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- 1. Value at RiskJune 7, 2013Amir Khwajawww.clarusft.com
- 2. Agenda The Need for VaR Definition of VaR Uses of VaR VaR Methods VaR - Historical Simulation Changes since the Financial Crises of 2008 Strengths and Weakness Summary
- 3. The Need for VaR Different Asset Classes use their own measures Fixed Income – Duration Interest Rates – DV01 FX – Currency position Commodity – Number of contracts Equities – Number of shares Using these to compare risk in these portfolios is likecomparing apples and oranges An investor or owner needs a simple measure that can beused in a consistent way to compare risk between theseportfolios And with the ability to aggregate risk appropriately Value at Risk is that risk measure
- 4. Definition of VaR How much could we lose over a specified holding periodwith a defined probability So if a portfolio has a VaR of $20 million We need to know the confidence level used to calculate We need to know the holding period (time horizon) Say confidence level is 99% and holding period is 5 days This then means “We would expect to lose $20 millionor more over a 5 day period, in 1 out of 100 businessdays” Note it does not tell us whether on that 1 day we couldlose $21 million or $200 million! So if we are relying only on VaR for the answer to thatthen we are going to be in trouble For that we need Tail Measures or Stress Testing
- 5. Uses of VaR Made public by JP Morgan in 1994 with RiskMetrics Widely adopted in the industry very quickly after that Particularly for Derivatives where measures such as grossnotional or position in contracts units, are not thatinsightful Basel II Capital Accord for Market Risk – 1995 Internal Model Capital is VaR times a multiplier set for eachbank by its regulator as between 3 & 4 Banks report VaR in Annual Financial Statements – 1997 Internal 1d VaR and Regulatory 10d VaR Clearing Houses for Initial Margin – 1999 (LCH SwapClear) Margin from defaulting member used to cover the market riskloss for the period it takes to close-out the portfolio
- 6. VaR Methods Three main methods Parametric (aka Variance-Covariance or Delta-Gamma) Historical Simulation Monte-Carlo Simulation Different assumptions, calculation steps, computeefficiency but similar numbers for standard portfolios The most common is Historical Simulation As easiest to understand Simple assumptions on distributions of returns So if for our $20 million VaR portfolio, we also said that wehad used 5 Years of history as well as 99% and 5d We would say that “given how the market has performedin the past 5 years” our VaR estimate is $20 million
- 7. VaR - Historical Simulation It relies on choosing A historical period, e.g. 4 Years A holding period e.g. 5 days Generating daily holding period returns in this period Calculating the P&L impact on a portfolio by applyingthese returns to today Ordering the P&L outcomes by decreasing loss Interpolating for a chosen confidence level e.g. 99%
- 8. VaR - Historical Simulation-80.00-60.00-40.00-20.000.0020.0040.0060.0080.00USD 5Y Swap Rate5d returns (bps)Sep08 to Sep1220Nov08 > -60bps13Dec10 > 20bps
- 9. VaR - Historical Simulation Assume our portfolio has a PV01 of $1million Assume for simplicity that USD 5Y Swap is the only risk factor For a 1 bps rise in the 5Y Swap rate, our Profit will be $1m For a 1 bps fall in the 5Y Swap rate, our Loss will be $1m We can calculate the PL Series for our portfolio by multiplying thebps returns on each day by $1 million, which is shown below-80.00-60.00-40.00-20.000.0020.0040.0060.0080.00Profit LossSep08 to Sep1220Nov08 > $60m
- 10. VaR - Historical Simulation This PL Series Has a PL value for each business day from 5 Sep 08 to 4 Sep 12 A total count of 1043 values Each corresponds to a specific scenario date, starting on 5 Sep 08 The first element represents the PL outcome of applying the 5-dayreturn shift between 1 Sep 08 and 5 Sep 08 to todays market dataand todays portfolio We call this the PL vector of the portfolio The first few elements of which are shown below-26.51-5.97-12.75-6.47-3.29-15.83-14.76-37.08-9.98-16.5522.7671.5509/05/200809/08/200809/09/200809/10/200809/11/200809/12/200809/15/200809/16/200809/17/200809/18/200809/19/200809/22/2008For these dates
- 11. VaR - Historical Simulation The PL vector can then be re-ordered by decreasing loss Keeping a note of the scenario date and PL of each The first part of this is shown below123456789101111/20/200812/17/200810/21/200810/22/200811/21/200806/17/200908/14/200912/18/200810/06/200810/07/200809/16/2008-62.58-56.16-47.79-46.24-44.95-42.47-41.29-39.73-39.62-37.45-37.08For these datesRe-order by PL Now we can determine the VaR Which we will define as 99% or the loss of the 11th worst PL (We could define as 10th worst or interpolate between 10th and 11th) So VaR is $37.08m Occurs on the scenario date of 16-Sep-08, we call this the VaR Date This is the week of Lehman’s bankruptcy filingVaR Date
- 12. VaR - Historical Simulation050100150200250-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Frequency5d PLsSep08 to Sep12Mean -1.21Standard Deviation 13.03Kurtosis 2.63Skewness 0.17Range 134.13Minimum -62.58Maximum 71.55VaR 99% -37.08Count 1043 A Histogram is a good way to view the PL vector Allocate each PL to a bin range Frequency is high for small PLs, giving the distribution below
- 13. VaR - Historical Simulation Zooming in to the largest lossesMean -1.21Standard Deviation 13.03Kurtosis 2.63Skewness 0.17Range 134.13Minimum -62.58Maximum 71.55VaR 99% -37.08Count 104311th largest lossLargest lossExpected Shortfall
- 14. Changes since the Financial Crises of 2008 Basell Capital Accord, introduced Stressed VaR So Trading Book Capital is the higher of Firm’s Multiplier *VaR or Multiplier * Stressed VaR Where Stressed VaR covers a period of Market Stress The Financial Crises of 2008 qualifies as a period of stressfor most major markets Wider use of Tail measures Expected Shortfall (ES) or Worst Case Loss (WCL) Renewed focus that Stress testing must be performed andthe definition and results of these discussed within the firmand with regulators Hence US & European Regulatory Stress Tests
- 15. Strengths and Weaknesses Strengths Reduces risk to a single $ amount Mark to market based measure (not original notional) Compare risk of different asset class portfolios Aggregate risk across portfolios Widely used since 1994 Weaknesses Reduces risk to a single $ amount Assumptions may be complex Depends on market prices being observable and similarbehaviour to that observed in the past Long-tailed properties of financial markets Portfolio diversification is not there in a Crisis So correlation goes to 1
- 16. Summary It is crucial to understand any assumptions For VaR, these are Method e.g. Historical Simulation Confidence level e.g. 99.7% Holding Period e.g. 5 days Historical Period Used e.g. 5 Years And not use just a single VaR measure Or indeed discard VaR (and replace with what?) So, in addition to VaR Use Tail Measures e.g. ES or WCL Stress Tests – Historical and Hypothetical Independent price verification Gross measures
- 17. Contact DetailsOur LinkedIn Page: Clarus Financial TechnologyOur Website: www.clarusft.comMy contact details: amir@clarusft.com

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