Work detail

Practical usage of optimal portfolio diversification using maximum entropy principle

Author: Mgr. Ostap Chopyk
Year: 2015 - summer
Leaders: prof. PhDr. Ladislav Krištoufek Ph.D.
Work type: Economic Theory
Language: English
Pages: 90
Awards and prizes:
Abstract: This thesis enhances the investigation of the principle of maximum entropy, implied in the portfolio
diversification problem, when portfolio consists of stocks. Entropy, as a measure of diversity, is used as the objective
function in the optimization problem with given side constraints. The principle of maximum entropy, by the nature
itself, suggests the solution for two problems; it reduces the estimation error of inputs, as it has a shrinkage
interpretation and it leads to more diversified portfolio. Furthermore, improvement to the portfolio optimization is made
by using design-free estimation of variance-covariance matrices of stock returns. Design-free estimation is proven to
provide superior estimate of large variance-covariance matrices and for data with heavy-tailed densities. To asses and
compare the performance of the portfolios, their out-of-sample Sharpe ratios are used. In nominal terms, the out-ofsample
Sharpe ratios are almost always lower for the portfolios, created using maximum entropy principle, than for
'classical' Markowitz's efficient portfolio. However, this out-of-sample Sharpe ratios are not statistically different, as it
was tested by constructing studentized time-series bootstrap confidence intervals.




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