Geometric Average Rate of Return Calculator

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Geometric Average Rate of Return Calculator

Enter each year's return separated by commas. For example: 0.05, 0.10, -0.02, 0.08

What is the Geometric Average Rate of Return?

The Geometric Average Rate of Return (GARR), often referred to as the compound annual growth rate (CAGR), is a measure of the average rate of growth of an investment over a period longer than one year. Unlike the arithmetic average return, the geometric average takes into account the compounding effect of returns. This makes it a more accurate representation of an investment's true historical performance.

Why is it Important?

The GARR is crucial for investors because it smooths out volatility and provides a realistic picture of how an investment has performed over time. It's essential for comparing the performance of different investments, setting realistic future expectations, and understanding the impact of compounding returns.

How it Differs from Arithmetic Average Return

The arithmetic average return simply adds up all the individual period returns and divides by the number of periods. This can be misleading, especially if there are significant fluctuations in returns. For instance, an investment that gains 100% in year 1 and loses 50% in year 2 has an arithmetic average return of (100% – 50%) / 2 = 25%. However, the actual outcome is that the initial investment is unchanged (1 * 2 * 0.5 = 1). The geometric average, on the other hand, would correctly show a 0% return for this two-year period.

Formula

The formula for the Geometric Average Rate of Return is:

GARR = [(1 + r₁)(1 + r₂)…(1 + rₙ)]^(1/n) – 1

Where:

  • r₁, r₂, …, rₙ are the individual period returns (expressed as decimals).
  • n is the number of periods.

Example Calculation

Let's say an investment had the following annual returns over three years:

  • Year 1: 10% (0.10)
  • Year 2: 20% (0.20)
  • Year 3: -5% (-0.05)

Using the formula:

  1. Calculate the product of (1 + return) for each year:
    • (1 + 0.10) = 1.10
    • (1 + 0.20) = 1.20
    • (1 – 0.05) = 0.95
  2. Multiply these values together: 1.10 * 1.20 * 0.95 = 1.254
  3. Take the n-th root (where n=3 for three years): (1.254)^(1/3) ≈ 1.0782
  4. Subtract 1 to get the geometric average rate of return: 1.0782 – 1 = 0.0782

So, the Geometric Average Rate of Return for this investment is approximately 7.82%.

function calculateGeometricAverageReturn() { var returnsInput = document.getElementById("returns").value; var resultDiv = document.getElementById("result"); if (!returnsInput) { resultDiv.innerHTML = "Please enter the annual returns."; return; } var returnStrings = returnsInput.split(','); var returns = []; var validReturns = true; for (var i = 0; i < returnStrings.length; i++) { var ret = parseFloat(returnStrings[i].trim()); if (isNaN(ret)) { validReturns = false; break; } returns.push(ret); } if (!validReturns) { resultDiv.innerHTML = "Invalid input. Please enter numerical returns separated by commas (e.g., 0.05, 0.10, -0.02)."; return; } if (returns.length === 0) { resultDiv.innerHTML = "Please enter at least one annual return."; return; } var productOfOnePlusReturns = 1; for (var i = 0; i < returns.length; i++) { productOfOnePlusReturns *= (1 + returns[i]); } var n = returns.length; var geometricAverage = Math.pow(productOfOnePlusReturns, 1 / n) – 1; if (isNaN(geometricAverage)) { resultDiv.innerHTML = "An error occurred during calculation. Please check your inputs."; } else { resultDiv.innerHTML = "

Result:

The Geometric Average Rate of Return is: " + (geometricAverage * 100).toFixed(2) + "%"; } }

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