Optimal portfolio selection under Expected Shortfall optimisation with Random Matrix Theory denoising
|Autor:||Mgr. Jan Šíla|
|Rok:||2018 - zimní|
|Typ práce:|| Diplomová
Finance, finanční trhy a bankovnictví
|Abstrakt:||This thesis challenges several concepts in finance. Firstly, it is the Markowitz’s
solution to the portfolio problem. It introduces a new method which denoises
the covariance matrix – the cornerstone of the portfolio management.
Random Matrix Theory originates in particle physics and was recently introduced
to finance as the intersection between economics and natural sciences
has widened over the past couple of years.
Often discussed Efficient Market Hypothesis is opposed by adopting the
assumption, that financial returns are driven by Paretian distributions, instead
of Gaussian ones, as conjured by Mandelbrot some 50 years ago.
The portfolio selection is set in a framework, where Expected Shortfall
replaces the standard deviation as the risk measure. Therefore, direct optimisation
of the portfolio is implemented to be compared with the performance
of the classical solution and its denoised counterpart. The results are evaluated
in a controlled environment of Monte Carlo simulation as well as using
empirical data from S&P 500 constituents.