A Risk Management Tool

A TEST OF THREE APPROACHES TO THE USE OF VALUE AT RISK (VaR) AS A RISK MANAGEMENT TOOL: A REPORT TO THE BOARD OF DIRECTORS, PRUDENT BANK, PLC

Introduction ............................................... 1

Review of Three Approaches to the Application of VaR ....... 2

Historical Simulation ................................... 4

Monte Carlo Simulation .................................. 4

Exponentially Weighted Moving Average ................... 8

Test Results and Evaluation ................................ 9

Conclusion ................................................. 12

Appendix A: Historic Simulation ............................ 13

Appendix B: Monte Carlo 90-day Simulation .................. 14

Appendix C: Monte Carlo 365-day Simulation ................. 15

Appendix D: EWMA Analysis .................................. 16

Bibliography ............................................... 17

Pursuant to the instructions of the Board of Directors, a test of the approached to the application of the Value at Risk (VaL) concept to portfolio management was conducted. As a concept, VaL is less than 15 years old. As an accepted tool for application in portfolio risk management, VaL is less than 10 years old.

In its relatively short life span, however, the VaL concept has developed some ardent supporters and a few detractors. Globalisation of the financial markets and the entrance of many new players, how

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rudent Bank, historical market prices for the three equity stock - BP, HSBC Holdings, and Vodafone - were collected for 50o hundred trading days over the inclusive period 13 March 2003 - 9 February 2005. Larger time horizons tend to yield greater accuracy in statistical analyses. In the simulation of market prices for financial securities, however, the larger the data set the older the earliest market prices are. Frequently, it is a disadvantage to include very old marker prices when one is attempting to project the impacts of future market prices. Another problem with large data sets is the potential for the inclusion in the data set of periods that are atypical of market trends. Economists specifically and financial analyses generally love to factor anomalies out of analyses. I real life, however, anomalies occur frequently. Thus, there is a sound argument for analyzing periods that include a variety of economic and financial conditions. The historical simulation is relatively easy and uncomplicated. As a consequence, it can be implemented easily. One limitation of the historical simulation approach to VaR analysis is the needs for large volumes of data. Most financial institutions will have access to the large volum

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