Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-$t$ and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-$t$ copulas, are best at reducing the portfolio risk.     

Forecasting and decomposition of portfolio credit risk using macroeconomic and frailty factors

This paper presents a dynamic portfolio credit model following the regulatory framework, using macroeconomic and latent risk factors to predict the aggregate loan portfolio loss in a banking system. The latent risk factors have three levels: global across the entire banking system, parent-sectoral for the intermediate loan sectors and sector-specific for the individual loan sectors. The aggregate credit loss distribution of the banking system over a risk horizon is generated by Monte Carlo simulation, and a quantile estimator is used to produce the aggregate risk measure and economic capital. The risk contributions of the individual sectors and risk factors are measured by combining the Hoeffding decomposition with the Euler capital allocation rule. For the U.S. banking system, we find that the real GDP growth rate, the global and sector-wide frailty risk factors and their spillovers significantly affect loan defaults, and the impacts of the frailty factors are not only economy-wide but also sector-specific. We also find that the frailty risk factors make more significant risk contributions to the aggregate portfolio risk than the macroeconomic factors, while the macroeconomic factors help to improve the accuracy and efficiency of the credit risk forecasts.     

Statistical Methodologies for the Market Risk Measurement

This paper classifies statistical methodologies available for the marketrisk measurement. With the help of the weighted likelihood, a broad class ofnon-normal distributions, which are not generally considered so far, areapplied to possibly hetero-scedastic financial variables. The approach is compared with popular procedures such as GARCH and J. P. Morgan's using daily dataof 12 financial variables.     

Linear Correlation and EVT: Properties and Caveats

Due to the current credit crisis, critical questions are beingasked concerning some of the quantitative methods used in riskmanagement under the Basel II proposals. In this paper I havegiven a critical look at Extreme Value Theory and Copulas. Boththeir potential applications and the possible caveats are discussed,and this mainly with the subprime crisis as a background.     

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.     

Deposit Insurance and Risk Management of the U.S. Banking System: What is the Loss Distribution Faced by the FDIC?

We examine the question of deposit insurance through the lens of risk management by constructing the loss distribution faced by the Federal Deposit Insurance Corporation (FDIC). We take a novel approach by arguing that the risk management problem faced by the FDIC is similar to that of a bank managing a loan portfolio, only in the FDIC’s case the risk arises from the potential for loss of the individual banks in its portfolio. We explicitly estimate the cumulative loss distribution of FDIC insured banks using two variations of the Merton model and find that reserves are sufficient to cover roughly 99.85% of the loss distribution, corresponding to about a BBB+ rating. However, under different stress scenarios (higher correlations, fat-tailed bank returns, increased loss severity) that level can be much lower: approximately 96% corresponding to about a B+ rating.JEL classification: G210, G280.Any views expressed represent those of the author only and not necessarily those of the Federal Reserve Bank of New York or the Federal Reserve System.     

Portfolio Optimization under Lower Partial Risk Measures

Portfolio management using lower partial risk (downside risk) measures is attracting more attention of practitioners in recent years. The purpose of this paper is to review important characteristics of these riskmeasures and conduct simulation using four alternative measures, lower semi-variance, lower semi-absolute deviation, first order below targetrisk and conditional value-at-risk.We will show that these risk measures are useful to control downside risk whenthe distribution of assets is non-symmetric. Further, we will propose a computational scheme to resolve the difficultyassociated with solving a large dense linear programming problems resulting from these models. We will demonstrate that this method can in fact solve problems consisting of10⁴ assets and 10⁵ scenarios within a practical amount of CPU time.     

Did financial deregulation help consumers? Access to market-yield instruments

The maturity effect (ME) of futures prices postulated by Samuelson (1965) is re-examined using three nonparametric tests. The consistent entropy asymmetry test by Racine and Maasoumi (2007) indicates that variance is an appropriate risk or uncertainty measure for ME, and value-at-risk and expected shortfall are also adopted. The Kolmogorov–Smirnov dominance test and Wilcoxon rank sum and signed rank test are employed to rank the estimates of the three risk measures under a moving-window framework. The testing outcomes are contingent on futures type, testing method and risk measures. The testing outcomes show mild support for ME.