To Become a Smarter Investor, Learn This One Calculation
Take a look at the table below, which shows Tesla’s (NSDQ: TSLA) yearly returns over the past seven years.
The first column lists the year. The second column indicates the percentage return of TSLA during that year. The third column shows what $1,000, invested at the very beginning of 2015, would be worth at the end of the year indicated.
As you can see from the table, $1,000 invested in TSLA and held until the end of 2021 would have become more than $23,000. Not bad at all.
My question for you is, what is Tesla stock’s average yearly return over this period?
Not as Simple as It Seems
Easy right? Just add up all the yearly returns and divide by 7! This is taking the simple average, aka the arithmetic mean.
And if we do that, we come up with 124.04%.
To test whether the answer is correct, let’s start with $1,000 and increase it by 124.04% every year for seven years.
The table shows that if TSLA returned 124.04% per year for seven years, $1,000 invested at the beginning of 2015 would become more than $283,000 by the end of 2021! This is more than 10 times the amount shown in the first table. Clearly something is wrong.
You see, just taking the simple average neglects the impact of compounding and overstates the annual return.
Don’t Forget Compounding
Consider the year 2019 in the first table as an example. The 25.71% return is calculated against the 2018 ending value (which is also the 2019 beginning value) of $1,496.40, resulting in a 2019 ending value of $1,881.07.
The key point here is that you earn the 25.71% return not only on the original $1,000 investment, but also on the $496.40 gain in the value of the shares. In fact, any return you achieve on the original investment will also earn return on their own. That’s the beauty of compounding.
Since simple average is not a good way to calculate the average return, how should we calculate an accurate average?
We need to figure out the geometric mean, aka the compound average growth rate.
Calculating the Geometric Mean
To calculate the geometric mean, we need to first take the product of the returns each year. To do this, first convert the percentage return to decimal form, and then add 1 to it.
Thus, for 2015, the 7.06% return becomes 1.076 (1 + 0.076). For 2016, it becomes 0.8975 (1 – 0.1025).
So the product of the returns are: 1.076 x 0.8975 x 1.4569 x 1.0689 x 1.2571 x 8.434 x 1.4976 = 23.8788.
But you are not done. You need to raise that number to the power of (1/N) and subtract 1. N is the number of years. In this case it’s 7.
The final step is therefore 23.8788 raised to the power of (1/7), or 0.14286, minus 1. (You will need Excel or a calculator with an exponential function.)
The answer comes out to be 57.35%. Clearly, this is a big difference from the simple average. But more importantly, is it correct?
Let’s test it out like we did for the simple average.
As you can see, the value at the end of 2021 comes out to be $23,881, very close to the $23,758 from the first table. The discrepancy between the two numbers is merely due to rounding. We have thus confirmed that Tesla stock’s average annual return from 2015 through 2021 was 57.35%.
Hopefully all the math didn’t make you roll your eyes. As annoying as the calculations seem at first, once you get the hang of how it’s done, they’re actually quite simple.
Knowing how to accurately calculate the geometric mean can help you not only in figuring out average returns, the formula can be applied to similar situations where you need to find an accurate average. For example, if you want to figure out a company’s revenue growth rate, the same formula applies.
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