Why Arithmetic Averages Fail
Imagine an investment that gains 100% in Year 1 and loses 50% in Year 2.
The Arithmetic Average is (+100% - 50%) / 2 = +25%.
However, if you started with $1,000, you'd have $2,000 after Year 1, and $1,000 after Year 2. Your Actual Return is 0%.
This discrepancy is known as "Volatility Drag." The more an investment swings up and down, the lower its geometric return (actual money in your pocket) will be compared to its reported average return.
Understanding CAGR
CAGR is the constant rate of return that would be required for an investment to grow from its starting balance to its ending balance, assuming the profits were reinvested at the end of each year.
How to Use This Calculator
We provide three distinct professional methodologies:
1. Simple Growth (CAGR)
Use this when you know where you started, where you ended, and how much time passed. This is the gold standard for comparing a single stock's performance against a benchmark like the S&P 500.
2. Cash Flow Analysis
Use this for your actual brokerage or bank accounts where you have made deposits or withdrawals over time. It calculates your Total ROI based on the net capital you actually risked.
3. Annual Return Linking
Use this when you have a list of annual performance percentages (e.g., from a fund prospectus). By geometrically linking these returns, you can see the cumulative impact of compounding over a multi-year period.
The Power of Compounding
Albert Einstein reportedly called compound interest the "eighth wonder of the world." Small differences in average annual returns lead to massive differences in terminal wealth over 20-30 years.
Important Disclaimers
Historical returns are not a guarantee of future performance. When calculating your future wealth, analysts recommend using "Real Returns" (inflation-adjusted). If a stock market returns 10% but inflation is 3%, your actual purchasing power only grew by 7%.