Average Return Calculator

Calculate and compare different ways to measure your investment returns, including arithmetic mean, geometric mean (CAGR), and time-weighted returns. Understand which method best represents your investment performance.

Average Return Calculator

Investment Return Inputs

Enter your investment returns for each period, or import values from a spreadsheet.

$

Enter your starting investment amount

Enter returns for each period as a percentage

Calculation Options

Understanding Investment Returns

Investment returns measure the gain or loss on an investment over time, expressed as a percentage of the initial investment. Different methods of calculating average returns can yield different results, which is why it's important to understand various metrics.

Measuring investment performance accurately is crucial for making informed financial decisions, comparing different investments, and assessing whether you're on track to meet your financial goals.

Different Ways to Calculate Average Returns

Arithmetic Mean Return

The arithmetic mean is the simple average of all period returns. It's calculated by summing all returns and dividing by the number of periods. While easy to calculate, it doesn't account for compounding effects and typically overstates returns for volatile investments.

$$\text{Arithmetic Mean} = \frac{R_1 + R_2 + ... + R_n}{n}$$

For returns of 10%, -5%, and 20%, the arithmetic mean is (10% + (-5%) + 20%) / 3 = 8.33%

Geometric Mean Return (CAGR)

The geometric mean, often expressed as Compound Annual Growth Rate (CAGR), accounts for the compounding effect of returns. It represents the constant rate of return that would yield the same final value if applied to each period.

$$\text{Geometric Mean} = \sqrt[n]{(1+R_1) \times (1+R_2) \times ... \times (1+R_n)} - 1$$

For returns of 10%, -5%, and 20%, the geometric mean is [(1 + 0.10) × (1 + (-0.05)) × (1 + 0.20)]^(1/3) - 1 = 7.71%

Time-Weighted Return (TWR)

The time-weighted return measures the compound rate of growth in a portfolio that eliminates the effects of cash flows. It's particularly useful for evaluating investment manager performance since the timing of deposits and withdrawals is beyond a manager's control.

$$\text{TWR} = [(1+R_1) \times (1+R_2) \times ... \times (1+R_n)] - 1$$

For returns of 10%, -5%, and 20%, the TWR is [(1 + 0.10) × (1 + (-0.05)) × (1 + 0.20)] - 1 = 24.9%

Which Return Metric Should You Use?

For Reporting Historical Performance

Geometric mean (CAGR) is typically the most appropriate metric for reporting historical performance of an investment or portfolio, as it accounts for compounding effects.

For Projecting Future Returns

Arithmetic mean might be used for projecting future one-period returns in some models, though it generally overstates expected returns for volatile investments.

For Evaluating Investment Managers

Time-weighted return is the standard for measuring and comparing investment manager performance, as it eliminates the impact of investor cash flows.

For Personal Investment Results

Money-weighted return (which considers timing and amount of cash flows) is often most relevant for individual investors to understand their actual experience.

How to Use the Average Return Calculator

  1. Enter your initial investment amount.
  2. Input the return percentage for each period (daily, monthly, quarterly, or annually).
  3. Set calculation options based on your preferences.
  4. Click 'Calculate Returns' to see a comprehensive analysis of your investment performance.
  5. Review the different return metrics to understand how your investment has performed.

This calculator helps you gain a more nuanced understanding of your investment performance beyond simple averages, allowing for better investment decisions and more accurate comparisons.