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Evaluating covariance matrix forecasts in a value-at-risk framework

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Author Info
Jose A. Lopez
Christian A. Walter

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Abstract

Covariance matrix forecasts of financial asset returns are an important component of current practice in financial risk management. A wide variety of models, ranging from matrices of simple summary measures to covariance matrices implied from option prices, are available for generating such forecasts. In this paper, we evaluate the relative accuracy of different covariance matrix forecasts using standard statistical loss functions and a value-at-risk (VaR) framework. This framework consists of hypothesis tests examining various properties of VaR models based on these forecasts as well as an evaluation using a regulatory loss function. ; Using a foreign exchange portfolio, we find that implied covariance matrix forecasts appear to perform best under standard statistical loss functions. However, within the economic context of a VaR framework, the performance of VaR models depends more on their distributional assumptions than on their covariance matrix specification. Of the forecasts examined, simple specifications, such as exponentially-weighted moving averages of past observations perform best with regard to the magnitude of VaR exceptions and regulatory capital requirements. These results provide empirical support for the commonly-used VaR models based on simple covariance matrix forecasts and distributional assumptions.

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Paper provided by Federal Reserve Bank of San Francisco in its series Working Papers in Applied Economic Theory with number 2000-21.

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Date of creation: 2000
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Handle: RePEc:fip:fedfap:2000-21

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Keywords: Financial markets ; Risk ; Econometric models ; Forecasting;

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Robert R. Bliss & Nikolaos Panigirtzoglou, 2001. "Recovering risk aversion from options," Working Paper Series WP-01-15, Federal Reserve Bank of Chicago. [Downloadable!]
  2. Jules Sadefo Kamdem, 2003. "Value-at-Risk and expected shortfall for linear portfolios with elliptically distributed risk factors," Quantitative Finance Papers math/0309211, arXiv.org. [Downloadable!]
    Other versions:
  3. Jeremy Berkowitz & James O'Brien, 2001. "How accurate are Value-at-Risk models at commercial banks?," Finance and Economics Discussion Series 2001-31, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  4. Gabriela De Raaij & Burkhard Raunig, 2005. "Evaluating density forecasts from models of stock market returns," European Journal of Finance, Taylor and Francis Journals, vol. 11(2), pages 151-166, April. [Downloadable!] (restricted)
  5. Ming-Yuan Leon Li & Hsiou-wei William Lin, 2004. "Estimating value-at-risk via Markov switching ARCH models - an empirical study on stock index returns," Applied Economics Letters, Taylor and Francis Journals, vol. 11(11), pages 679-691, September. [Downloadable!] (restricted)
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