By Moorad Choudhry
The value-at-risk dimension technique is a widely-used software in monetary industry threat administration. The fourth version of Professor Moorad Choudhry's benchmark reference textual content An creation to Value-at-Risk bargains an obtainable and reader-friendly examine the concept that of VaR and its varied estimation tools, and is aimed particularly at newbies to the marketplace or these surprising with glossy possibility administration practices. the writer capitalises on his event within the monetary markets to provide this concise but in-depth insurance of VaR, set within the context of possibility administration as a complete.
Topics coated comprise:
- Defining value-at-risk
- Variance-covariance technique
- Monte Carlo simulation
- Portfolio VaR
- Credit hazard and credits VaR
issues are illustrated with Bloomberg monitors, labored examples, workouts and case experiences. comparable concerns reminiscent of statistics, volatility and correlation also are brought as worthy history for college students and practitioners. this is often crucial interpreting for all those that require an creation to monetary marketplace probability administration and value-at-risk.
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Extra info for An Introduction to Value-at-Risk
Bond 2 has a very low positive correlation with Bond 1, and we conclude that there is very little relationship in the price movement of these two bonds. 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. 5 Cell C 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Observation 1 2 3 4 5 6 7 8 9 10 Mean return Volatility Correlation with bond 1 Excel formula Mean return Volatility Correlation with bond 1 Correlation.
It was also the first methodology introduced by JP Morgan in 1994. To apply it, a bank would require data on volatility and correlation for the assets in its portfolio. These data are actually available from the RiskMetrics website (and other sources), so a bank does not necessarily need its own data. It may wish to use its own datasets, however, should it have them, to tailor the application to its own use. 3 Asset 1 Asset 2 Asset 3 Correlation matrix: three-asset portfolio.
The sum of all probabilities must be 100%. From probability values then, the mean is given by: P pi xi ð2:3Þ EðXÞ i n The variance is the average weighted by the probabilities of the squared deviations from the mean; so, of course, the standard deviation – which we now call volatility – is the square root of this value. 1 we show the calculation of mean, variance and standard deviation as calculated from an Excel spreadsheet. The expectation is the mean of all the observations, while the variance is, as we noted earlier, the sum of squared deviations from the mean.