Butler_Schachter_1997

Butler_Schachter_1997 - ESTIMATING VALUE-AT-RISK WITH A...

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ESTIMATING VALUE-AT-RISK WITH A PRECISION MEASURE BY COMBINING KERNEL ESTIMATION WITH HISTORICAL SIMULATION J. S. Butler Professor of Economics Department of Economics and Business Administration Vanderbilt University, Nashville, TN, USA Barry Schachter Market Risk Portfolio Manager Chase Manhattan Bank, New York, NY, USA This version: May 1, 1997 Original version: May 1, 1996 We thank seminar participants at the OCC and the 1996 Chicago Fed Bank Structure Conference for their comments. We also thank Rene Stulz for comments and suggestions and Amy Crews for guidance concerning kernel estimation. The views expressed herein are those of the authors and do not necessarily represent the views of the Chase Manhattan Bank or any of its staff or of the Office of the Comptroller of the Currency or members of its staff. Address correspondence to Barry Schachter, Vice President, Market Risk Portfolio Manager, Chase Manhattan Bank, 6th Floor, 270 Park Avenue, New York, NY 10017; telephone: 212-834-5196, fax 212-834-
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6544, email: [email protected]
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2 ESTIMATING VALUE-AT-RISK WITH A PRECISION MEASURE BY COMBINING KERNEL ESTIMATION WITH HISTORICAL SIMULATION J. S. Butler Vanderbilt University, Nashville, TN, USA Barry Schachter Chase Manhattan Bank, New York, NY, USA In this paper we propose an alternative way to implement the historical simulation approach to Value-at- Risk (VaR) measurement, employing a non-parametric kernel quantile estimator (Sheather and Marron (1990)) of the probability density function (pdf) of the returns on a portfolio. Then we derive an expression for the pdf of any order statistic of the return distribution. Finally, because that pdf is not analytic, we employ numerical integration to obtain the moments of the order statistic, the mean being the VaR estimate, and the standard deviation allowing the construction of a confidence interval around the estimate. We apply this method to trading portfolios provided by a financial institution. I. Introduction For several years financial institutions have been searching for the best means to represent the risk exposure of the financial institution ’s trading portfolio in a single number. Folklore attributes the inception of this quest to Dennis Weatherstone at J. P. Morgan who was looking for a way to convey meaningful risk exposure information to the financial institution ’s board without the need for significant technical expertise on the part of the board members. The appeal of the idea of a risk-revealing statistic has become sufficiently great that it forms the centerpiece both of many risk management systems and proposed regulatory approaches to capital regulation. Despite the popularity of this concept of measuring risk, no consensus has yet developed as to the best implementation of this risk measurement approach. This absence of consensus derives in part from the realization that each method of implementation currently in use has some significant drawbacks. Every approach to developing a comprehensive risk measurement statistic seeks to extract information
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Butler_Schachter_1997 - ESTIMATING VALUE-AT-RISK WITH A...

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