# 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?

Can someone explain it please?

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

ImBruces wrote:

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.

¯\_(ツ)_/¯ It be like that sometimes.

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