1 / 29

FIN 685: Risk Management

FIN 685: Risk Management. Topic 6: VaR Larry Schrenk, Instructor. Topics. Types of Risks Value-at-Risk Expected Shortfall. Types of Risk. Types of Risk. Market Risk Credit Risk Liquidity Risk Operational Risk. VaR. History.

tambre
Download Presentation

FIN 685: Risk Management

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FIN 685: Risk Management Topic 6: VaR Larry Schrenk, Instructor

  2. Topics • Types of Risks • Value-at-Risk • Expected Shortfall

  3. Types of Risk

  4. Types of Risk • Market Risk • Credit Risk • Liquidity Risk • Operational Risk

  5. VaR

  6. History • J. P. Morgan Chairman, Dennis Weatherstone and the 4:14 Report • 1993 Group of Thirty • 1994 RiskMetrics

  7. VaR • Probable Loss Measure • Multiple Methods • Comprehensive Measurement • Interactions between Risks

  8. VaR • There is an x percent chance that the firm will loss more than y over the next z time period.”

  9. Methods • Correlation • Historical Simulation • Monte Carlo Simulation

  10. Method Commonalities • Historical Prices • Various periods • Values Portfolio in Next Period • Generate Future Distributions of Outcomes

  11. Pro’s and Con’s • Variance-covariance • Assume distribution, use theoretical to calculate • Bad – assumes normal, stable correlation • Historical simulation • Good – data available • Bad – past may not represent future • Bad – lots of data if many instruments (correlated) • Monte Carlo simulation • Good – flexible (can use any distribution in theory) • Bad – depends on model calibration Finland 2010

  12. Use • Basel Capital Accord • Banks encouraged to use internal models to measure VaR • Use to ensure capital adequacy (liquidity) • Compute daily at 99th percentile • Can use others • Minimum price shock equivalent to 10 trading days (holding period) • Historical observation period ≥1 year • Capital charge ≥ 3 x average daily VaR of last 60 business days Finland 2010

  13. Limits • At 99% level, will exceed 3-4 times per year • Distributions have fat tails • Only considers probability of loss – not magnitude • Conditional Value-At-Risk • Weighted average between VaR & losses exceeding VaR • Aim to reduce probability a portfolio will incur large losses Finland 2010

  14. 1. Correlation Method • E.G. RiskMetrics • Steps • Means, Variances and Correlations from Historical Data • Assume Normal Distribution • Assign Portfolio Weights • Portfolio Formulae • Plot Distribution

  15. Portfolio Formulae

  16. Plot Distribution • Assuming normal distribution • 95% Confidence Interval • VaR -1.65 standard deviations from the mean • 99% Confidence Interval • VaR -2.33 standard deviations from the mean

  17. Plot Distribution

  18. Example • Two Asset Portfolio

  19. Var (5%) • s = 0.1658 • 5% tail is 1.65*0.1658 = 0.2736 from mean • Var = 0.16 - 0.2736 =-0.1136 • There is a 5% chance the firm will loss more than 11.35% in the time period

  20. Var (1%) • s = 0.1658 • 1% tail is 2.33*0.1658 = 0.3863 from mean • Var = 0.16 - 0 0.3863 =-0.2263 • There is a 1% chance the firm will loss more than 22.63% in the time period

  21. Var

  22. 2. Historical Simulation • Steps • Get Market Data for Determined Period • Measure Daily, Historical Percentage Change in Risk Factors • Value Portfolio for Each Percentage Change and Subtract from Current Portfolio Value

  23. 2. Historical Simulation • Steps • Rank Changes • Choose percentile loss • 95% Confidence • 5th Worst of 100 • 50thWorst of 1000

  24. 3. Monte Carlo Simulation • Model changes in risk factors • Distributions • E.g.rt+1 = rt+ a + brt + et • Simulate Behavior of Risk Factors Next Period • Ranks and Choose VaR as in Historical Simulation

  25. Var Critique • One Number • Sub-Additive • Historical Data • No Measure of Maximum Loss

  26. Choosing VaR Parameters • Holding period • Risk environment • Portfolio constancy/liquidity • Confidence level • How far into the tail? • VaR use • Data quantity

  27. VaR Uses • Benchmark comparison • Interested in relative comparisons across units or trading desks • Potential loss measure • Horizon related to liquidity and portfolio turnover • Set capital cushion levels • Confidence level critical here

  28. VaR Limitations • Uninformative about extreme tails • Bad portfolio decisions • Might add high expected return, but high loss with low probability securities • VaR/Expected return, calculations still not well understood • VaR is not Sub-additive

  29. Sub-additive Risk Measures • A sub-additive risk measure is • Sum of risks is conservative (overestimate) • VaR not sub-additive • Temptation to split up accounts or firms

More Related