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Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?

Paper:ewp-fin/9810002
From:    
Date: Thu, 8 Oct 1998 17:21:58 -0500

Title: Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?
Author: Xiongwei Ju (University of Illinois at Urbana-Champaign) and Neil D. Pearson(University of Illinois at Urbana-Champaign)
Contact:
Comments: Type of Document - PDF; prepared on pc; to print on HP; pages: 31; figures: included. Office for Futures and Options Research (OFOR)at University of Illinois at Ubana -Champaign. Working Paper 98-08. For a complete list of OFOR working papers see http://w3.ag.uiuc.edu/ACE/ofor
Keywords: Value-at-Risk
JEL:
EWPA-references:
Report-no: OFOR-98-08

Abstract:

We study a source of bias in value-at-risk estimates that has not previously been recognized. Because value-at-risk estimates are based on past data, a trader will often have a good understanding of the errors in the value-at-risk estimate, and it will be possible for her to choose portfolios for which she knows that the value -at-risk is less than the "true" value at risk. Thus, The trader will be able to take on more market risk than risk limits based on value-at-risk permit. Biases can also arise if she doesn't have a good understanding of the errors, but uses the estimated covariance matrix to achieve certain portfolio objectives. We assess the magnitude of these biases for three different assumptions about the motivations and behavoir of the trader and find that in all cases, value-at-risk estimates are systematically downward biased. In some circumstances the biases can be very large. Our study of the distributions of the biases also suggests a way to adjust the estimates to "correct" the biases.

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