We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial...

Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis...

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio...

The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given...

A statistical analysis of the Budapest Stock Index (BUX) is presented. The high time resolution (5 s sampling) makes it possible to extract information on market functioning which does not emerge from daily data. The main results are as follows: from a statistical point of view the large drop in...

Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is used. We also show...

Using public data (Forbes Global 2000) we show that the distribution of asset sizes for the largest global firms follows a Pareto distribution in an intermediate range that is “interrupted” by a sharp cutoff in its upper tail, which is totally dominated by financial firms. This contrasts...

Correlations and other collective phenomena are considered in a schematic model of pairwise interacting, competing and collaborating agents facing a binary choice and situated at the nodes of the complete graph and a 2-dimensional regular lattice, respectively. The agents may be subjected to an...

The problem of estimation error of Expected Shortfall is analyzed, with a view of its introduction as a global regulatory risk measure.