📊 Average Return Calculator

What is the Average Return Calculator?

This tool analyzes a series of historical investment returns (gains or losses) over several periods to calculate two critical measures of performance: the **Arithmetic Mean Return (AMR)** and the **Geometric Mean Return (GMR)**. These metrics are used by investors to quantify the typical historical performance of a portfolio, stock, or mutual fund.

Why You Need This Tool and Its Purpose

Understanding average returns is crucial for realistic financial planning, but using the wrong average can lead to significant forecasting errors. The purpose of this calculator is to provide the most accurate view of compounded performance:

1. **Identify True Growth (GMR):** The **Geometric Mean Return** is the only accurate way to determine the constant, compounded rate of return that would have yielded the observed end result. This is the figure you should use when projecting future portfolio value.
2. **Understand Volatility (AMR):** The **Arithmetic Mean Return** is always higher than the GMR (unless all annual returns are identical). The difference between the AMR and the GMR is directly related to the **volatility** or risk of the investment. The larger the difference, the riskier the investment has been.

How This Calculator Works

The calculator takes a list of annual returns (R) and uses the number of periods (N) to perform two distinct calculations:

1. **Arithmetic Mean Return (AMR):** This is the simple average of all annual returns. It is calculated by summing all returns and dividing by the number of periods: AMR = (Sum of all Annual Returns) / (Number of Periods)
2. **Geometric Mean Return (GMR):** This calculation incorporates the effect of compounding. It multiplies the return factors (1 + R) for each period, takes the Nth root of the product, and subtracts 1: GMR = [ (Product of (1 + Return in each Year)) ^ (1 / Number of Periods) ] - 1