The project that we have done based on the Markowitz and Sharp methodologies that allow investors to build an efficient portfolio. An efficient portfolio is defined as the portfolio that maximizes the expected return for a given amount of risk (standard deviation), or the portfolio that minimizes the risk subject to a given expected return.
Markowitz method determines the asset allocation that produces the highest expected return for each unit of risk. The calculation is based on forecasts of each asset's long-term return and volatility and correlations among the various assets. Method showed how the variances of individual stock returns and the correlations of those returns can be combined to calculate a value for the variance of a portfolio made up of those stocks. Based on the received data of possible asset allocation we were able to draw an efficient frontier.
The efficient frontier is the curve that shows all efficient portfolios in a risk-return framework.
The general solution to the shortcomings of the Markowitz method for estimate stock portfolio risk is the use of common factor models. The most known common factor model is Sharp’s single-index model. The single-index model assumes that there is only 1 macroeconomic factor that causes the systematic risk affecting all stock returns and this factor can be represented by the rate of return on a market index, such as the S&P 500. According to this model, the return of any stock can be decomposed into the expected excess return of the individual stock due to firm-specific factors, commonly denoted by its alpha coefficient (α), the return due to macroeconomic events that affect the market, and the unexpected microeconomic events that affect only the firm.
To build covariance matrix we used the regression analysis to get α vector, residual standard deviation and, as a result, residual variance that we needed to build the covariance matrix inverse of variance -...