# LP: Adv. Statistics & Markov Chain Projection for the 10 Most Traded ETFs in USA, FREE (12/21/2021)

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***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.***

The ** Top10 traded ETFs in USA** are compounded by

**. Pairs as**

*SQQQ, SPY, XLF, QQQ, UVXY, TQQQ, VXX, EEM, IWM, and XLE***are expected to obviously have a**

*(TQQQ;SQQQ)***correlation of**

*near perfect negative***, while so does the pair**

*minus one***but in the**

*(SPY;XLF)***direction. Even though the Top10 ETFs are**

*positive***to generate great**

*not expected***alternatives, it is of importance to find out**

*diversification***are one from each other as they are commonly used by**

*how significantly different***.**

*speculators*The picture at the beginning of this post shows that, ** apparently**, all of them count with

**(variance) then there are two hypotheses to test and the first one would be:**

*same expected return and risk***. The**

*"all means are equal"***report in the sheet**

*Anova***from the following Excel report:**

*"Summary"*Gives the answer: * "At a 95% confidence level, the hypothesis of all means being equal can be rejected as there is a probability of 0,034% that the difference in the observed means is coincidential"*. As the Anova report indicates that

*of the means is significantly different, a*

**at least one***test is undertook to spot this or these means. All 45 compared pairs but*

**Honest Significant Difference (HSD)***count with a*

**(TQQQ;SQQQ)***that goes*

**confident interval***; therefore, the expected ETF*

**over zero***is the only with a significant difference.*

**SQQQ**What does it mean? If a speculator or investor holds in his portfolio two or more of this Top10 ETFs, he would be holding alternatives that yield * significant equality* in expected

*. Thus, to complement the assessment a*

**returns***is also computed. As the 45 compared pairs yield a test*

**Minitab MC Test for the Variance***of*

**p-value***, it can be affirmed that*

**0.2335***in this study count with the*

**all ETFs***at a 95% confidence level. Consequently, it is*

**same level of risk***to use them as a*

**not adviced***.*

**diversification tool**As can be seen in the above correlation heatmap, all values are extremely * high* compared with a desired

*(for more discussion on Markowitz definitions visit*

**negative value around zero**__this link__). Therefore, as no diversification can be suggested for the Top10 ETFs in USA and all of them represent

*at a certain level of risk, it should be analyzed which ones offer the best*

**significant same return***to pick them up for speculative purposes (the risk free rate taken is the*

**Sharpe ratio***).*

**Treasury Yield for a 10-y bond**The Sharpe ratio values go from * -0,2973*, for the minimum risk portfolio at an expected return of -1,5192%, to

*for*

**0,2212***. Even though the right process would be to run a*

**QQQ***, the highest ratio can be selected as such tests have been already evaluated for the mean and risk (elaborated explanation of why a visual selection is enough in*

**MC Test for Proportions**__this link__). The following scatter trace shows the

*in terms of*

**location***for the Top10 ETFs in USA, five portfolios equally separated, Naive, and Market Portfolio:*

**risk and return**Regarding the * market portfolio*, the program

*(developed by ML Perspective) yields to*

**"MGM_v3_2_decimals"***results between*

**accurate***and*

**33%***of the times the algorithm is run. This percentage could have not been improved since the first version*

**50%***, therefore, further actions have been taken to solve it and get success rate improved on later versions. However, it may also be due to a*

**"MGM_v1_0_fractions"***of the algorithm itself coming from the provider as for small samples work well.*

**limitation***Markov Chains Projections*

*Markov Chains Projections*

Each ETF sheet counts with * six tables* (for elaboration on each table visit

__this link__), the

*column is the one that will*

**category***, over time,*

**determine***that can be easily identified with this approach rather than on the classic one based on the quotes themselves. Main outcomes are as follows:*

**changes in trends**, most likely weekly return/loss: between*SQQQ*and*-3,00 USD*. If in one week the ETF loses up to 36,92 USD, it is highly probable that the following week will record a loss of at least 3,00 USD. On the*13,96 USD (65,19%)*, it is expected weekly returns from*long run*to*-19,96 USD*.*13,96 USD (92,08%)*for the positive side*Odds*.*1,08*, if in a week records returns of*SPY*or*15,55 USD*, one can expect to get a certain return on the following week between*higher*and*-11,85 USD*with*15,55 USD*for the positive side of*odds*.*1,5*, if a return between*XLF*or*2,09 USD*is recorded, a*higher*of up to*correction*can be expected to be certain. Unlike SPY,*-2,48 USD*for the positive side on the long run are*odds*.*0,39*

*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.*