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on Risk Management |
| By: | Marno Verbeek; Jeroen VK Rombouts |
| Abstract: | In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S\&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed |
| Keywords: | multivariate GARCH, semi-parametric estimation, Value-at-Risk, asset allocation |
| JEL: | C14 C22 |
| Date: | 2005–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:sce:scecf5:40&r=rmg |
| By: | Mattia Ciprian (mciprian@gmail.com); Stefano d'Addona (sd2123@columbia.edu) |
| Abstract: | We estimate time varying risk sensitivities on a wide range of stocks' portfolios of the US market. We empirically test, on a 1926-2004 Monthly CRSP database, a classic one factor model augmented with a time varying specification of betas. Using a Kalman filter based on a genetic algorithm, we show that the model is able to explain a large part of the variability of stock returns. Furthermore we run a Risk Management application on a GRID computing architecture. By estimating a parametric Value at Risk, we show how GRID computing offers an opportunity to enhance the solution of computational demanding problems with decentralized data retrieval. |
| JEL: | G |
| Date: | 2005–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpfi:0511007&r=rmg |
| By: | Guenter Franke; Jan Pieter Krahnen |
| Abstract: | This paper contributes to the economics of financial institutions risk management by exploring how loan securitization affects their default risk, their systematic risk, and their stock prices. In a typical CDO transaction a bank retains through a first loss piece a very high proportion of the default losses, and transfers only the extreme losses to other market participants. The size of the first loss piece is largely driven by the average default probability of the securitized assets. If the bank sells loans in a true sale transaction, it may use the proceeds to expand its loan business, thereby affecting systematic risk. For a sample of European CDO issues, we find an increase of the banks’ betas, but no significant stock price effect around the announcement of a CDO issue. |
| JEL: | D82 G21 D74 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11741&r=rmg |
| By: | Kai Detlefsen; Giacomo Scandolo |
| Abstract: | We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. As an example we consider the class of conditional entropic risk measures. A new regularity property of conditional risk measures is defined and discussed. Finally we introduce the concept of a dynamic convex risk measure as a family of successive conditional convex risk measures and characterize those satisfying some natural time consistency properties. |
| Keywords: | Conditional convex risk measure, robust representation, regularity, entropic risk measure, dynamic convex risk measure, time consistency |
| JEL: | D81 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2005-006&r=rmg |
| By: | Dr. Brian J. Jacobsen |
| Abstract: | One of the challenges of using downside risk measures as an alternative constructor of portfolios and diagnostic devise is in their computational intensity. This paper outlines how to use downside risk measures to construct efficient portfolios and to evaluate portfolio performance in light of investor loss aversion |
| Keywords: | downside risk, portfolios, performance measure |
| JEL: | G11 |
| Date: | 2005–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:sce:scecf5:5&r=rmg |
| By: | Jiali Liao; Theodore V. Theodosopoulos |
| Abstract: | Collateral is one of the most important and widespread credit risk mitigation techniques used by practitioners. This paper studies the effect of mark-to-market (MTM) timing in collateral agreements on the contingent credit risk exposure. We measure contingent credit risk exposure using Potential Future Exposure (PFE), the maximum amount of exposure expected to occur at a specified confidence during the remaining duration of the underlying contract. The parameters of a collateral agreement that can affect the contingent credit risk exposure include the frequency and timing of marking-to-market, trigger level for margin calls and the level of collateralization. However, these decisions are often made in an ad-hoc manner, without reference to an analytical framework. While the frequency of mark-to-market and collateral level has been studied, very little academic research has addressed the quantitative analysis of mark-to-market timing. The goal of this research is to fill this theoretical gap and propose a framework for optimizing the timing of mark-to-market in collateral agreements to minimize potential future exposure. Our framework computes the probability of maximum risk exposure of the underlying contract above a specified level during its remaining time until maturity using one or two MTMs whose timing is decided simultaneously at the contract initiation, or in a sequential manner. This probability is expressed as a function of the parameters of the underlying contract which is assumed to follow a Brownian motion and the decision variables in collateralization, including initial margin, trigger level and variation margin. Numerical examples are investigated with different values of volatility and duration of the underlying contract. Sensitivity analysis and numerical results reveal the optimal timing of MTM that minimizes PFE. Simulations are used to test preliminary conclusions from numerical analysis |
| Keywords: | Mark-to-Market. Potential Future Exposure, Contingent Credit Risk |
| JEL: | C69 |
| Date: | 2005–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:sce:scecf5:220&r=rmg |
| By: | Ritirupa Samanta; Blake LeBaron |
| Abstract: | Equity market crashes or booms are extreme realizations of the underlying return distribution. This paper questions whether booms are more or less likely than crashes and whether emerging markets crash more frequently than developed equity markets. We apply Extreme Value Theory (EVT) to construct statistical tests of both of these questions. EVT elegantly frames the problem of extreme events in the context of the limiting distributions of sample maxima and minima. This paper applies generalized extreme value theory to understand the probability of extreme events and estimate the level of �fatness� in the tails of emerging and developed markets. We disentangle the major �tail index� estimators in the literature and evaluate their small sample properties and sensitivities to the number of extreme observations. We choose to use the Hill index to measure the shape of the distribution in the tail. We then apply nonparametric techniques to assess the significance of differences in tail thickness between the positive and negative tails of a given market and in the tail behavior of the developed and emerging region. We construct Monte Carlo and Wild Bootstrap tests of the null of tail symmetry and find that negative tails are statistically significantly fatter than positive tails for a subset of markets in both regions. We frame group bootstrap tests of universal tail behavior for each region and show that the tail index is statistically similar across countries within the same region. This allows us to pool returns and estimate region wide tail behavior. We form bootstrapping tests of pooled returns and document evidence that emerging markets have fatter negative tails than the developed region. Our findings are consistent with prevalent notions of crashes being more in the emerging region than among developed markets. However our results of asymmetry in several markets in both regions, suggest that the risk of market crashes varies significantly within the region. This has important implications for any international portfolio allocation decisions made with a regional view |
| Keywords: | Extreme value theory, fat tails, emerging markets |
| JEL: | G12 G15 |
| Date: | 2005–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:sce:scecf5:140&r=rmg |