Alternative risk approaches in portfolio optimization

Abstract

One of the most complicated part in the investment process when we build our portfolio, once the selection of the types of the assets in which we want to invest our capital has been done, is the allocation of our money among the different chosen assets. To understand which fraction of our capital must be devoted to each asset in our portfolio a lot of mathematical models have been discussed in the literature, starting from the intuitive naïve approach in which we just divide our capital into the different assets in equal proportion, the first real model was introduced in the 50’s by Harry Markowitz, his model can appear simple and outdated today as the financial environment developed a lot in the last decades, in that period the computing power was also very different from today, his model has been improved more and more in the following years. In this paper we will start from the Markowitz model to understand its pros and cons and we will try to deal with some of the negative aspects which today make it too simplistic and not efficient to realize a good portfolio structure, we will try to apply some other more recent models to allocate the assets in our investment portfolio. We will consider the risk measure used in the Markowitz model, the variance of the returns, and try to understand whether a different approach can provide us a better overall result even during a crisis context as in 2020