Depending on whether you know the final percentage change or the final total, you can pick the easier formula to get the answer. Let's walk through the same example again using this formula with a 3 year timeframe, a $1,000 starting point, and a $780 ending point:Īs you can see, either formula gets us to the same point. t0 is the '0 time' or start, 'tn' is the final time, after n periods. In this formula, we take the starting and ending point to find a 'total return', then compute the CAGR. (Of course, maybe not from the perspective of your stomach!) Compound Annual Growth Rate and Generic Geometric Mean Formulas Geometric Mean FormulaĪs we said in the last section, the geometric mean is based on the product of a set of numbers, so the Geometric Mean formula looks like this: The real answer? You finished with $780, or a compound annual growth rate of -7.948% a year:Īs you can see, "-50%, +30%, +20%" and "-7.948%, -7.948%, -7.948%" are equivalent from the perspective of your investment. For the third year, you gain 20%.Ī simple average of the three gains would give you: -50% + 30% + 20% = 0% gain a year. In the first year you lose 50% of your money. It's best illustrated in a simple example: Literally, a geometric mean is the central tendency of the product of a set of numbers, while a simple average is based on the sum of a set of numbers.Ī simple average doesn't work in the investing case because it doesn't have the same concept of history as the CAGR simple averages can't deal with volatility. You ignore the path and only see what constant percentage would have left your investment in the current state. Since investing almost always means volatility, with portfolios moving up and down based on value in the market, CAGR strips out that volatility to only concentrate on the starting and ending point. The compound annual growth rate is a special label applied in the business world to the so-called Geometric Mean.įor us investors, it is the percentage which applied equally to every period would leave us with the final amount. 1.5 What's next? Why Use CAGR instead of a Simple Average?
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