On measuring the sensitivity of the optimal portfolio allocation

In this paper we consider the sensitivity problem connected with portfolio optimization results when different measures of risk such as portfolio rates of return standard deviation, portfolio VaR, CVaR are minimized. Conditioning the data (represented by spectral condition index of the rates of return correlation matrix) plays, as it is shown, a crucial role in describing the properties of the models. We report on the research conducted for 13 largest firms on Warsaw Stock Exchange.portfolio selection, Value-at-Risk, conditional Value-at-Risk

Portfolio selection models: A review and new directions

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean-risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a risk value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance

Dynamic asset (and liability) management under market and credit risk

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a mul- tistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present a index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate our approach. In this way we are able to demonstrate the feasibility and flexibility of the chosen framework

Hedge fund return predictability; To combine forecasts or combine information?

While the majority of the predictability literature has been devoted to the predictability of traditional asset classes, the literature on the predictability of hedge fund returns is quite scanty. We focus on assessing the out-of-sample predictability of hedge fund strategies by employing an extensive list of predictors. Aiming at reducing uncertainty risk associated with a single predictor model, we first engage into combining the individual forecasts. We consider various combining methods ranging from simple averaging schemes to more sophisticated ones, such as discounting forecast errors, cluster combining and principal components combining. Our second approach combines information of the predictors and applies kitchen sink, bootstrap aggregating (bagging), lasso, ridge and elastic net specifications. Our statistical and economic evaluation findings point to the superiority of simple combination methods. We also provide evidence on the use of hedge fund return forecasts for hedge fund risk measurement and portfolio allocation. Dynamically constructing portfolios based on the combination forecasts of hedge funds returns leads to considerably improved portfolio performance

Measuring the risk of a nonlinear portfolio with fat tailed risk factors through probability conserving transformation

This paper presents a new heuristic for fast approximation of VaR (Value-at-Risk) and CVaR (conditional Value-at-Risk) for financial portfolios, where the net worth of a portfolio is a non-linear function of possibly non-Gaussian risk factors. The proposed method is based on mapping non-normal marginal distributions into normal distributions via a probability conserving transformation and then using a quadratic, i.e. Delta–Gamma, approximation for the portfolio value. The method is very general and can deal with a wide range of marginal distributions of risk factors, including non-parametric distributions. Its computational load is comparable with the Delta–Gamma–Normal method based on Fourier inversion. However, unlike the Delta–Gamma–Normal method, the proposed heuristic preserves the tail behaviour of the individual risk factors, which may be seen as a significant advantage. We demonstrate the utility of the new method with comprehensive numerical experiments on simulated as well as real financial data

Risk in Transport investments

We discuss how the standard Cost-Benefit Analysis should be modified in order to take risk (and uncertainty) into account. We propose different approaches used in finance (Value at Risk, Conditional Value at Risk, Downside Risk Measures, and Efficiency Ratio) as useful tools to model the impact of risk in project evaluation. After introducing the concepts, we show how they could be used in CBA and provide some simple examples to illustrate how such concepts can be applied to evaluate the desirability of a new project infrastructure.Cost-Benefit Analysis, Risk, transportation, large project, Value at Risk, Conditional Value at Risk.

Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails

Forecasting Startup Return using Artificial Intelligence Methods and Econometric Models and Portfolio Optimization Using VaR and C-VaR

In this paper, we have tried to study the main role of startups in economy, their characteristics, main goals and etc. The main goal of article is prediction of startup's return using artificial intelligence methods such as genetic algorithm (GA) and artificial neural network (ANN). Some global indices such as S&P500, DJAI, and economic indicators such as 10 years Treasury yield, Wilshire 5000 Total Market Full Cap Index along with some other special indicators in startups like team, idea, timing and etc. are used as input variables. GA is used as feature selection and finding the most important variables. ANN is used as an optimization model and prediction of startup's returns. We used econometric models such as regression analysis. We have estimated Value at risk (VaR) and Conditional Value at risk (C-VAR) for considered portfolios including three startups (public company) such as Dropbox, Inc. (DBX), Scout24 SE (G24.DE) and TIE.AS and optimal portfolio formation. The results show that AI based methods are more powerful in prediction of startup's return. On the other hand, VaR and C-VaR models are very beneficial approach in minimizing risk and maximizing return