Minimizing Basel III Capital Requirements with Unconditional Coverage Constraint

• Author: Wing Lon Ng,Manuel Kleinknecht
• DOI: http://doi.org/10.1002/isaf.1370
• Published date: 01 October 2015
• Date: 01 October 2015

MINIMIZING BASEL III CAPITAL REQUIREMENTS WITH

UNCONDITIONAL COVERAGE CONSTRAINT

MANUEL KLEINKNECHT AND WING LON NG*

Centre for Computational Finance and Economic Agents (CCFEA),University of Essex, Colchester, UK

SUMMARY

The new Basel III framework increases the banks’market risk capital requirements. In this paper, we introduce a

new risk management approach based on the unconditional coverage test to minimize the regulatory capital re-

quirements. Portfolios optimized with our new minimum capital constraint successfully reducethe Basel III market

risk capital requirements. In general, portfolios with value-at-risk and conditional-value-at-risk objective functions

and underlying empirical distribution yield better portfolio risk profiles and have lower capital requirements. For

the optimization we use the threshold-accepting heuristic and the common trust-region search method.

Keywords: Basel III capital requirements; heuristic portfolio optimization; threshold accepting; unconditional

coverage

1. INTRODUCTION

In portfolio optimizsation, the financial literature usually focuses on standard portfolio measures, e.g. the

Sharpe ratio, to evaluate the efficiency of a model. However, with increasing market risk capital require-

ments under the new Basel III framework, the minimum capital requirements for a portfolio become

increasingly important. In this paper, we aim to provide a new risk management approach based on an

unconditional coverage (UC) test constraint to minimize the Basel III capital requirements. More speci-

fically,we investigate how well different risk measures reduce the capital requirements with and without

our new constraint.

The financial crisis in 2008 made clear to the financial regulators that they had to enhance the regu-

latory framework to prevent the financial market and the economy from future negative impacts. The

major focus of the revision of the Basel framework was mainly on the capital and liquidity standards

to improve the stability of financial institutions.

In 1995, the Basel Committee introduced the market risk rules on minimum capital requirements

(Basel Committee on Banking Supervision, 1995). The r ules were set to strengthen the stability of

financial institutions. Thus, as a result of the financial crisis in 2008, the committee published a revision

of the market risk framework in July 2009 (Basel Committee on Banking Supervision, 2009a), which is

now part of the 2010 Basel III framework (Basel Committee on Banking Supervision, 2010).

The Basel III framework consists of three ‘pillars’. The revision is part of Pillar 1 of the framework

Basel Committee on Banking Supervision (2010), which focuses on minimum capital requirements

based on risk-weighted assets (RWA), while Pillar 2 concentrates on risk management and supervision,

* Correspondence to: Wing Lon Ng, Centre for Computational Finance and Economic Agents (CCFEA), University of Essex,

Colchester, UK. E-mail: wlng@bracil.net

Copyright © 2015 John Wiley & Sons, Ltd.

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT

Intell. Sys. Acc. Fin. Mgmt. 22, 263–281 (2015)

Published online 9 June 2015 in Wiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/isaf.1370

and Pillar 3 discusses the issue of market discipline. This paper focuses on the market risk framework,

which, among the credit risk and the operational risk framework, is part of Pillar 1.

The market risk framework requires banks to calculate their individual minimum market risk capital

requirements to cover potential losses that might arise from their market activity (Basel Committee on

Banking Supervision, 1996). The framework suggests a standardized or an internal approach to calcu-

late the capital requirements. With the internal approach, banks have the alternative to use their internal

value-at-risk (VaR) models to calculate their minimum capital requirements. However, these internal

models are required to meet a series of quantitative and qualitative standards. One essential criterion

is to calculate the rolling 1-day 99% VaR based on at least 250 days of empirical data (Basel Committee

on Banking Supervision, 2009b).

The new Basel III framework increases the minimum capital requirements of financial institutions.

Hence, banks are increasingly interested to find ways to decrease their capital requirements. Existing

literature suggests to either (i) maximize the return for a given VaR limit (e.g. Sentana, 2003;

Alexander et al., 2007) or (ii) to minimize the amount of regulatory capital required to underlie a

certain investment (e.g. McAleer et al., 2010; Santos et al., 2012). This paper focuses on the second

case. We propose a new method based on the UC test to reduce the regulatory capital requirements.

In contrast to the existing literature, our model minimizes the empirical VaR of a portfolio while

avoiding to select a portfolio that over- or underestimates the number of daily VaR violations. Hence,

compared with the work of McAleer et al. (2010) and Santos et al. (2012), our approach does not

prefer portfolios without violation but portfolios with an optimal number of exceedings. Our model

can easily be run with different types of objective functions. Intuitive objective functions to reduce

the capital requirements are downside risk measures; that is, VaR and conditional-VaR (CVaR).

Often, however, downside risk measures lead to nonlinear optimization problems; for example, see

Alexander et al. (2006).

Optimization problems with multiple local extremes can be solved using heuristic methods. Dueck

and Winker (1992) proposed heuristic search algorithms in portfolio optimization and applied the

threshold-accepting (TA) algorithm, introduced in Dueck and Scheuer (1990), to a bond portfolio

optimization problem.

In this paper, we apply a heuristic model to a Basel III constraint optimization problem and study

how well different downside risk measures can reduce the market capital requirement. While portfolio

optimization procedures using VaR objective functions were proposed before, optimization constraints

particularly addressing the Basel III requirements have, to our best knowledge, not been considered in

the literature so far. Our aim is to provide a new quantitative risk management approach based on the

UC test and we illustrate this using the TA method. As objective functions we use meanvariance (MV)

and the downside risk measures VaR and CVaR with underlying historical and normal distribution. We

also optimize the portfolios with the common trust-region (TR) local search algorithm to compare our

results and to check that the proposed optimization constraint does not heavily rely on the optimization

procedure used. Other popular heuristic methods proposed in the literature are particle swarm optimi-

zation (Eberhart & Kennedy, 1995), or ant colony optimization (Dorigo et al., 1999). We refer the in-

terested reader to Maringer (2005) and Gilli et al. (2011), who give a good overview of the most

common heuristic search methods.

The remainder of the paper is structured as follows: Section 2 defines the methodology used in this

paper. It discusses the objective functions and algorithms used in the optimization process, as well as

the models used for backtesting and our new constraint to minimize the capital requirements.

Section 3 describes the optimization and backtesting results of the portfolios for the empirical data.

Section 4 concludes.

264 M. KLEINKNECHT AND W. L. NG

Copyright © 2015 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt., 22, 263–281 (2015)

DOI: 10.1002/isaf