The Value-at-Risk Methodology of Basel II and Basel III

Introduction

There are three different VaR methodologies—variance-covariance; historical and Monte Carlo simulation. As discussed in this chapter, under the Basel II & III frameworks, backtesting and stress testing were adopted as complementary to VaR, The next chapter however argues that Extreme Value Theory (EVT) is able to capture tail risks better, and that Copula methods can assist VaR for accurate risk aggregation by combining the specific marginal distributions with a dependence function to create a joint distribution of the portfolio.

After first addressing the weakness of VaR associated with sub-additivity, the discussion then explores the effectiveness of an alternative approach to VaR—Expected Shortfall (ES) that is advocated by certain academics. Related, another risk measure—distortion risk measure, which is closely related to coherent measure, sheds further light on limitations of VaR and ES.

Based on the belief that both ontological and epistemic factors interact to determine a model outcome, decision-making in the financial world soon becomes complicated with the inclusion of risk and uncertainty premiums. In Keynes uncertainty and Minsky’s notion of Financial Instability Hypobook, uncertainty premiums are closely related to uncertainty aversion and liquidity preference. They must be taken into account technically, by drawing the mathematical equivalence between two capacity-based representations of uncertainty aversion (multiple-prior setting and sub-additive probabilities), as established by Gilboa and Schmeidler (1989), and Tversky and Wakker’s Cumulative Prospect Theory (1995), to provide a sound platform for discussion.

Risk is simply the potential for deviation from expected results, particularly adverse deviation. Behind every future cash flow, earnings result, or change in value there lays a probability distribution of potential results. The relative magnitude of risk could be defined by a measure of spread or dispersion in that distribution such as the standard deviation or variance. However, variance is not necessarily sufficient for capturing risk—two distributions with dramatically different shapes and differing amounts of downside risk can have the same variance (Rosenberg & Schuermann, 2004).

Measures such as skewness and kurtosis can be used to quantify the risk that is not adequately described by variance alone. Another approach is to examine the percentiles of the distribution, as is done in the Value-at-Risk (VaR) approach. Jorion (2001, p. 107) argues that the greatest advantage of VaR is that it summarizes in a single, easy to understand number the downside risk of any institution arising out of financial market variability.

Apart from the above, other characteristics of the VaR approach that give it an edge over the more traditional risk assessment methods used in capital markets context are:

• 1.

  It provides a common measure of risk across different positions and risk factors, while traditional methods are more limited¹;

• 2.

  VaR enables us to aggregate the risks of positions taking into account the ways in which risk factors correlate with each other, most traditional risk measures do not allow for the “sensible” aggregation of component risks; and

  • 3. VaR is holistic in that it takes full account of all driving risk factors, whereas traditional measures only look at risk factors one at a time (i.e. Greek).

Value-at-risk (VaR) is widely used to measure the risk of loss on a specific portfolio of financial assets. Banks, brokerage firms, investment funds, and regulators have widely endorsed statistical-based risk-management systems rooted in VaR calculations.

The newer Basel Accords (Basel II & Basel III) acknowledge the important role of value-at-risk (VaR)² as a basis of risk measurement and regulatory capital calculation. Particularly, for regulatory purposes, a risk measure approach needs to have the ability to adequately capture all the risks facing an institution, which encompass market risk, credit risk, operational risk, and other risks.