In the aftermath of the Global Financial Crisis, some risk management practitioners have advocated wider adoption of Bayesian inference to replace Value- at-Risk (VaR) models in order to minimize risk failures. Despite its limitations, the Bayesian methodology has significant advantages. Just...

In aftermath of the Financial Crisis, some risk management practitioners advocate wider adoption of Bayesian inference to replace Value-at-Risk (VaR) models for minimizing risk failures (Borison & Hamm, 2010). They claim reliance of Bayesian inference on subjective judgment, the key limitation...

Traditional mean variance optimization assumes that future returns and covariances of all the assets in the universe are known exactly. In practice, these input parameters are subject to estimation errors that may render the output of the optimization algorithm essentially useless. Here we...

Risk assessments often encounter extreme settings with very few or no occurrences in reality. Inferences about risk indicators in such settings face the problem of insufficient data. Extreme value theory is particularly well suited for handling this type of problems. This paper uses a...

We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest...

We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and...

Tail risk refers to the possibility that a rare event would adversely affect the value of a portfolio in a significant manner. It became much more relevant due to recent periods of strong market turbulence.We describe how to quantify such risk, which tail risk protection strategies were...

This paper is aimed at presenting application of bootstrap interval estimation methods to the assessment of financial investment’s effectiveness and risk. At first, we give an overview of various methods of bootstrap confidence interval estimation, i.e. bootstrap-t interval, percentile...

Model-selection uncertainty corresponds to the uncertainty about the true lag order of the autoregressive process that should be picked. This paper shows that all model-selection criteria perform poorly in small samples. Model-selection uncertainty adds to the bias and variability in the...