2015/10/16 by Fabio Caccioli, Caccioli, Fabio, Imre Kondor +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Portfolio Management (q-fin.PM) #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.1510.04943
openalex publication_date 2015/10/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The contour maps of the error of historical resp. parametric estimates for\nlarge random portfolios optimized under the risk measure Expected Shortfall\n(ES) are constructed. Similar maps for the sensitivity of the portfolio weights\nto small changes in the returns as well as the VaR of the ES-optimized\nportfolio are also presented, along with results for the distribution of\nportfolio weights over the random samples and for the out-of-sample and\nin-the-sample estimates for ES. The contour maps allow one to quantitatively\ndetermine the sample size (the length of the time series) required by the\noptimization for a given number of different assets in the portfolio, at a\ngiven confidence level and a given level of relative estimation error. The\nnecessary sample sizes invariably turn out to be unrealistically large for any\nreasonable choice of the number of assets and the confidence level. These\nresults are obtained via analytical calculations based on methods borrowed from\nthe statistical physics of random systems, supported by numerical simulations.\n