Forex Risk: Measurement and Evaluation using Value-at-Risk

Abstract

Over the past decade the growth of trading activity in financial markets, numerous instances of financial instability, and a number of widely publicised losses on banks' trading books have resulted in a re-analysis of the risks faced, and how they are measured. The most widely advocated approach to have emerged to measure market risk is that of Value-at-Risk (VaR). This methodology was designed in J.P. Morgan to give their chief executive a single figure that would provide a daily summary of the evolving risk of the Banks investment portfolio. VaR methods estimate the distribution of losses/gains on a portfolio of assets/liabilities over a given horizon. From the estimated distribution one can then find, for the loss on the portfolio, a bound that will only be exceeded rarely. This bound is the VaR. The term “rarely” is often taken to refer to an event that occurs one or five times per hundred periods. In actual applications users are free to define “rarely” to suit their own needs. VaR can be calculated in various ways and its value depends on the assumptions made and models used. This paper looks at six different measures of the VaR of an Irish investor holding an equally weighted portfolio of foreign exchange positions in the currencies of Ireland’s major trading partners. The basic data used are daily exchange rates covering the period 1990 to 1998. Daily VaRs for four different holding periods are calculated, using six alternative approaches to estimating the distribution of the underlying risk. The measured VaRs are compared graphically and statistically with actual losses/gains over the period. Recently developed techniques are used to measure the performance and accuracy of the estimates of the VaR estimates. For the portfolios considered here the method based on Exponentially Weighted Moving Averages is superior to the others. This may of course be due to the statistical properties of the FOREX returns being considered. The article provides a framework for the comparison of different measures of VaR. These can be adapted for the evaluation of alternative VaR models for risk control within an organisation. This framework can also serve as an input to the validation of in-house models proposed for the calculation of capital adequacy under the Capital Adequacy Directive.