# Free Reading: Advance Statistics for the LATAM ETFs, 01/08/2022

***Remember that when an interactice chart is cited on the post, by clicking on it the source code will be shown, In order to visualize it on the right way, download the file as html and open it with your browser.***

***Remember that when an interactice chart is cited on the post, by clicking on it the source code will be shown, In order to visualize it on the right way, download the file as html and open it with your browser.***

** **

If prior posts have been checked by the reader, it will be already known that the ** four methodologies** used are:

**. As stock quotes are stochastic processes,**

*Linear programming (LP), Simulation (Sim), Bootstrapping plus LP (Bootlp), and Bootstrapping plus sim (Bootsim)***will only be revealed as approaches are**

*hidden behaviors***to each other, at least two needed to use one as a**

*compared***. A simple example, the picture¹ below that has been selected as this post's header:**

*benchmark*According to ** LP**,

**of the expected returns from the LATAM ETFs quoting in USA is**

*none***from the others meaning that if by investing in one of them one gets a higher/lower return than others, the**

*significantly different***would be only**

*difference***. However, here a more interesting case has been revealed: while**

*coincidential***gave similar results**

*bootlp***didn't, the latter recorded that at least one of the means is not different from the others by chance but statistically significant:**

*bootsim*It is not task of this post neither website to be a teacher on the field; then, main takeaways are as follows:

The pair

are significantly different.*('MEXX', 'BZQ')*The

merely goes*CI*, why?*over zero*The algorithm doesn't use

to generate the bootstrap, therefore, every run*feed*.*differs*

Additionally, to check out why three out of four tests didn't find the significantly different pair, the ** boxplots** give the clue on explaining this result²:

First outcome, not major differences around the mean or median. Secondly, ** LP** shows a slightly

**, the reason lies on the fact that while**

*less scattered expected returns against Bootlp***has total**

*LP***of**

*degrees of freedom***,**

*3401***records**

*Bootlp***. Lastly, there are three ETFs expected to count with a significant higher risk form the others**

*18719***,**

*BRZU***, and**

*MEXX***, all with**

*UBR***. A strongly based statement can be said after the**

*pronounced outliers***is inspected:**

*anova report for the variance*While the ** p-value** with the

**and**

*LP***method gives**

*Sim***indicating**

*0.19***among the LATAM ETFs traded in USA,**

*no significant difference in risks***and**

*Bootlp***find it with**

*Bootsim***at**

*p-values***and**

*0,003***. According to the latter, The risk of EWZ is significantly different from that one of MEXX and BZQ; indeed,**

*0,001***. Moreover, as in the**

*37 pairs count with signficant difference*__prior case analyzed__, LATAM ETFs

**, the following heatmaps show**

*don't give major diversification opportunities***within methodologies:**

*no distinct results*No sense to show the other heatmaps as all of them have only slight differences. For the other heatmaps:

At the same time, the missing comprehensive report for Bootlp can be accessed __here__.

Finally, let's have a look at the four scatter plots:

** Sharpe Ratios** (SR) go from -16,84% to 5,02%.

** Naive** portfolio returns 0,098% with a risk of 4,60% at a SR of 1,06%.

** Minimum variance** portfolio returns -0,01% with risk 1,23% and SR -4,83%.

** Efficient portfolio** returns 0,3% with risk 4,99% and SR 5,02%, composition:

EWW: 3,98%

ARGT: 86,6%

FLMX: 4,31%

MEXX: 5,10%

** SRs** go from -0,78% to 2,67%.

** Minimum variance** portfolio returns -0,04% with risk 2,81% and SR -0,42%.

** Efficient portfolio** returns 0,19% with risk 5,26% and SR 2,67%.

** SRs** go from -16,83% to 4,32%.

** Naive** portfolio returns 0,01% with a risk of 4,85% at a SR of -0,68%.

** Minimum variance** portfolio returns -0,12% with risk 1,01% and SR -16,83%.

** Efficient portfolio** returns 0,27% with risk 5,25% and SR 4,31%, there is an implied higher risk asociated as this is not a portfolio but a security:

**.**

*ARGT*** SRs** go from 1,11% to 4,49%.

** Minimum variance** portfolio returns 0,11% with risk 2,80% and SR 2,07%.

** Efficient portfolio** returns 0,27% with risk 5,01% and SR 4,49%.

Otucomes:

, it depends on the decision maker's profile e.g. a +40 years old married with children investor may choose to follow the simulation method as it is more concervative while a single one on the 20s would take a decision based on the Bootlp method.*There is not best methodology*Despite prior statement, are the efficient portfolio's return, risk and SR signficant different from each other? Here it would be correct to say that

as the sample is not big enough (only 18 ETFs).*results are not conclusive*could be the portfolio with expected return 0,11%, 2,20% risk and SR 2,75% that invests mostly in Argentinian and Brazilian securities.*Best option*

*¹ This post includes comprehensive Excel reports by clicking on the images.*

*² Sim and Bootsim are not shown here as simulation only makes a difference in the scatter plots.*

*All these calculations are based on probabilities, which can fail sometimes; however, the developed algorithm to reach those numbers has been thought to reduce such failures to their lowest level.*