The CAGR Formula

The CAGR Formula

CAGR stands for ‘compound annual growth rate’ and is used in business, investing, and trading as a term for the measurement as a geometric progression ratio providing a constant rate of return over a specific time period. While CAGR is not an accounting term it is still used to describe the return in segments of  business, investment portfolios, and trading systems smoothed for draw downs. CAGR filters the impact of volatility of returns over time periods and make returns alone less relevant and the average return path involved in creating those returns over time most important. The CAGR is specifically useful to compare the rates of growth from different sets of return data in business, investing, and trading. 

Commonly average annual return is what most people look at to measure the success of returns from an investment but CAGR is a much better measure of an investment’s real return over a time period as it considers an investment’s losses on the path to those returns. 

CAGR is not an actual rate of return, it is a representation of a smoothing of returns. It is a number that expresses the rate an investment would have grown with the same rate of return each year with the new capital reinvested each year. This sort of precise measurement of performance is just a smoothing performance not an accurate reading of future returns. CAGR is used to easily understand comparative returns from multiple investment strategies or systems. 

A CAGR smooths out the fluctuations in returns for an investment’s performance and prevents outlying years from distorting the final result.

CAGR is defined as:

where  is the initial value, is the end value, and  is the number of years.

Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion.

Also with the overall growth rate, (FV-PV)/PV, for an investment or strategy over a period of days, the CAGR can be calculated by using the CAGR formula = (1+Growth Rate)^(365/Days)-1, where (End Value / Start Value)=(1+Growth Rate) and (1/Years)=(365/Days).

What the CAGR is used for:

  1. Calculating the average returns of money managers and mutual funds. 
  2. To compare performance of different investment strategies.
  3. Using historical returns of different asset classes to compare returns and risk.

The CAGR Formula