# Hidden Outcomes Revealed: To Invest Across Sectors is not Enough, All¹ ETFs in Europe, 20/12/2021

***Remember that when an interactive 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 interactive 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***. Therefore, the following post contains three sections that will be analyzed as follows:**

*benchmark*Reports for the*Anova*and*Mean*: LP/Sim vs Bootlp/Bootsim.*Variance*Heatmaps: LP/Sim vs Bootlp/Bootsim.*Correlation*: All four methods compared.*Efficient Portfolios*

Consequently, regarding Anova reports, the results are as follows² (click on image to access full report):

According to ** LP**,

**of the expected returns from the ETFs in Europe is**

*none***from the others, it means that the difference among their returns is**

*significantly different***. Again, as in the case of the USA Top10, Top95, and LATAM ETFs, to invest within**

*only coincidential***, it means that, despite investing**

*one single region does not truly diversify risk***, within a**

*across sectors***the**

*same region***is not overcome. Thus, may bootstrapping reveal something that solely LP can not? its Anova reports are as follows:**

*unsystematic risk*Results ** don't differ³** between them but with LP/Sim regarding the null hypothesis as it is rejected with a

**. However, let's analyze pairwise the HSD test to check if any dissimilarities arise between both runs:**

*p-value near zero**Bootlp*

different : 1.066 pairs (77%)*Non-significantly*different : 312 pairs (23%)*Significantly*

*Bootsim*

different : 1.049 pairs (76%)*Non-significantly*different : 329 pairs (24%)*Significantly*

As can be seen, proportions are ** around** the

**ratio, which could seem to differ from the**

*75/15***found in**

*85/15***(it can't be confirmed they are different, why?). Consequently, if one would want to hold**

*USA***an option could be**

*whole Europe***(EURO STOXX 50), its expected return counts with a significant difference against**

*EUEA.AS***and**

*BX4.PA, BXX.PA, XSD2.L, 3ITS.MI, XACT-BEAR-2.ST, XACT-BEAR.ST, XBRMIB.MI,***all**

*3BAL.MI***with the two latter being long while the former short.**

*leveraged*Therefore, any of these pairs has a ** real diversification opportunity**? at first glance, the answer would be

**because the leveraged ETFs would either delete one's profits (short) or multiply his risk (long). Similarly, looking at the correlation matrix it is confirmed that**

*not***has an option with**

*none***at**

*correlations***and**

*-0,4049, -0,4002, -0,4049, -0,5055, -0,0675,***. A brief look at the heatmaps will help to identify how possible it is to diversify within the European ETFs :**

*0,0814*From a graphical point of view both look pretty similar; however, there are slightly differences within their values e.g. the pair (** BTP10.MI**;

**) with**

*BX4.PA***records a correlation of -**

*LP***up from -**

*0,38***recorded by**

*0,13***Generally,**

*Bootlp.***computes**

*LP***against**

*higher correlations***; nonetheless, both ratify the non-possibility to diversify within a region: the former's**

*bootstrapping***would be**

*only option***(-0,0008) but both are**

*BX4.PA:XACT-OBLIGATION.ST***significantly different thus such mixture**

*not***.**

*raises risk*In addition, this pairs do the same e.g. ** BTP10.MI** is the ETF of

**while**

*Italy's Government bonds***is the**

*BX4.PA***by two of the**

*leveraged inverse***meaning that in a**

*CAC 40***investors would move funds towards these type of options thus**

*bear market***. About the latter promising option the case is exactly the same. The**

*move in same direction***-instead of being positive- may be the fact that these have been calculated as**

*nagtive correlation***and not as**

*USD***, the original currency.**

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

** Sharpe Ratios** (SR) go from -16,48% to 16,58%, up from -38,3% and 11,90%

**⁴**respectively.

** Naive** portfolio returns 0,14%, up from 0,04%, with a risk of 2,13% also up from 1,43%, at a SR of 5,42%, up from -2,46%.

** Minimum variance** portfolio returns -0,09%, down from -0,02%, with risk 0,88%, up from 0,73%, and SR -13,26%, unchanged from -13,37%.

** Efficient portfolio** returns 0,57%, unchanged from 0,51%, with risk 3,27%, down from 3,63%, and SR 16,58%, up from 11,92%, weights are:

XSMC.SW, 8,66%.

2INVE.MC, 23,10%.

XACT-BULL-2.ST, 68,24%.

** SRs** go from -0,56%, up from -15,42%, to 8,31%, up from 2,87%.

** Minimum variance** portfolio returns 0,05%, unchanged from -0,02%, with risk 1,34%, up from 0,85%, and SR 1,89%, up from -11,40%.

** Efficient portfolio** returns 0,24%, unchanged from 0,14%, with risk 2,62%, up from 2,29%, and SR 8,31%, up from 2,87%.

** SRs** go from -18,18%, up from -41,1%, to 12,59%, down from 15,8%.

** Naive** portfolio returns 0,10%, up from 0,06%, with a risk of 3,06%, up from 1,42%, at a SR of 2,43%, up from -1,10%.

** Minimum variance** portfolio returns -0,05%, unchanged from -0,02%, with risk 1,73%, up from 0,75%, and SR -4,46%, up from -12,28%.

** Efficient portfolio** returns 0,86%, up from 0,62%, with risk 6,61%, up from 3,43%, and SR 12,59%, down from 15,81%, weights are:

OBXD.OL, 8,66%.

XACT-BULL-2.ST, 91,34%.

** SRs** go from -0,47%, up from -15,61%, to 6,02%, up from 2,45%.

** Minimum variance** portfolio returns 0,04%, unchanged from -0,03%, with risk 3,52%, up from 0,73%, and SR 0,30%, up from -14,87%.

** Efficient portfolio** returns 0,30%, up from 0,12%, with risk 4,64%, up from 1,82%, and SR 6,02%, up from 2,45%.

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

; however, as this sample is*results are not conclusive*(checked by the degrees of freedom) the portfolio got with the*big enough*method could be suggested.*Bootlp*LP and Bootlp recommend

in big proportion, this is a leveraged ETF by two of the*XACT-BULL-2.ST*index from*OMXS30 Gross*; therefore, according to the code*Sweden*it is expected a__"Pattern Search"__weekly return for this index towards August 2022, it equals*1.04%*up to*37,81%*, looking at the*01/08/2022*between*real data*and that date this ETF returned*20/12/2021*in*55,23%*⁵.*USD*All SR ranges have

shifted upwards, but is it enough to confirm that Europe is*seemingly*than USA? The answer is not, why?.*more profitable*As in Top10 and Top95 USA, and Latam, to invest

is not enough to diversify risk, it*through sectors*be needed to invest*may*but such study has not been done yet.*through continents*

*¹ All ETF's whose historical prices are available on public domain.*

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

*³ Both bootstrapping methods can differ from each other as the option 'seed' to generate the random numbers is not used; therefore, each run is unique.*

*⁴ All comparisons are with USA Top95 ETFs.*

*⁵ Price USD 20/12/2021: 181.625*

* Price USD 01/08/2022: 117,0*

* (181.625-117)/117 = 0,5523*

*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.*