What Is A Geometric Average

So, there I was, in the middle of a heated debate with my math-loving friend, Alex. We were discussing our latest investments, and I mentioned that my average return was around 15%. Alex, with a raised eyebrow, asked, "Are you sure about that? Because when I calculate the geometric average, it's a bit lower." I was taken aback. I mean, I knew my math wasn't perfect, but I was pretty sure I could handle an average. Turns out, there's more to averages than meets the eye. Let's dive into the fascinating world of geometric averages, shall we?

When Arithmetic Averages Aren't Enough

You know how we usually calculate averages, right? You add up all the numbers and then divide by the count. That's called an arithmetic average. It's simple, it's easy, and it works most of the time. But here's the thing, folks - it doesn't always tell the whole story. Especially when we're dealing with percentages or rates that can compound over time, like our investments.

Let me give you an example. Say you have three investments. The first doubles in the first year, the second stays the same, and the third doubles in the second year. If you calculate the arithmetic average, you'll get a return of 50% over two years. Sounds great, right? But if you try to double your money with that average return, you'll be disappointed. Why? Because the arithmetic average doesn't account for the compounding effect. That's where the geometric average comes in.

Enter the Geometric Average

The geometric average, on the other hand, takes into account the compounding effect. It's calculated by multiplying all the numbers together and then taking the nth root, where n is the number of values. In our investment example, the geometric average return would be 0% over two years. Now, that's more like it!

Here's a little secret, though. The geometric average is also the average return you'd get if you reinvested all your profits at the end of each period. Isn't that neat? It's like the math is telling us to keep our money working for us. Now, who's ready to become a math whiz and impress their friends at the next investment club meeting?

Geometric Average Example at Arthur Poulsen blog

Why Geometric Averages Matter

So, why should you care about geometric averages? Well, for one, it gives you a more accurate picture of your returns when you're dealing with compounding growth. It's especially useful in finance, economics, and even in physics when you're dealing with rates of change. Plus, it's a great way to bust some myths about averages. Like the one that says you can average a million dollars a day for a month and still be a millionaire. Spoiler alert: you can't. Not unless you're starting with a pretty penny.

But here's the thing, folks. While geometric averages are more accurate in certain situations, they're not always the best tool for the job. Arithmetic averages are simpler to calculate and understand, and they're often good enough for a quick, rough estimate. It's all about using the right tool for the job. And now, you've got another tool in your toolbox. You're welcome.

PPT - Definitions PowerPoint Presentation, free download - ID:2761697

How to Calculate a Geometric Average

Alright, so you're convinced. You want to start calculating geometric averages like a pro. I've got you covered. Here's a simple way to calculate it:

1. List out all the numbers you want to average. Let's say it's a list of annual returns: 10%, 20%, -5%, 15%, and 30%.
2. Convert the percentages to decimals. So, our list becomes: 0.1, 0.2, -0.05, 0.15, and 0.3.
3. Multiply all the numbers together. In our case, that's 0.1 * 0.2 * (-0.05) * 0.15 * 0.3. The result is -0.00045.
4. Take the fifth root of the result (since we have five numbers). The fifth root of -0.00045 is approximately -0.038.
5. Convert the result back to a percentage. So, our geometric average return is approximately -3.8%.

And there you have it! You've just calculated a geometric average. Isn't that something? Now, go forth and impress your friends with your newfound math skills. Just remember, with great math comes great responsibility. Don't go around confusing people with your fancy averages. Use your powers for good, not evil.