Analysis of investment in financial markets: Markowitz against Value at Risk historical approach

Abstract

This study compares three approaches to portfolio optimization, the approach suggested by Markowitz (1952), and the approach based on employing the historical approach to Value at Risk (VaR), at both the 90% and 95% levels of confidence, as risk measure. To fulfill this purpose, real data of stock prices for seven different companies that have been listed on the Ibex 35 were used to empirically obtain optimal portfolios according to these three approaches. To do it, the program used was Excel, with special relevance to the tool Solver, obtaining optimal portfolios for eight different levels of expected returns. Although the behaviour of the asset’s weights in the different portfolios that minimize risk measured by VaR is quite erratic, in general portfolios that minimize risk measured by 95% VaR are more similar to the ones obtained under Markowitz’s (1952) approach than portfolios that minimize risk measured by 90% VaR.