FIN 685: Risk Management

1. FIN 685: Risk Management Larry Schrenk, Instructor

2. Topics • Course Details • What is Risk? • What is Risk Management? • Introduction to VaR • Sources of Market Risk

3. Course Details

4. Mechanics • Course Pages • http://auapps.american.edu/~schrenk/FIN685/FIN685.htm • Class • Lecture 5:30 PM to 8:00 PM • Review/Excel and Office Hours 8:00 PM+ • Exams 3; Excel Projects 1; Case 1

5. Prerequisites • MSF, not MBA, Course • Statistics • Finance • Derivatives • Mathematics • Economics • Accounting

6. Book • Philippe Jorion, Financial Risk Manager Handbook (FRMH)

7. schedule Part I: Risk in General 1. What is Risk? How Do We Measure It? FRMH 10, 11   2. How Do We Deal with Risk? Why Should We Care? FRMH 12, 13 Part II: Dealing with Risk 3. Dependencies TBA 4.  The World of Monte Carlo–Simulation, not Gambling FRMH 4   5. The Hot Techniques: Value at Risk (VaR), etc. FRMH 14, 15 Exam 1 (through Topic 4) Part III: Specific Applications 6. Credit Risk I FRMH 18, 19   7. Credit Risk II FRMH 20, 21   8. Credit Risk III FRMH 22, 23   9. Operational Risk FRMH 24 Exam 2 (through Topic 8)   10. Liquidity Risk FRMH 25 11.  Managing Risk across the Firm FRMH 16, 26   12. Our Friends in Basel FRMH 29, 30 Exam 3 (through Topic 12); Case and Projects Due

8. Review/Excel schedule 1. Probability Measures FRMH 2 2. Linear Regression FRMH 3 3. Time Value of Money and Bonds FRMH 1 4. Stocks, FX, Commodities FRMH 9 5. Exam 1, No Review 6. Derivatives: Introduction FRMH 5 7. Derivatives: Black-Scholes FRMH 6 8. Derivatives: Binomial Model FRMH 6 9. Exam 2, No Review 10. Fixed-Income FRMH 7 11. Fixed-Income Derivatives FRMH 8 12. Exam 3, No Review

9. Professional Organizations • Global Association of Risk Professionals (GARP) • Financial Risk Manager Certificate • Professional Risk Managers’ International Association (PRMIA) • Professional Risk Manager Certificate

10. What is Risk?

11. Risk versus Uncertainty • Uncertainty: Ignorance • I have no idea what a box may contain. • Risk: ‘Distributional’ Knowledge • I may not know which color I will get, but I know that the probability is 50-50 for each color. • Risk  Rational Expectation

12. Risk Definition • Risk is… • The possibility that the actual (or realized) result may deviate from the expected result. • Financial Risk is (often)… • The possibility that the actual (or realized) return may deviate from the expected return.

13. Risk Definition • Different Risks; Different Possibilities • Greater/Lesser Risk; Greater/Lesser Deviation • Upside and Downside Risk

14. Risk analysis • Stages of Risk Analysis 1. Identify Exposure 2. Measure Amount 3. Price

15. Step 1–Identify Risk • Identify risk exposure • Profit of a firm • Input price changes • Labor problems • Shifts in consumer tastes • Bond • Interest rate risk • Default risk • Foreign investment • Exchange rate risk • Result: Asset exposed to risks X, Y, etc.

16. Step 2–Measure Risk • Measure/quantify the risk • ‘Cardinal Ordering’ • Use of statistics • Historical volatility/standard deviation • Correct measure of specific risks • Result: Asset exposure to risk X is 8 units.

17. Step 3–Price Risk • Price the Risk • Compensation for specific level of risk. • Return, not dollar, compensation • Higher risk  higher return • Result: Asset exposure to 8 units of X risk yields a risk premium of 10%. Recall: Risk premium = E[r] – rf

18. Over-Simplified Example • Risk Exposure: Return Volatility • Risk Measure: Standard Deviation • Risk Price: 1% risk premium per 2% Standard Deviation • Alternate: CAPM

19. The Quantification of Risk • Past Data • Historical prices • Forward-looking data • Assumption: Future behaves like past • Statistical Distribution • Distribution, • Mean, • Variance, etc.

20. Quantification Example • Historical Data: • Normally distributed, m = 10%, s = 20% • Forecast • E[r] = 10% • Confidence intervals, standard error, etc.

21. Coherent risk measure • Criteria • Monotonicity • Sub-additivity • Positive homogeneity • Translation invariance

22. Monotonicity • Expression • If portfolio Z2 always has better values than portfolio Z1 under all scenarios then the risk of Z2 should be less than the risk of Z1.

23. Sub-additivity • Expression • Indeed, the risk of two portfolios together cannot get any worse than adding the two risks separately: this is the diversification principle.

24. Positive homogeneity • Expression • Loosely speaking, if you double your portfolio then you double your risk.

25. Translation invariance • Expression • The value a is just adding cash to your portfolio Z, which acts like an insurance: the risk of Z + a is less than the risk of Z, and the difference is exactly the added cash a.

26. Coherent risk measure • References: • Artzner, P., Delbaen, F., Eber, J.M., Heath, D. (1997). Thinking coherently. Risk 10, November, 68-71 • Artzner, P., Delbaen, F., Eber, J.M., Heath, D. (1999). Coherent measures of risk. Math. Finance 9(3), 203-228

27. What is Risk Management?

28. Risk profile • Natural▪ • Engineered▪

29. Types of risk • Market Risk • Liquidity Risk • Operational Risk • Inflation Risk • Default Risk • ‘risk-free asset’

30. Market Risk • The uncertainty of an instrument’s earnings resulting from changes in market conditions such as the price of an asset, interest rates, market volatility, and market liquidity.

31. Market Risk • Capital Asset Pricing Model (CAPM) • Diversification • Market versus Non-Market Risks • Beta

32. Possible Betas b >1 Market (b =1)▪ b < 1

33. Building the SML Return Return rM Market rf Risk Free Asset 0 1 Beta

34. What Happens in Stock Diversification?▪ Non-Market Risk Volatility of Portfolio Market Risk Number of Stocks

35. Some approaches to risk • Notional Amount • Sensitivity Analysis • Inputs • VaR • Scenario Analysis • Events

36. Value-at-Risk (VaR)

37. Var Overview • Sensitivity Measure • ‘Worst-Case-Scenario’ • Downside Risk Only • Lower Tail • 1/100 Year Flood Level

38. Var definition • Value at Risk… • The maximum dollar amount that is expected to be lost over X time at Y significance. • EXAMPLE: VaR = $1,000,000 in the next month at 99% significance. • Expectation (typically) relative to historical performance of assets(s).

39. VaR Advantages • Risk -> Single number • Firm wide summary • Handles futures, options, and other complications • Relatively model free • Easy to explain • Deviations from normal distributions

40. Value at Risk (VaR)History • Financial firms in the late 80’s used it for their trading portfolios • JP Morgan, 1990’s • RiskMetrics, 1994 • Currently becoming: • Wide spread risk summary • Regulatory

41. Use • Basel Capital Accord • Banks encouraged to use internal models to measure VaR • Use to ensure capital adequacy (liquidity) • Compute daily at 99th percentile • Minimum price shock equivalent to 10 trading days (holding period) • Historical observation period ≥1 year

42. VaR Calculation Approaches • Historical simulation • Good – data available • Bad – past may not represent future • Bad – lots of data if many instruments (correlated) • Variance-covariance • Assume distribution, use theoretical to calculate • Bad – assumes normal, stable correlation • Monte Carlo simulation • Good – flexible (can use any distribution in theory) • Bad – depends on model calibration

43. Possible problems • At 99% level, will exceed 3-4 times per year • Distributions have fat tails • Probability of loss – Not magnitude

44. Defining VaR • Mark to market (value portfolio) • 100 • Identify and measure risk (future value) • Normal: mean = 100, std. = 10 over 1 month • Set time horizon of interest • 1 month • Set confidence level: • 95%

45. Varexample • Portfolio value today = 100 • Normal value (mean = 100, std = 10 per month), time horizon = 1 month, • 95% VaR = 16.5 0.05 Percentile = 83.5

46. VaR Definitions in Words • Measure initial portfolio value (100) • For 95% confidence level, find 5th percentile level of future portfolio values (83.5) • The amount of this loss (16.5) is the VaR • What does this say? • With probability 0.95 your losses will be less than 16.5

47. Increasing the Confidence Level • Increase level to 99% • Portfolio value = 76.5 • VaR = 100-76.5 = 23.5 • With probability 0.99, your losses will be less than 23.5 • Increasing confidence level, increases VaR

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

49. 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

50. 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