How to Calculate Geometric Mean Rate of Return in Excel

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Geometric Mean Rate of Return Calculator

Example: 10 for 10%, -5 for -5%.

Results

Geometric Mean Return:
Total Compounded Growth:
Arithmetic Mean (Reference):
function calculateGeometricMean() { var inputStr = document.getElementById("return-series").value; var resultArea = document.getElementById("result-area"); var geoMeanDisplay = document.getElementById("geo-mean-result"); var totalGrowthDisplay = document.getElementById("total-growth"); var arithmeticDisplay = document.getElementById("arithmetic-mean"); // Split and clean inputs var strArray = inputStr.split(','); var returns = []; var sum = 0; for (var i = 0; i < strArray.length; i++) { var val = parseFloat(strArray[i].trim()); if (!isNaN(val)) { returns.push(val); sum += val; } } if (returns.length < 1) { alert("Please enter at least one valid return percentage."); return; } // Calculation Logic // Formula: [(1 + r1) * (1 + r2) * … * (1 + rn)]^(1/n) – 1 var product = 1; for (var j = 0; j < returns.length; j++) { var decimalReturn = returns[j] / 100; product = product * (1 + decimalReturn); } var n = returns.length; var geometricMean = Math.pow(product, 1 / n) – 1; var arithmeticMean = (sum / n) / 100; // Display Results geoMeanDisplay.innerText = (geometricMean * 100).toFixed(4) + "%"; totalGrowthDisplay.innerText = ((product – 1) * 100).toFixed(2) + "%"; arithmeticDisplay.innerText = (arithmeticMean * 100).toFixed(4) + "%"; resultArea.style.display = "block"; }

Understanding the Geometric Mean Rate of Return in Finance

In the world of investing, the simple average (arithmetic mean) often lies to you. If you lose 50% one year and gain 50% the next, your average return is 0%, but your wallet is actually down 25%. This is why financial professionals use the Geometric Mean Rate of Return.

The geometric mean accounts for the effects of compounding, providing a true "time-weighted" rate of return. It represents the single rate of return that would get you from your starting balance to your ending balance over a specific period.

How to Calculate Geometric Mean Rate of Return in Excel

Excel does not have a single "Geometric Return" button that handles percentages directly, but there are two primary ways to calculate it accurately.

Method 1: Using the GEOMEAN Function

The GEOMEAN function in Excel requires positive numbers. Since investment returns can be negative (e.g., -5%), you must add 1 to each return before using the formula.

=GEOMEAN(range_of_returns_plus_1) – 1

Step-by-step:

  1. If your returns are in cells A1:A5 (e.g., 0.05, -0.02, etc.), create a helper column in B.
  2. In cell B1, type =1+A1 and drag it down to B5.
  3. In a new cell, type: =GEOMEAN(B1:B5)-1.
  4. Format the result as a percentage.

Method 2: Using the RRI Function

If you only know the starting value, the ending value, and the number of periods, use the RRI function. This is often easier for long-term compound annual growth rate (CAGR) calculations.

=RRI(number_of_periods, start_value, end_value)

Practical Example

Imagine a portfolio with the following annual returns:

  • Year 1: 10% (1.10)
  • Year 2: -15% (0.85)
  • Year 3: 20% (1.20)

Step 1: Multiply the factors
1.10 × 0.85 × 1.20 = 1.122

Step 2: Take the nth root (where n = 3 years)
1.122 ^ (1/3) = 1.0391

Step 3: Subtract 1
1.0391 – 1 = 0.0391 or 3.91%

The arithmetic mean would have suggested a return of 5% [(10-15+20)/3], but the geometric mean correctly shows that your actual compounded growth was only 3.91% per year.

Why the Difference Matters

The "Volatility Tax" is the reason the geometric mean is always equal to or lower than the arithmetic mean. High volatility drags down actual returns. For investors, the geometric mean is the only metric that accurately reflects the growth of their wealth over time, making it essential for comparing mutual funds, ETFs, or personal portfolio performance.

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