Managing Market Risk and Controlling VAR

Managing Market Risk and Controlling VAR

DOI: 10.4018/978-1-5225-7280-0.ch004

Abstract

The market risk management in a portfolio selection of correlated assets is considered in this chapter. The chapter elaborates how to construct and select an optimal portfolio of correlated assets in order to control VAR considering the risk associated limits. Stochastic optimisation is used to construct the efficient frontier of minimal mean variance investment portfolios with maximal return and a minimal acceptable risk. Monte Carlo simulation is utilised to stochastically calculate and measure the portfolio return, Variance, Standard Deviation, VAR and Sharpe Ratio of the efficient frontier portfolios. Six Sigma process capability metrics are also stochastically calculated against desired specified target limits for VAR and Sharpe Ratio of the Efficient Frontier portfolios. Simulation results are analysed and the optimal portfolio is selected from the Efficient Frontier based on the criteria of maximum Sharpe Ratio.
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Introduction

Market risk is the risk of losses due to adverse market movements depressing the values of the positions held by market players. The market parameters fluctuating randomly are called “risk factors”: they include all interest rates, equity indexes or foreign exchange rates.

Market risk depends on the period required to sell the assets as the magnitude of market movements tends to be wider over longer periods. The liquidation period is lower for instruments easily traded in active markets, and longer for exotic instruments that are traded on a bilateral basis (over the counter). Market risk is a price risk for traded instruments. Instruments that are not traded on organised markets are marked-to-market because their gains or losses are accounted for as variations of value whether or not materialised by a sale.

Kupiec and O’Brien (1998) published this paper when there was no regulatory capital requirement that accounts for market risks in banks' trading accounts. Bank regulators were considering a capital charge for such risks based directly on risk estimates from banks' internal models typically used to measure one-day exposures. While an improvement over an earlier proposal that would rely on a regulatory risk measurement system, the internal models approach has significant drawbacks. A bank reports that the models are not appropriate for estimating trading account market risk exposure over a relatively lengthy period of interest to regulators and it is extremely difficult to validate the risk estimate. These difficulties were eliminated in an alternative approach developed in this paper, referred to as a “pre-commitment” approach. Under this alternative approach, the bank pre-commits to a maximum loss exposure over a fixed subsequent period that takes into account risk management and trading objectives and allocates capital to cover that exposure. The regulator determines the likelihood of the bank's market trading losses exceeding its capital allocation through the incentive effects of capital penalties or fines imposed in the event of a violation of the commitment.

Wong et al. (2003) adopted the back-testing criteria of the Basel Committee to compare the performance of a number of simple value-at-risk (VAR) models. These criteria provide a new standard on forecasting accuracy. Currently central banks in major money centres, under the auspices of the Basel Committee of the Bank of International settlement, adopt the VAR system to evaluate the market risk of their supervised banks. Banks are required to report VARs to bank regulators with their internal models. These models must comply with the Basel’s back-testing criteria. If a bank fails the VAR back-testing, it will be imposed higher capital requirements. VAR is a function of volatility forecasts. Past studies mostly conclude that ARCH and GRACH models provide better volatility forecasts. However, this paper finds that ARCH-based and GARCH-based VAR models consistently fail to meet with the Basle’s back-testing criteria. These findings suggest that the use of ARCH-based and GARCH-based models to forecast their VARs is not a reliable way to manage a bank’s market risk.

Dowd (2005) published a book for measuring the market risk. This book is purposed for experienced professionals dealing with market risk assessment and management. The book covers the practical aspects of market risk management, elaborating the theoretical concepts as well. It includes elaboration on options risk management, as well as substantial information on parametric risk, non-parametric measurements and liquidity risks. Also, it provides for practical information to help with specific calculations, and new examples including case studies.

Andersen et al. (2007) proposed practical applications of recent developments in financial econometrics dealing with time-varying volatility to the measurement and management of market risk, stressing parsimonious models that are easily estimated. The authors’ ultimate goal is to stimulate dialog between the academic and practitioner communities, advancing best-practice market risk measurement and management technologies by drawing upon the best of both worlds.

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