The Four Ways to Measure Investment Returns
Investment return measures compared with same 50% up then 50% down example
| Measure | Definition | When to Use | Example with 50% up then 50% down |
|---|---|---|---|
| Arithmetic average | Sum of annual returns divided by years | Comparing returns across periods | 0% average |
| Geometric mean (CAGR) | Actual compound growth rate | What you actually earned | -13.4% CAGR: $10K became $7,500 |
| Time-weighted return | Return ignoring cash flows | Comparing fund managers | Performance before your deposits |
| Money-weighted return (IRR) | Return including your cash flows | Your personal actual return | Includes when you added or withdrew money |
A fund that goes up 50% then down 50% has an arithmetic average return of 0%. But $10,000 becomes $15,000 (up 50%) then $7,500 (down 50%). You lost 25% of your money despite the 0% average return. The CAGR correctly shows -13.4% annually. Never use arithmetic average to understand what you actually earned. Always use CAGR.
How the Investment Calculator Uses Returns
The investment calculator uses compound annual growth rate (CAGR) by default: it projects your future value using a consistent annual compounding rate. When you enter 7%, it assumes 7% compounded annually, equivalent to the geometric mean. This correctly represents actual compound growth rather than the optimistic arithmetic average that investment marketing sometimes uses.
The Volatility Drag: Why CAGR Is Lower Than Arithmetic Average
Volatile returns produce lower CAGRs than arithmetic averages because of mathematical asymmetry: a 50% loss requires a 100% gain to recover, not a 50% gain. The more volatile the returns, the larger the gap between arithmetic average and CAGR. For the S&P 500: arithmetic average annual return approximately 11.5%, CAGR approximately 9.8%. The 1.7% gap is the volatility drag from the index's year-to-year swings.
Volatility drag examples: arithmetic average vs. CAGR with identical starting average return
| Year-by-Year Returns | Arithmetic Average | Actual CAGR | Volatility Drag | $10K Starting Value After 2 Years |
|---|---|---|---|---|
| +20% then -20% | 0% | -2% CAGR | -2% | $9,600 |
| +30% then -30% | 0% | -4.5% CAGR | -4.5% | $9,100 |
| +50% then -50% | 0% | -13.4% CAGR | -13.4% | $7,500 |
| +100% then -50% | 25% | 0% CAGR | -25% | $10,000 |
| +10% every year | 10% | 10% CAGR | 0% | $12,100 |
What Return Rate to Enter in the Calculator
Always enter the expected CAGR (compound growth rate) when using the investment calculator. The S&P 500 10% long-run figure is typically quoted as CAGR. When evaluating a specific fund, use its annualized total return figure (shown as 10-year annualized return in fund data), which is a CAGR. Arithmetic averages shown in some marketing materials overstate true compound returns by the volatility drag amount.
How to Calculate CAGR on Your Own Portfolio
CAGR formula: (Ending Value divided by Beginning Value) raised to the power of (1 divided by number of years) minus 1. Example: $10,000 grew to $25,000 over 10 years. CAGR = (25,000 divided by 10,000) to the power of (1 divided by 10) minus 1 = (2.5) to the power 0.1 minus 1 = 1.0960 minus 1 = 9.60% annually. This is the true compound annual return regardless of year-to-year fluctuations.
Enter Your CAGR for Accurate Investment Projections
Use the geometric mean return (CAGR) from your investment history for accurate future projections.