Average Return Calculator

Arithmetic vs. Geometric Average Return & Volatility Drag

When evaluating mutual funds or investment portfolios, financial institutions often advertise their simple average return (arithmetic mean). However, the simple average systematically overstates how much your money actually grew. To understand true wealth accumulation, you must calculate the geometric average return, also known as the Compound Annual Growth Rate (CAGR).

The Mathematics of Volatility Drag

Volatility drag is the negative impact that fluctuations and variance in year-to-year returns exert on your compounded terminal balance. In simple terms, losses hurt you more than equivalent percentage gains help you. For example, if a portfolio gains 50% in Year 1 and loses 50% in Year 2, the arithmetic average return is exactly 0%:
Arithmetic Average = (50% + -50%) / 2 = 0%

However, if you started with $10,000, a 50% gain makes it $15,000, and a subsequent 50% loss reduces it to $7,500. You have lost 25% of your initial capital. The true compound rate of return (geometric average) is actually -13.4% per year.

How to Use Volatility Stats

By inputting your annual return percentages or chronological year-end asset values, our calculator computes the standard deviation of returns to measure risk. It also estimates the volatility drag using the standard approximation:
Volatility Drag ≈ (Standard Deviation)² / 2

This helps you understand why portfolios with lower volatility (steady gains) can sometimes outperform highly volatile ones, even if the simple average return of the volatile portfolio is higher.

Frequently Asked Questions About Average Returns