mutual fund factsheets report returns over three, five and ten years as CAGR.
• Company growth in revenue or profits is often quoted as CAGR.
• Advertisements sometimes use average returns, which can look better.

Limits of CAGR

CAGR shows a smooth path that never happened. It hides the ups and downs along the way and doesn’t handle regular investments like SIPs well. For those, XIRR is better.