Academic journal article Journal of Economics and Finance

Incorporating Correlation Regimes in an Integrated Stressed Risk Modeling Process

Academic journal article Journal of Economics and Finance

Incorporating Correlation Regimes in an Integrated Stressed Risk Modeling Process

Article excerpt

Abstract

The practice of using stress tests to complement Value at Risk (VaR) estimates suffers from some limitations such as the lack of coherence between a statistical risk measure and a subjective one. On the other hand there is a wide consensus that using the same correlation matrix to design various stress tests is not likely to provide an accurate representation of relationship amongst risk factors in periods of market stress. In this paper we introduce a solution to these problems by explicitly considering different correlation regimes and incorporating the result of the stress test to the traditional market risk measurement models.

Keywords Stress test * Value at risk * Modeling process * Expected tail loss * Correlation breakdown * Market regimes

JEL Classifications G10 * G15

1 Introduction

Value at Risk (VaR) has become a standard market risk measure for institutions worldwide, and is enjoying rapid and wide-ranging success. Its main appeal lies in its simplicity; a single number offers information about what a firm may expect to lose over a time horizon, uncovers uncertainties of the firm, and provides crucial information of the overall firm's risk profile to senior management, traders, shareholders, investors, auditors, rating agencies, and regulators.

There are several approaches to estimating VaR (see Dowd 2002 for a comprehensive review of alternative VaR methodologies). Parametric approaches require estimating the parameters of the underlying distribution using observed data; under the assumption of normality VaR, for linear portfolios, may be estimated as a predetermined quantile of a Gaussian distribution.

Another popular approach to estimating VaR is by using Monte Carlo simulation. This technique requires the assumption of a predetermined distribution of the stochastic variable(s). Hypothetical paths for the value of our portfolio are constructed by drawing a set of random values of the stochastic variables which determine the value of the instruments within the portfolio and revaluing that portfolio under the new simulated market prices. Monte Carlo simulation enables the calculation of quite complex portfolios including those with non-linear risk factors or path-dependent instruments.

There are also a set of non parametric approaches which do not require making strong assumptions about the distribution of profits and losses or returns. The most popular non parametric approach is historical simulation where market prices are simulated according to their historical price behaviour on any given period and the current portfolio is revalued under each of those simulated market prices. After estimating and ordering the simulated historical profit and loss (return) observations of the portfolio under consideration, VaR is the predetermined p-quantile of the distribution for the given confidence level.

While VaR does not provide any guidelines about what to expect when losses are greater than VaR itself, ETL does give us an indication of what we may expect in "bad times". Therefore, Expected Tail Loss numbers are rapidly gaining acceptance amongst risk managers as a complementary measure to VaR. ETL provides an indication of the average expected loss in the tail, and therefore can complement VaR numbers to provide a more complete picture of portfolio tail risk.

Artzner et al. (1999) developed a theory of coherent risk measures and concluded that VaR does not satisfy certain key conditions, in particular, it does not, in general, satisfy sub-additivity while ETL does and therefore benefits from all the attractions of sub-additivity. As Dowd (2002, p. 36) points out "Unlike VaR, the ETL satisfies the conditions for a coherent risk measure, and coherent risk measures have a number of attractive features. ...users of VaR would be well advised to switch over".

Most VaR measures rely on too many simplistic assumptions about market and portfolio behavior, particularly with regards to extreme market conditions. …

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