Imagine you have three different graphs showing your investment portfolio. Which one represents an 8% average annual return each year?
Surprisingly, all of them do! One of the most common and useful statistics in personal finance is the idea that stocks will yield an average return of 8% annually. This figure comes from looking at stock market trends over almost a century.
Even though past returns don’t guarantee future outcomes, many investors rely on the notion that investing in a stock index fund will provide this 8% return in the long run. For you and me, this means a $10,000 investment could hypothetically grow to this amount over time:
But in reality, your investment rarely follows such a smooth path. Wouldn’t it be great if your money only went up consistently?
The real value of this 8% figure is in planning. For example, if you’re 30 years away from retirement, knowing an index fund might return 8% can help you estimate how much to save each month to meet your goals.
However, when someone mentions the average return of an investment, they might not be giving you the most accurate or useful number. There are two ways to calculate the average of a set of data: the arithmetic average and the geometric average.
What’s the difference? A lot! Here’s what $10,000 would look like in 5 years using each average:
Which one is correct? Let’s crunch some numbers to find out:
The geometric average is the one that aligns with our example. Why? Without getting too technical, the geometric average accounts for compounding effects, while the arithmetic average does not. In our 8% index fund example, the 8% grows on top of the total amount from the previous year. That’s the power of compounding returns.
Interestingly, the geometric average is also called the annualized rate of return, and it’s commonly used in professional documents. Remember, if someone gives you a set of data, they might not be using the geometric average, so their return rates could be misleading. Understanding the calculation method will help you validate the data.
If you have annual return data and want to calculate it yourself, it’s pretty easy, especially if you’re good with Excel. The equation looks like this:
G=[ R1×R2×…×Rn ]^(1/n)
Where:
R=(1+r)
In simpler terms, add 1 to each yearly return, multiply them all, then apply an exponent of 1 divided by the number of values.
Here’s our example with the math shown in Excel.
Give it a try and see if you get the same results. Knowing how to do this lets you explore many “what-if” scenarios. For instance, what if you had invested in a particular stock or bond? With the annual history of any investment, you can calculate your own rates of return and make informed decisions. The possibilities are endless!
1) How to Buy an Index Fund
2) Why Compound Interest Makes You Rich!
3) Six Easy Steps to Figuring Out Your Retirement
