By Moorad Choudhry
The value-at-risk size method is a widely-used software in monetary marketplace chance administration. The 5th version of Professor Moorad Choudhry’s benchmark reference textual content An creation to Value-at-Risk deals an available and reader-friendly examine the concept that of VaR and its diverse estimation tools, and is aimed particularly at newbies to the industry or these unexpected with sleek danger administration practices. the writer capitalises on his adventure within the monetary markets to provide this concise but in-depth insurance of VaR, set within the context of possibility administration as a whole.
Topics coated include:
- Defining value-at-risk
- Variance-covariance methodology
- Portfolio VaR
- Credit probability and credits VaR
- Stressed VaR
- Critique and VaR in the course of crisis
Topics are illustrated with Bloomberg displays, labored examples and workouts. similar concerns reminiscent of facts, volatility and correlation also are brought as invaluable heritage for college students and practitioners. this can be crucial examining for all those that require an advent to monetary industry probability administration and danger size techniques.
Foreword by means of Carol Alexander, Professor of Finance, collage of Sussex.
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Additional info for An Introduction to Value-at-Risk
What are we to make of these four different sovereign names with regard to portfolio diversiﬁcation? On ﬁrst glance, Bonds 1 and 3 would appear to offer perfect diversiﬁcation because they are strongly negatively correlated. However, calculating a diversiﬁed VaR for such a portfolio would underestimate risk exposure in times of market correction – which is, after all, when managers most want to know what their risk is. This is because, even though the bonds are negatively related, they can both be expected to fall in value when the market overall is dropping.
1 Z2 PðZ ¼ ZÞ ¼ pﬃﬃﬃﬃﬃﬃ exp À 2 ð2:6Þ 2 2 The Central Limit Theorem (known also as the law of large numbers) is the basis for the importance of the normal distribution in statistical theory, and in real life a large number of distributions tend towards the normal, provided that there are a sufﬁcient number of observations. This explains the importance of the normal distribution in statistics. If we have large numbers of observations – for example, the change in stock prices, or closing prices in government bonds – it makes calculations straightforward if we assume that they are normally distributed.
71. Of course, a bank’s trading book will contain many hundreds of different assets, and the method employed above, useful for a twoasset portfolio, will become unwieldy. Therefore, matrices are used to calculate the VaR of a portfolio where many correlation coefﬁcients are used. This is considered below. 1(i). The standard deviation of each asset has been calculated on historical observation of asset returns. Note that returns are returns of asset prices, rather than the prices themselves; they are calculated from the actual prices by taking the ratio of closing prices.