Investment Return Calculator
Model total portfolio returns, Compound Annual Growth Rates (CAGR), and inflation-discounted purchasing power across conservative (-2%), baseline, and aggressive (+2%) market cycles.
Return Settings
1. Mathematical Foundations of Investment Returns & CAGR
Formulas for geometric compounding, volatility drag, cumulative ROI, and Fisher real purchasing power
In professional financial economics, evaluation of performance requires distinguishing between arithmetic averages and geometric compounding. When asset prices fluctuate year over year, the simple arithmetic mean always overstates investor returns due to mathematical asymmetry: a 50% loss requires a subsequent 100% gain merely to break even.
Compound Annual Growth Rate (CAGR)
The smoothed geometric annual rate of return that would take an investment from starting balance PV to final wealth FV over t years.
Cumulative Return on Investment (ROI)
Total percentage gain realized over the entire investment lifecycle relative to cumulative out-of-pocket cash capital deployed.
Fisher Real Return Formula
Calculates purchasing power expansion by discounting nominal rate r_nom by annual inflation i. Real balance = FV / (1 + i)^t.
The relationship between geometric CAGR and arithmetic mean is formalized through the variance approximation: CAGR ≈ Arithmetic Mean - (σ² / 2), where σ represents annual portfolio volatility standard deviation. This penalty is known as volatility drag: higher volatility mechanically reduces terminal wealth even if arithmetic average returns appear identical.
2. Historical Asset Allocation Return & Volatility Matrix
Multi-decade historical CAGR, real returns after inflation, maximum drawdown, and risk-adjusted Sharpe ratios
| Portfolio Allocation Strategy | Historical CAGR (Nominal) | Real CAGR (After CPI) | Annual Volatility (σ) | Historical Max Drawdown | Sharpe Ratio (Rf=3%) |
|---|---|---|---|---|---|
| 100% Equities (All-Stock / S&P 500) | 10.2% | 7.0% | 15.8% | -50.8% (2008 GFC) | 0.46 |
| 80/20 Growth (80% Stock / 20% Bond) | 9.3% | 6.1% | 12.9% | -41.5% | 0.49 |
| 60/40 Classic Balanced (60% Stock / 40% Bond) | 8.4% | 5.2% | 10.2% | -31.2% | 0.53 (Optimal Balance) |
| 40/60 Conservative Income (40% Stock / 60% Bond) | 7.1% | 3.9% | 7.8% | -20.4% | 0.52 |
| All-Weather / Permanent Portfolio | 6.8% | 3.6% | 6.9% | -13.8% (Smooth Ride) | 0.55 |
Frequently Asked Questions
Authoritative answers regarding Compound Annual Growth Rates, volatility drag, and return metrics
How does Compound Annual Growth Rate (CAGR) differ from arithmetic average return?
Arithmetic mean simple average distorts volatile returns, whereas CAGR measures the true geometric mean annualized growth rate required to take an investment from starting balance to terminal wealth.
Why does sequence of returns risk dramatically impact realized investment returns?
While order of returns does not alter a pure buy-and-hold lump sum, experiencing negative returns early during periodic contribution or withdrawal phases drastically impairs long-term terminal wealth.
How does inflation erosion alter the difference between nominal returns and real purchasing power?
Nominal returns indicate numerical account balance growth, but real returns calculate actual economic purchasing power expansion using the Fisher equation: Real Rate = (1 + Nominal) / (1 + Inflation) - 1.
What is the mathematical formula for total Return on Investment (ROI)?
Total ROI is calculated as: ROI = [(Final Portfolio Value - Total Capital Invested) / Total Capital Invested] × 100%, expressing cumulative percentage gain over the entire holding duration.
How do conservative and aggressive scenarios account for equity market volatility?
The tool bounds returns within a ±2% range around your baseline assumption, providing a realistic sensitivity corridor reflecting market cycles, bull runs, and bear market contractions.