# Calculate the geometric mean return of SLASX

If you have all positive returns, in the formula, let`s suppose:

Year 1 - 34,9% year 2 - 6,13% year 3 - 2,69% year 4 - 11,66% year 5 - 21,77%

in the book the answer is:

(1,349)*(1,.0613)*(1,0269)*(1,1166)*(1,2177)^1/5 - 1

(1,349)*(1,.0613)*(1,0269)*(1,1166)*(1,2177)^0,2 - 1

My question is why instead of putting like 0,349 you need to add a 1 in all of them?

Its ^1/5 because there`s 5 elements, right?

This is “true”, however, I think you ought to familiarize yourself with how percentages work a little more, and then your question of “why you have to add 1” will dissappear.

Think of it in terms of growing a \$100K investment. If you invested \$100k at the beginning of that 5 years, at the end, you’d have a portfolio worth \$199,901.57 - do you follow this? in the first year it grew by 34.9%, then 6.13%… etc. until it’ finally worth \$199,901.57. which is a return of 99.9016% over 5 years.

The geometric mean gives you the annualized growth rate of your investment. Which is 14.8585%. A 99% return is expressed as 1.99 - but we know that 99% is earned over five years which is why we take the fifth root of 1.99 to find the annualized return.

An investor who earned 34.9% in year 1, then 6.13% in year 2, then 2.69% in year 3, then 11.66% in year 4, and finally 21.77% in year five, has effectively done the same thing as earning 14.8585% throughought every year.

I think I’ve repeated myself multiple times in all of that above. But hope it helps you.

Yes the example of the 100K investment helped me understanding why the 1, thank you.