# Compound Annual Growth Rate (CAGR)

# Introduction

The *compound annual growth rate*, or CAGR, is the average annual growth rate for any value or amount that grows over time, such as the **rate of return **of a stock or entire portfolio, factoring in reinvestment and therefore compounding.

CAGR is a widely accepted way of smoothing out investment returns which allows comparing the performances of different assets or asset classes with each other, let’s say of stocks with bonds, or the portfolio performances of different fund managers.

Because CAGR normalizes different time horizons to an annualized basis, it allows comparing investment returns resulting from different time frames with each other.

# Calculation

To calculate CAGR, we simply divide the final value by the beginning value, raise it to the power of 1 over the number of years, and subtract one. Multiplying by 100 converts the number to a percentage.

# Calculating CAGR of a stock

Let’s look at an example. Stock XYZ’s share price on January 01, 2015, was $15. Seven years later, on January 01, 2022, the stock price has increased (without stock splits) to $78. That’s all the information we need to calculate the stock’s CAGR: