In this article, we’re going to talk about how to calculate the geometric average rate of return which is also known as the compound annual rate of return or the compounded annual growth rate. So when we think about this compounded rate of return what we’re going to do to calculate it is, we’re going to take the return of each period, so let’s say we’ve got years 1, years 2, and 3 here and we’ve got a rate of return of 25% in year 1, a rate of return of negative 40% in year 2 and a rate of return a 30% in year 3. So we’re going to take those rates of return and we’re going to compound them over time.
So our formula is going to be as follows we’re going to say 1.25 and we’ll just take one point two five forget the percent for a moment we’ll convert back to that later, (1.25 ✕ .6 ✕ 1.3). Now here’s how I come up with these numbers if we had $100 at the beginning of the year and we’re at the beginning of year 1 and we’re thinking “How does that increase while there’s a 25% rate of return.” So we would multiply that $100 by 1.25 that’s how we would get what we have at the end of the period, and then the next period we’re saying hey we have to multiply by (1 – 0.4) because we’re losing actually 40%. So what are we going to keep if we’re losing 0.4 proportion or 40%? that means we’re keeping 60% or 0.6 of our investment. So we multiply our initial investment would be (1.25 ✕ .6 ✕ 1.3) as we go 30% at the end of the period.
Now all of this we’re going to take we’re going to raise that to power and that power is going to be 1 divided by the number of periods, so we’ll say 1 divided by N and in this case “n” is going to be 3 because we have three years here. Then we’re going to take this whole thing and then we’re going to subtract 1 from this whatever results in we get here. So if you do the math there that’s going to give you, and this is going to be rounded here but it’s going to give you a negative 0.0008. Let’s say to make it easier to interpret we are going to round this number and this will be negative 0.01, which is the same as saying negative 1%.