**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 traditional method developed by **Harry Markowitz** bases its investment recommendation on an

**between**

*optimization***-mean- and**

*estimated return***-standard deviation-. As this post does not intend to give a lesson on this method, only results will be shown and briefly discussed as the**

*risk***developed by ML Perspective also outputs this:**

__code__As indicated by the orange triangles, the highest **Sharpe Ratio** -6,06%- corresponds to the portfolio with mean 0.33% and std 3,93%, the components of this portfolio are as follows:

BRE.PA 3,19%.

XSMC.SW 0,09%.

*LVC.PA 39,10%*DSB.PA 0,04%

*AETF.AT 49,65%*2INVE.MC 7,84%

Consequently, assuming the **Pareto Rule **thus focusing on LVC.PA and AETF.AT at a ratio of 4/5, the real return for a period of 46 days towards

**is as shown below:**

*18/12/2023*Hence, applying the ratio 4/5, the earnings of a fictional investment of ** 1.000,00 USD** yields 126,14 and 68,67 USD respectively, which records a return of

**in**

*17,87%***or**

*49 days***. Therefore, what was the**

*240,42% annually***contribution of the**

*new***to attribute itself such return? Let's have a look at what it used to give its**

__estimates code__**:**

*recommendations*First data input is the **Markov Chain** itself labeled with key

**, the**

*'dfs'***is also needed, the bins' positive, negative and average components -following three keys-, and the**

*'last_price'***and**

*'mean'***-standard deviation-**

*'sd'***on an**

*based***. To check details on how these last two features are calculated check the source code here.**

*average expectation*After here, the keys:** 'std_avg_dif'**,

**, and**

*'positive_estimate_array'***-and similar-, are features calculated based on the prior ones, developers can check the source code, in the**

*'positive_final_estimates'***linked above, to check and/or modify them according to their believes. Consequently, all these features yield to the following data frame:**

*estimates code*** 'Metric'** is a measure of

**are the**

*how spread***calculated, the**

*final features***the value the**

*lower***it is. However,**

*better***are not taken into account yet; hence, a graph helps to**

*base-features***options as follows:**

*visually discard*A ** red** arrow indicates that the instance is

**either in the down or up side, a**

*underperforming***one that it is**

*green***, while**

*overperforming***and**

*pale coral***indicate that the performance is**

*lightblue***e.g. second, fifth, eight, etc. instances are underperformers; thus, not recommended for positive expectations.**

*not significantly different from the median*The ** black** crosses are just the Pareto Markov States nodes

**multiplied by the upper bin limits at the same positions. The logic of this metric is to evaluate**

*probability***is the**

*how shrunk***of**

*distribution***among the 20-80 nodes, the**

*returns***this result is to the positively predicted price the**

*closer***the latter one would be.**

*more accurate*So, according to the graph and data frame ** LVC.PA** is in the 14th place, but if the four

**are not taken into account, would be the tenth; therefore, how those first ten places performed compared to the real records? These are the results:**

*underperformers*EXS3.DE: Real 16,19%, Predicted [23,81%;23,85%]

IBEXA.MC: Real 28,69%, Predicted [32,78%;39,03%]

XB4A.DE: Real 13,50%, Predicted [16,67%;20,28%]

EL4B.DE: Real 15,66%, Predicted [17,08;18,16%]

VEUR.AS: Real 13,18%, Predicted [11,74%;16,25%]

3BAL.MI: Real 34,35%, Predicted [128,22%;132,07%]

FOO.PA: Real 6,43%, Predicted [17,09%;17,44%]

EXXX.DE: Real 13,61%, Predicted [17,55%;20,53%]

BNK.PA: Real 10,17%, Predicted [18,38%;20,29%]

*LVC.PA: Real 26,25%, Predicted [19,92%;26,77%]*

Consequently, if the same investor would have placed ** equally weighted** sums of money on these ten recommendations, the real return would have been

*17,80%*in

**or**

*49 days***, very close to the return obtained with the Markowitz portfolio and**

*238,81% annually***.**

*nearly 100% over the market return*
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