Měření averze ke ztrátě soukromého investora

Purpose of the article: This paper gives an empirical view on behaviorance of private investor who is loss averse and whether a loss aversive private investor should invest into such risky assets as equity? The main focus is on the use of robust statistical methods and prospect theory for estimation of equity indexes’ selected characteristics, mainly risk characteristics. The paper contains a detail discussion, which one risk metric for assets seems suitable for private investor who is loss averse. Scientific aim of this article: The aim of the article is a critically describe the problems related with private investor’s loss aversion behaviorance and how the concept of loss aversion should by applied into equities (or equity indices) investment. The crucial problem is how to measure loss aversion of private investor investing in equities. Methodology/methods: The primary and secondary research was applied. Selected scientific articles and other literature published with the topic of prospect theory and risk measurement are mainly used to support a critical analyse of how private investor’s loss aversion should be define and measured in the reality – in the financial/investment area. Next the primary research was done with selected equity indexes. As the representants of equity indexes were chosen not only “typical” representative as MSCI World index but mainly some derivatives of indexes which track a dividend strategy (indexes comprising stocks of companies that pay dividends). Findings: Loss aversive investor worries about any loss of value of their wealth. If these investors choose to invest in stocks they should prefer to invest in the stock indexes with down-side risk close to zero, respectively those indexes whose down-side risk is lowest among all. This down-risk should by measure with using belowtarget semivariance. A standard deviation method as a tool for measurement of risk for loss aversive investor is not so proper due the fact that large positive outcomes are treated as equally risky as large negative ones. In practice, however, positive outliers should be regarded as a bonus and not as a risk. Conclusions: A loss averse investors should some part of his/her wealth invest into equity indexes (may be 15%, max.25%). As the best equity index for a loss adverse investor was chosen Natural Monopoly Index 30 Infrastructure Global with the smallest down side risk

Robust Mean-Variance Portfolio Selection

This paper investigates model risk issues in the context of mean-variance portfolio selection. We analytically and numerically show that, under model misspecification, the use of statistically robust estimates instead of the widely used classical sample mean and covariance is highly beneficial for the stability properties of the mean-variance optimal portfolios. Moreover, we perform simulations leading to the conclusion that, under classical estimation, model risk bias dominates estimation risk bias. Finally, we suggest a diagnostic tool to warn the analyst of the presence of extreme returns that have an abnormally large influence on the optimization results.Mean-variance e .cient frontier; Outliers; Model risk; Robust es-timation

Cleaning large correlation matrices: tools from random matrix theory

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.Comment: 165 pages, article submitted to Physics Report

Demand uncertainty In modelling WDS: scaling laws and scenario generation

Water distribution systems (WDS) are critical infrastructures that should be designed to work properly in different conditions. The design and management of WDS should take into account the uncertain nature of some system parameters affecting the overall reliability of these infrastructures. In this context, water demand represents the major source of uncertainty. Thus, uncertain demand should be either modelled as a stochastic process or characterized using statistical tools. In this paper, we extend to the 3rd and 4th order moments the analytical equations (namely scaling laws) expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users. Also, we describe how the probability density function (pdf) of the demand signal changes with both the increase of the user’s number and the sampling rate variation. With this aim, synthetic data and real indoor water demand data are used. The scaling laws of the water demand statistics are a powerful tool which allows us to incorporate the demand uncertainty in the optimization models for a sustainable management of WDS. Specifically, in the stochastic/robust optimization, solutions close to the optimum in different working conditions should be considered. Obviously, the results of these optimization models are strongly dependent on the conditions that are taken into consideration (i.e. the scenarios). Among the approaches for the definition of demand scenarios and their probability-weight of occurrence, the moment-matching method is based on matching a set of statistical properties, e.g. moments from the 1st (mean) to the 4th (kurtosis) order

Realtime market microstructure analysis: online Transaction Cost Analysis

Motivated by the practical challenge in monitoring the performance of a large number of algorithmic trading orders, this paper provides a methodology that leads to automatic discovery of the causes that lie behind a poor trading performance. It also gives theoretical foundations to a generic framework for real-time trading analysis. Academic literature provides different ways to formalize these algorithms and show how optimal they can be from a mean-variance, a stochastic control, an impulse control or a statistical learning viewpoint. This paper is agnostic about the way the algorithm has been built and provides a theoretical formalism to identify in real-time the market conditions that influenced its efficiency or inefficiency. For a given set of characteristics describing the market context, selected by a practitioner, we first show how a set of additional derived explanatory factors, called anomaly detectors, can be created for each market order. We then will present an online methodology to quantify how this extended set of factors, at any given time, predicts which of the orders are underperforming while calculating the predictive power of this explanatory factor set. Armed with this information, which we call influence analysis, we intend to empower the order monitoring user to take appropriate action on any affected orders by re-calibrating the trading algorithms working the order through new parameters, pausing their execution or taking over more direct trading control. Also we intend that use of this method in the post trade analysis of algorithms can be taken advantage of to automatically adjust their trading action.Comment: 33 pages, 12 figure