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Calculating VaR (Value at Risk) – Part 1a – Theoretical Overview




Description: In part 1a, we take a detailed look at Value at Risk, VaR. We consider its various definitions and the questions that it may be used to answer. We see how the tool may be extended from its traditional market risk application to other applications such as margin management and profitability calculations. We consider how VaR is used to estimate capital for capital allocation purposes, marginal capital needed for additional investments made, to make comparisons of risk measures over time. We look at the general stepbystep process followed for calculating VaR and an introduction on the difference and uses between Rate VaR and Price VaR for calculating risk on Fixed Income securities. 


Calculating VaR (Value at Risk) – Part 1b – VaR Qualifications




Description: In Part 1b, we continue with our discussion of Value at Risk, VaR, starting with the difference between Price and Rate VaR. We move onto another VaR Case study which looks at the determination of VaR using the historical simulation approach. Next we review in detail the processes behind the calculation of each of the three VaR methods, issues with each method and comparisons between them. We see how the calculation is impacted for a change in the liquidation or holding period assumption. Lastly we look at Nicholas Nassim Talebs views on VaR in particular his rules for risk management. 


Calculating VaR (Value at Risk) – Part 1c – Calculating VaR for a single security using VCV & Historical Simulation approaches




Description: In part 1c, we walk through the process of calculating VAR for currencies. We start with a simple data sheet and construct an excel sheet that handles the calculation of VaR for each currency under the variance covariance (VCV) & historical simulation approaches. We see how daily, annualized, holding period and 10day Trailing volatility are calculated. We present a crude approximation of worst case loss using the maximum trailing volatility figure and use it to present the disconnect between actual loss and that given by the VCV VaR measure. We review the installation of the Data Analysis function in Excel and use the inbuilt Histogram function to determine the worst case loss for the historical simulation approach. Finally we compare VAR results under both approaches. 


Calculating VaR (Value at Risk) – Part 1d – Extending the VaR model to a portfolio. Calculating portfolio VaR without a VCV matrix




Description: In part 1d, we extend the earlier discussion regarding VaR calculation for currencies to commodities. We then demonstrate how to calculate Value at Risk for a portfolio of securities using both the Variance Covariance (VCV) approach as well as the Historical Simulation Approach. We use a short cut method for the VCV approach that bypasses the need to construct a VCV matrix. However we also cross check the results from this short cut method with those obtained from the matrix method. During this course we demonstrate the use of EXCEL’s inbuilt TRANSPOSE and MMULT functions. 


Calculating VaR (Value at Risk) – Part 1e – Value at risk for Fixed income securities – Rate and Price VaR; Delta and Full Valuation approaches




Description:In part 1e, we review how the VaR measure is calculated for Fixed Income bonds using the Rate VaR approach and the Full Valuation Price VaR approach and the difference between the results of these two approaches. We see how a Delta Normal approximation applied to the Rate VaR approach improves on the results as it adjusts the measure for the specific characteristics of the bond (i.e. maturity, yield, interest rate sensitivity, etc). We discuss how this approximation can be further improved by considering the convexity adjustment. Finally we illustrate the difference between Rate VaR and Price VaR by looking at the histograms of daily rate and price returns respectively. 






Description:We consider how VAR is used in allocating, calculating and defining optimal levels for limits: Stop Loss Limits, PreSettlement Risk (PSR) Limits and Margin haircuts for bonds. We discuss how to set up stop loss thresholds without hindering trading while taking into account market volatility, i.e. median likelihood trading loss threshold. We consider how a financial institution’s board of directors interprets and assesses the credibility of VAR results. We show how Stop Loss may be calibrated to the VaR threshold. For PSR limits we review the market practice of using average volatility in the calculation of counterparty limits and we highlight the value of using a measure based on the maximum trailing volatility as well as the importance of carrying out a frequent, dynamic review of the limits management system in light of a changing market environment. 


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