build a portfolio of securities chosen from the main Index of the São Paulo Stock, the IBOVESPA Index, which in synthesis represent the most traded shares of the stock exchange  (B3 for more details). These securities will be chosen by criteria of expected return and volatilities (risk-return) found in famous papers published between 1950 and 1980 - since this work is dedicated to explore the beginning of the sophistication of the financial industry, being sheltered for a later work the most modern theories - Among those papers we have: Portfolio Selection from Harry Markowitz \cite{Markowitz_1952}, Lifetime Portfolio Selection By Dynamic Stochastic Programming, Paul A. Samuelson \cite{Samuelson_1969} and Mutual Fund Performance \cite{Sharpe_1966}.  These portfolios will be tested against various economic indicators such as: GDP, interest rate, Inflation, commodities index and others. The goal is to build a portfolio where we can maximize the return and minimize the risk in order to overcome our benchmark, the IBOVESPA Index and over perform the Fixed Income and Brazilian Bound Market, by the return point of view (once we cant compare directly the risk in those types of investment), alongside we will adquire knowledge of how those macroeconomic variables affect portfolios, hence, we will have a better understanding of the Brazilian capital market and how to manage a Investment Fund. 

Determine the sensitivity of an investment portfolio against important economics variables in each country its the first step to build a strong investment index that can beat its benchmarks at a better risk return rate. Any country has its own particularity, its own degree of exposure against other economys, against one or more particular commoditie index, its own political system and so on. Because of that its meaningful to test how a model is going to behave in Brazil, a country with an historic of high inflation and interest rates with a strong dependence of agricultural and commodities index, moreover the fixed income and Brazilian Bound Market had a relative high return in comparison with other countries with relative little risk, that requires that managers have a competent risk management and deliver very strong incomes. Besides that this study its an opportunity to explore a field in finance and investment that is not to very well explored in the Academy. Students, managers and professionals from finance could also use the data showed here as a tool to better observe how macroeconomics variables affect investment decision models.

In order to fulfill our goal we will extract all the data from pre determined periods of all the securities that comprise the IBOVESPA index, and we will statistically estimate the expected return and volatile so we can have a risk-return model. Following the rule that an investor should consider the expected return a desirable thing and variance of the return undesirable \cite{Markowitz_1952}, or in other words, that the investor is risk averse and prefere a less risk investment choice over a riskier one, if they have the same return, and using the rule that investors have the same risk-tolerance in all periods of life, as showed at Lifetime Portfolio Selection \citep{Samuelson_1969}, we can maximize a portfolio selection with a risk management 

This work aims the identification, registration and analyses of the time series of IBOVESPA shares (the main Index of the Sao Paulo Stock Exchange) applied in well know financial models of risk-return. After the data collection, an analysis of the relationships between the variables will be performed for a subsequent determination of the resulting effects. Those caracteristics fit the Descritive research configuration. 

Our data sources are websites of trust and public faith such as the, the stock Exchange of Sao Paulo, Yahoo Finance,  Getúlio Vargas Institute, IBGE, Central Bank of Brazil, Bloomberg, CFA Institute, Economática, and others. Our references came from consecrated models from papers, case-studies and books from finance and economy, among them the mean-variance of returns and risk from Markowtiz, Lintner, Samuelson, Sharpe.

The results showed in this work will be exposed in a quantitative approach. Every data will be processed in the Python environment and the time series of the securities will be directly downloaded inside the program witch the authors are developing and coding. Once the calculations and linear regressions described in the models take place inside the program we will be able to choose the optimal portfolio and unveil it trough charts and tables.