Average Return Calculator
Calculate various return metrics including Arithmetic, Geometric (CAGR), Time-Weighted (TWR), and Money-Weighted (IRR) returns.
Enter a list of returns for each period (e.g., annual returns). Use this for Arithmetic and Geometric Mean.
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Explanation of Metrics
- Arithmetic Mean Return
- The simple average of a series of returns. Best for forecasting the return for a single, future period but can be misleading for historical performance due to its failure to account for compounding.
- Geometric Mean Return
- The average rate of return on an investment that is compounded over multiple periods. It represents the constant growth rate needed to get from the initial to the final value. It is a more accurate measure of past performance than the arithmetic mean.
- CAGR (Compound Annual Growth Rate)
- The annualized geometric mean return. It's the standard metric for describing an investment's growth over time.
- Time-Weighted Return (TWR)
- Measures the compound growth rate of a portfolio. It removes the distorting effects of cash inflows and outflows, making it the industry standard for judging a portfolio manager's performance.
- Money-Weighted Return (MWR / IRR)
- Calculates the return rate that sets the net present value of all cash flows (initial investment, contributions, withdrawals, and ending value) to zero. It is influenced by the timing of cash flows, making it a good measure of an individual investor's actual performance.
- Volatility (Standard Deviation)
- A statistical measure of the dispersion of returns for a given investment. Higher volatility indicates higher risk.
- Sharpe Ratio
- Measures the risk-adjusted return of an investment. It is calculated by subtracting the risk-free rate from the portfolio's return and dividing by the portfolio's volatility. A higher Sharpe ratio indicates better performance for the amount of risk taken.
- Maximum Drawdown
- The maximum observed loss from a peak to a trough of a portfolio, before a new peak is attained. It is an indicator of downside risk over a specified time period.
Formulas
Arithmetic Mean: $ R_{arith} = \frac{1}{n} \sum_{i=1}^{n} R_i $
Geometric Mean: $ R_{geo} = \left( \prod_{i=1}^{n} (1 + R_i) \right)^{1/n} - 1 $
CAGR: $ \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{1/\text{Years}} - 1 $
Volatility (Std Dev): $ \sigma = \sqrt{\frac{\sum_{i=1}^{n} (R_i - \bar{R})^2}{n-1}} $
Sharpe Ratio: $ S = \frac{R_p - R_f}{\sigma_p} $
XIRR: Solve for $r$ in: $ 0 = \sum_{i=1}^{n} \frac{C_i}{(1+r)^{(d_i - d_0)/365}} $
FAQ
What is an average return?
The average return is a measure of the historical performance of an investment over a specific period. There are several ways to calculate it, with the most common being the arithmetic mean (simple average) and the geometric mean (which accounts for compounding).
What is the difference between arithmetic and geometric mean returns?
The arithmetic mean is the simple average of a series of returns and is best for estimating a single period's expected return. The geometric mean (or CAGR) accounts for the effect of compounding over multiple periods and represents the constant growth rate an investment would have needed to achieve the final result. The geometric mean is almost always lower than the arithmetic mean and is a more accurate measure of an investment's true historical performance.
What is CAGR (Compound Annual Growth Rate)?
CAGR is the annualized geometric mean return. It tells you the constant annual rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming profits were reinvested at the end of each year.
When should I use Time-Weighted Return (TWR) vs. Money-Weighted Return (MWR/IRR)?
Use TWR to evaluate the performance of a portfolio manager or strategy, as it removes the distorting effects of cash inflows and outflows. Use MWR (also known as Internal Rate of Return or IRR) to evaluate the performance of your personal portfolio, as it accounts for the timing and size of your specific contributions and withdrawals.
What is required to calculate IRR / Money-Weighted Return?
To calculate IRR, you need a series of dated cash flows, including an initial investment (a negative cash flow), any subsequent contributions (negative) or withdrawals (positive), and a final ending market value (treated as a positive cash flow on the end date). The series must contain at least one positive and one negative cash flow.
How accurate is this calculator?
This calculator uses standard financial formulas and high-precision JavaScript calculations to provide accurate results. The IRR/XIRR solver uses iterative numerical methods (Newton-Raphson with a Bisection fallback) to find a precise rate of return. However, all results should be considered for informational purposes and not as financial advice. Always verify with a professional.
