Average Return Calculator
Determine true investment performance. Compare arithmetic average returns against geometric mean (CAGR) across volatile multi-year holding periods.
Investment Average Return & CAGR Calculator
Measure true geometric compound annual growth rate (CAGR) vs simple arithmetic mean
Annual Return Rates
Year-over-Year Portfolio Trajectory
Comprehensive Guide & Calculation Principles: Average Return Calculator
The Average Return Calculator delivers precision calculations for chronological time, calendar durations, payroll shift logs, and international timezone coordinates.
Governing Principles of Average Return Calculator
Time calculations operate on a sexagesimal (base-60) foundation for minutes and seconds, combined with 24-hour solar days and Gregorian calendar algorithms. Accurately tracking intervals requires properly accounting for leap years, variable month lengths (28 to 31 days), timezone offsets, and fractional decimal hours.
Our engine processes all temporal arithmetic client-side with millisecond resolution, ensuring instantaneous and reliable results for personal planning, project management, and payroll compliance.
Step-by-Step Instructions
Enter Annual Return Percentages
Input periodic investment returns or portfolio percentage changes for each consecutive year or period.
Set Initial & Ending Capital
Optionally specify starting portfolio balance and final liquidation value to compute dollar-weighted returns.
Compute Arithmetic vs Geometric Means
Evaluate simple arithmetic average return alongside Compound Annual Growth Rate (CAGR / Geometric Mean).
Analyze Volatility Drag
Review how annual performance variance and market drawdowns impact true geometric compound wealth.
Key Features & Capabilities
- Arithmetic Mean versus Geometric Mean (CAGR) calculation: $\text{CAGR} = \left(\prod (1 + R_i)\right)^{1/n} - 1$
- Volatility Drag quantification demonstrating the mathematical difference between average and compound returns
- Time-Weighted Return (TWR) versus Money-Weighted Return (Internal Rate of Return / IRR) comparison
- Inflation-adjusted real annualized return calculation based on historical CPI
Frequently Asked Questions
Why does the Arithmetic Average return give a misleading impression of portfolio growth?
The arithmetic average simply sums periodic returns and divides by the number of periods, ignoring compounding order and volatility drag. For example, a +50% gain followed by a -50% loss yields an arithmetic average of 0% [(50 - 50) / 2], but an investor with $100 drops to $150 and then crashes to $75—a real geometric compound loss of -25% (CAGR of -13.4% per year).
What is Compound Annual Growth Rate (CAGR) and how is it calculated?
CAGR represents the constant annual rate of return that would be required for an investment to grow from its beginning balance to its ending balance over a specified number of years: CAGR = (Ending Value / Beginning Value)^(1 / Years) - 1. It provides the most accurate standard for comparing investments across varying holding periods.
What is Volatility Drag in portfolio management?
Volatility Drag (or variance drain) is the mathematical reduction in geometric compound return caused by portfolio fluctuations. Approximated by the formula: Geometric Return ≈ Arithmetic Return - (Variance / 2). High portfolio volatility permanently lowers the long-term compound accumulation of wealth.
What is the difference between Time-Weighted Return (TWR) and Money-Weighted Return (MWR)?
Time-Weighted Return (TWR) measures the pure performance of the underlying investment strategy by eliminating the distorting impact of external cash inflows and outflows. Money-Weighted Return (MWR / IRR) accounts for the timing and magnitude of investor deposits and withdrawals, reflecting the individual's actual realized dollar return.
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