## September 9, 2017

### Compound Annual Growth Rate - CAGR explained with examples

The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

CAGR can be used to calculate the average growth of a single investment. Because of market volatility, the year-to-year growth of an investment may be difficult to interpret. For example, an investment may increase in value by 8% in one year, decrease in value by 2% the following year and increase in value by 5% in the next. With inconsistent annual growth, CAGR may be used to give a broader picture of an investment’s progress.

To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.

This can be written as follows: CAGR is not the same as simple interest rate.

Example:

A stock has rallied from 100 to 130 over 5 years. So it has gained 30%. Sounds good but this is not the CAGR.

The CAGR is (130/100)^(1/5)-1=0.05 or 5%

Another example:

A stock has doubled in 5 years... 100% return? too good.

The CAGR is (2/1)^(1/5)=0.15 or 15% pa

In stock markets, CAGR over 5 years does not make sense. One has to look at min 10-20 years. This will (hopefully) take into account the bull and bear phases.