Entropy in portfolio optimization / Yasaman Izadparast Shirazi - Yasaman Izadparast, Shirazi (2017)
In this thesis, we investigate the properties of entropy as an alternative measure of risk. Entropy has been compared with the traditional risk measure, variance from different point of views. It has been established that though variance is computationally simple and very popular among practitioners, a more flexible measure of risk is demanded to cope with the uncertainty in real data that are typically non-normally distributed. Entropy, however, is not computationally easy but is not restricted to the assumption of normality. In this study we explore and investigate the application of entropy in portfolio models. More specifically, we use multi-objective models that are the mean-entropy-entropy (MEE). The purpose of this new model is to overcome the limitations as observed in a traditional model; that is, having performance close to Markowitz’s mean-variance (MV) model when data comes from a normal distribution, but exhibit better performance when data comes from a non-normal distribution. The special advantage of the new model is that it is more diversified than any other models available in the literature. Also in this thesis, we address the issue of robust estimation of entropy. Special attention has been paid to entropy estimation with kernel density, which is popular among practitioners. The failure of this technique has been investigated and an adaptive beta-divergent method is proposed to ensure robust estimation. The usefulness of this technique has been verified with Monte-Carlo simulation in the context of portfolio analysis. Details of the algorithms which include entropy estimation which would enhance the application of a proper risk measure like entropy, is provided. Finally, the models are compared with Monte-Carlo simulation experiments and real data examples.