A study on value at risk as a risk management tool

Abstract

The thesis work documented here, is a study of basic methods for estimating Value at Risk, which is a new financial risk management tool for managing market risk. Value at Risk concept, has emerged in the last few years in the finance world where the inadequacy of the conventional methods of risk management forced investment firms for new measures that could capture the risk introduced by the growing derivatives market (P.Best 1998 p8-9). Value at Risk measures the maximum potential adverse change in value of a portfolio for a given confidence level over a specified time horizon. The portfolio can be one single position or any combination of positions (P.Jorion 1997 p19). The fundamental quality of Value at Risk is that the risk incurred by different instruments in a portfolio can be aggregated in one single number. Value at Risk values can be compared regardless of the underlying portfolios as long as they have the same confidence level and time horizon (T.J. Linsmeier, N.D. Pearson 1996 p 17) There is also a regulatory framework that encourages the use of Value at Risk. The Capital Adequacy Directive is the casting form for regulations on capital requirement in the European Community since January 1996 and it acknowledges Value at Risk as an approach for calculating the capital requirements (P.Best 1998 p181-194). In the core of all the methods for estimating Value at Risk, is a return model for the changes in the underlying prices. The price changes mentioned are often assumed to be normally distributed because of the practical and theoretical attractiveness of the distribution. Three basic methods for estimating Value at Risk are studied; Covariance Value at Risk, Historical Simulation Value at Risk and Monte Carlo Simulation Value at Risk. The Covariance Value at Risk method assumes that returns are normally distributed. This method is easy to understand and implement but for large portfolios the computation is hard to do. The core assumption of normally distributed returns leads to misleading results for the cases where fat tails are observed in the distribution of portfolio returns (P.Best 1998 p16). The Historical Simulation Value at Risk method does not assume any distribution model for the returns, thus is free of model based errors. This method relies on the observed time series of returns for the portfolio at hand and understanding, implementing and computing the method is relatively easy. But the drawback for Historical Simulation Value at Risk is the fact that the time series chosen is extremely important. A stable, nonfluctuating return rates era with an appropriate length of time must be chosen, otherwise, a faulty sample would result in a biased measurement (Z.Wiener 1997 p11). The Monte Carlo Simulation Value at Risk is the final method that is studied. The actual return model is used to generate price samples. These are then used to value the portfolio. This is repeated for a large number of price samples. The resulting portfolio value changes is then used as an estimate of the distribution of the change in portfolio value, from which the Value at Risk estimate can be found. The method is computationally demanding but very robust (P.Jorion 1997 p231). All three Value at Risk methods are tested on a portfolio of foreign-exchange positions where Türkiye Cumhuriyeti Merkez Bankası exchange rates over five years for DEM, USD and GBP are used in the test .