Average Return Calculator Arithmetic Mean Geometric Mean Annualized Return CAGR ...
Average Return Calculator
Arithmetic Mean Return
Enter annual returns separated by commas, spaces, or new lines:
Arithmetic Mean = (R₁ + R₂ + ... + Rₙ) / n
Geometric Mean Return
Enter annual returns separated by commas, spaces, or new lines:
Geometric Mean = [(1+R₁) × (1+R₂) × ... × (1+Rₙ)]^(1/n) - 1
Annualized Return
Total Return (%)
Investment Period (years)
Compounding Frequency
Annualized = (1 + Total Return)^(1/Years) - 1
Compound Annual Growth Rate (CAGR)
Beginning Value (£)
Ending Value (£)
Number of Years
CAGR = (Ending Value / Beginning Value)^(1/Years) - 1
Click "Print or Save as PDF" above → Choose "Save as PDF" as your printer → Click "Save".
Results
Annual Returns
When to Use Arithmetic Mean:
Best for estimating expected returns for a single period or when returns are not reinvested.
Compounding Effect
When to Use Geometric Mean:
Best for measuring actual compounded returns over multiple periods when returns are reinvested.
Growth Over Time
Compounding Frequencies:
CAGR Growth Path
CAGR Applications:
Understanding Average Return Calculations
Calculating average returns is essential for investment analysis, portfolio management, and financial planning. However, not all averages are created equal, and choosing the right method depends on your specific needs and the nature of your data.
Arithmetic mean is the simple average of returns and represents the expected return for a single period. It's useful for estimating future returns but doesn't account for compounding effects over multiple periods.
Geometric mean accounts for compounding and represents the actual annualized return earned over multiple periods. It's always less than or equal to the arithmetic mean, with the difference increasing as volatility increases.
Annualized returns standardize returns to a yearly basis, making it easier to compare investments with different time horizons. CAGR (Compound Annual Growth Rate) is a specific type of annualized return that shows the consistent rate at which an investment would have grown if it had compounded at the same rate each year.
Frequently Asked Questions
A: Geometric mean accounts for the compounding effect of losses and gains. When you lose money, you need a larger percentage gain to recover. For example, a 50% loss requires a 100% gain to break even. This asymmetry causes the geometric mean to be lower than the arithmetic mean, with the difference increasing as volatility increases.
A: Use arithmetic mean when estimating expected returns for a single future period or when returns are not reinvested. Use geometric mean when measuring actual historical performance over multiple periods with reinvested returns, as it reflects the true compounded growth rate.
A: Annualized return can refer to any method of converting a return to an annual basis, including simple annualization of periodic returns. CAGR specifically refers to the constant rate that would produce the same final value as the actual investment, assuming compound growth at that constant rate.
A: More frequent compounding results in higher effective annual returns for the same nominal rate. However, when calculating annualized returns from total returns, more frequent compounding actually results in lower annualized rates because the same total return is achieved with more compounding periods.
A: Yes, geometric mean can be negative if the product of (1 + return) terms is less than 1. This happens when losses are severe enough that the investment value decreases over the entire period. However, if any single return is -100% or less, the geometric mean is undefined (since you can't take the root of zero or negative numbers in this context).
A: Negative returns are handled naturally in all these calculations. For geometric mean, ensure no return is -100% or worse (which would make the investment worthless). The formulas automatically account for the mathematical reality that losses have a greater impact than equivalent gains.
A: The practical difference can be substantial over long periods. For example, with the sample returns (12%, 8%, -5%, 15%, 10%), the arithmetic mean suggests $14,693 from a $10,000 investment, but the actual geometric result is $14,233—a $460 difference that compounds significantly over longer periods.