## Implementing Value at RiskImplementing Value at Risk Philip Best Value at Risk (VAR) is an estimate of the potential loss on a trading or investment portfolio. Its use has swept the banking world and is now accepted as an essential tool in any risk manager's briefcase. Perhaps the greatest strength of VAR is that it can cope with virtually all financial products, from simple securities through to complex exotic derivatives. This allows the risk taken, across diverse trading activities, to be compared. This said, VAR is no panacea. It is as critical to understand when the use of VAR is inappropriate as it is to understand the value VAR can add to a bank's understanding and control of its risks. This book aims to explain how VAR can be used as an integral part of a risk and business management framework, rather than as a stand-alone tool. The objectives of this book are to explain: What VAR is - and isn't! How to calculate VAR - the three main methods Why stress testing is needed to complement VAR How to make stress testing effective How to use VAR and stress testing to manage risk How to use VAR to improve a bank's performance VAR as a regulatory measure of risk and capital Risk management practitioners, general bank managers, consultants and students of finance and risk management will find this book, and the software package included, an invaluable addition to their library. Finance/Investment |

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### Contents

1 Defining risk and VAR | 1 |

2 Covariance | 14 |

3 Calculating VAR using simulation | 32 |

4 Measurement of volatility and correlation | 57 |

5 Implementing value at risk | 103 |

6 Stress testing | 128 |

7 Managing risk with VAR | 141 |

8 Risk adjusted performance measurement | 149 |

9 Regulators and risk management | 174 |

10 Introduction to the spreadsheets | 197 |

199 | |

201 | |

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### Common terms and phrases

assume back testing bank basis point Basle behaviour business unit calculated cash flow cash ﬂows chapter conﬁdence interval conﬁdence level considered convenience yield correlation matrix counterparty covariance credit rating credit risk currency decay factor delta described discussion eigenvalues eigenvectors ensure equation equity estimate EWMA example expected credit loss exposure Figure ﬁnancial markets ﬁrst ﬂoating gamma GARCH given gold hedged historical simulation holding period implemented implied volatility interest rate large number market risk maturity measure of volatility method Monte Carlo simulation normal distribution observation period percentage price changes portfolio value changes position present value price change distribution Rand random numbers RAROC rating agencies recovery rate reﬂect regulators revenue volatility risk capital risk factors risk management risk measures scenario scenario testing sensitivity sensitivity-based Sharpe ratio shows signiﬁcant speciﬁed spreadsheet standard deviation stress test limits stress testing swap Table value at risk volatility and correlation volatility model yield curve zero