By Moorad Choudhry
The value-at-risk dimension technique is a widely-used device in monetary marketplace threat administration. The fourth version of Professor Moorad Choudhry's benchmark reference textual content An advent to Value-at-Risk bargains an obtainable and reader-friendly examine the concept that of VaR and its diversified estimation tools, and is aimed in particular at rookies to the industry or these unexpected with smooth 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 chance administration as an entire.
Topics coated comprise:
- Defining value-at-risk
- Variance-covariance method
- Monte Carlo simulation
- Portfolio VaR
- Credit chance and credits VaR
subject matters are illustrated with Bloomberg displays, labored examples, routines and case stories. similar matters similar to records, volatility and correlation also are brought as useful historical past for college kids and practitioners. this can be crucial studying for all those that require an advent to monetary marketplace threat administration and value-at-risk.
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Extra info for An Introduction to Value-at-Risk
VaR is defined as follows: VaR is a measure of market risk. It is the maximum loss which can occur with X% confidence over a holding period of t days. VaR is the expected loss of a portfolio over a specified time period for a set level of probability. So, for example, if a daily VaR is stated as £100,000 to a 95% level of confidence, this means that during the day there is a only a 5% chance that the loss will be greater than £100,000. VaR measures the potential loss in market value of a portfolio using estimated volatility and correlations.
With normal distributions all the historical information is summarised in the mean, variance and covariance of the returns (market factors), so users do not need to keep all the historical data. Calculate portfolio variance and VaR If all the market factors are assumed to be normally distributed, the portfolio, which is the sum of the individual instruments, can also be assumed to be normally distributed. This means that the portfolio variance can be calculated using standard statistical methods (similar to modern portfolio theory), namely: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 2j 2j þ 2k 2k þ 2j k jk j k ð3:1Þ where j ¼ Home-currency present value of the position in market factor j; 2j ¼ Variance of market factor j; jk ¼ Correlation coefficient between market factors j and k.
A vector of alternative values is created for each of the market factors by adding the current value of the market factor to each of the values in the vector of simulated changes. Once this vector of alternative values of the market factors is obtained, the current and alternative values for the portfolio, the changes in portfolio value and the VaR are calculated exactly as in the historical method. Variance–covariance, analytic or parametric method This is similar to the historical method in that historical values of market factors are collected in a database.