PDF Ebook Estimation Risk in Financial Risk Management
Value-at-Risk (VaR) is increasingly used in portfolio risk measurement, risk capital allocation and performance attribution. Financial risk managers are therefore rightfully concerned with the precision of typical VaR techniques.
The purpose of this paper is to assess the precision of common dynamic models and to quantify the magnitude of the estimation error by constructing confidence intervals around the point VaR and expected shortfall (ES) forecasts. A key challenge in constructing proper confidence intervals arises from the conditional variance dynamics typically found in speculative returns. Our paper suggests a resampling technique which accounts for parameter estimation error in dynamic models of portfolio variance.
Value-at-Risk (VaR) is increasingly used in portfolio risk measurement, risk capital allocation and performance attribution, and financial risk managers are rightfully concerned with the precision of typical VaR techniques. VaR is defined as the conditional quantile of the portfolio loss distribution for a given horizon (typically a day or a week) and for a given coverage rate (typically 1% or 5%), and the expected shortfall (ES) is defined as the expected loss beyond the VaR. The VaR and ES measures are thus statements about the left tail of the return distribution and in realistic sample sizes (500 or 1000 daily observations) such statements are likely to be made with considerable error.
The purpose of this paper is twofold: First, we want to assess the potential loss of accuracy from estimation error when calculating VaR and ES. Second, we want to assess our ability to quantify ex-ante the magnitude of this error via the construction of confidence intervals around the VaR and ES measures. This issue of estimation risk for VaR has been considered previously in the i.i.d. return case by for example Jorion (1996) and Pritsker (1997). But a key challenge in constructing proper VaR and ES confidence intervals arises from the conditional variance dynamics typically found in speculative returns. We quantify these dynamics using the celebrated GARCH model of Engle (1982) and Bollerslev (1986). Due to its ability to capture salient features of the eturn dynamics in very parsimonious and easily estimated specifications, GARCH has become the workhorse model in financial risk management. Nevertheless, and surprisingly, very little is known about the uncertainty in the GARCH VaR and ES forecasts arising from parameter estimation error.
Our paper extends the resampling technique of Pascual, Romo and Ruiz (2001), which accounts for parameter estimation error in dynamic models of portfolio variance, to the case of VaR and ES forecasts. To our knowledge no asymptotic theory has been established for calculating confidence intervals for risk measures in this context. The resampling technique we propose can be relatively easily extended to longer horizons, to multivariate risk models, and to allowing for model specification error.
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PDF Ebook Estimation Risk in Financial Risk Management
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