FIN 685: Risk Management Larry Schrenk, Instructor

 Course Details  What is Risk?  What is Risk Management?  Introduction to VaR  Sources of Market Risk

Course Details

 Course Pages –  Class – Lecture 5:30 PM to 8:00 PM – Review/Excel and Office Hours 8:00 PM+  Exams 3; Excel Projects 1; Case 1

 MSF, not MBA, Course  Statistics  Finance – Derivatives  Mathematics  Economics  Accounting

 Philippe Jorion, Financial Risk Manager Handbook (FRMH)

P ART I: R ISK IN G ENERAL 1. What is Risk? How Do We Measure It?FRMH 10, How Do We Deal with Risk? Why Should We Care?FRMH 12, 13 P ART II: D EALING WITH R ISK 3. DependenciesTBA 4. The World of Monte Carlo–Simulation, not GamblingFRMH 4 5. The Hot Techniques: Value at Risk (VaR), etc.FRMH 14, 15 Exam 1 (through Topic 4) P ART III: S PECIFIC A PPLICATIONS 6. Credit Risk IFRMH 18, Credit Risk IIFRMH 20, Credit Risk IIIFRMH 22, Operational Risk FRMH 24 Exam 2 (through Topic 8) 10. Liquidity Risk FRMH Managing Risk across the FirmFRMH 16, Our Friends in BaselFRMH 29, 30 Exam 3 (through Topic 12); Case and Projects Due

1. Probability MeasuresFRMH 2 2. Linear RegressionFRMH 3 3. Time Value of Money and BondsFRMH 1 4. Stocks, FX, CommoditiesFRMH 9 5. Exam 1, No Review 6. Derivatives: IntroductionFRMH 5 7. Derivatives: Black-ScholesFRMH 6 8. Derivatives: Binomial ModelFRMH 6 9. Exam 2, No Review 10. Fixed-IncomeFRMH Fixed-Income DerivativesFRMH Exam 3, No Review

 Global Association of Risk Professionals (GARP)GARP – Financial Risk Manager Certificate Financial Risk Manager Certificate  Professional Risk Managers’ International Association (PRMIA)PRMIA – Professional Risk Manager Certificate Professional Risk Manager Certificate

What is Risk?

 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 for each color. – Risk  Rational Expectation

 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.

 Different Risks; Different Possibilities  Greater/Lesser Risk; Greater/Lesser Deviation  Upside and Downside Risk

 Stages of Risk Analysis 1. Identify Exposure 2. Measure Amount 3. Price

 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.

 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.

 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] – r f

1. Risk Exposure: Return Volatility 2. Risk Measure: Standard Deviation 3. Risk Price: 1% risk premium per 2% Standard Deviation  Alternate: CAPM

 Past Data – Historical prices – Forward-looking data – Assumption: Future behaves like past  Statistical Distribution – Distribution, – Mean, – Variance, etc.

 Historical Data: – Normally distributed,  = 10%,  = 20%  Forecast – E[r] = 10% – Confidence intervals, standard error, etc.

 Criteria – Monotonicity – Sub-additivity – Positive homogeneity – Translation invariance

 Expression – If portfolio Z 2 always has better values than portfolio Z 1 under all scenarios then the risk of Z 2 should be less than the risk of Z 1.

 Expression – Indeed, the risk of two portfolios together cannot get any worse than adding the two risks separately: this is the diversification principle.

 Expression – Loosely speaking, if you double your portfolio then you double your risk.

 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.

 References: – Artzner, P., Delbaen, F., Eber, J.M., Heath, D. (1997). Thinking coherently. Risk 10, November, – Artzner, P., Delbaen, F., Eber, J.M., Heath, D. (1999). Coherent measures of risk. Math. Finance 9(3),

What is Risk Management?

 Natural ▪  Engineered ▪

 Market Risk  Liquidity Risk  Operational Risk  Inflation Risk  Default Risk – ‘risk-free asset’

 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.

 Capital Asset Pricing Model (CAPM) – Diversification – Market versus Non-Market Risks – Beta

Market (  =1)▪  >1  < 1

Beta Return rMrM rfrf 01 Risk Free Asset Market

Number of Stocks Volatility of Portfolio Market Risk Non-Market Risk

 Notional Amount  Sensitivity Analysis – Inputs – VaR  Scenario Analysis – Events

Value-at-Risk (VaR)

 Sensitivity Measure  ‘Worst-Case-Scenario’  Downside Risk Only  Lower Tail  1/100 Year Flood Level

 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).

 Risk -> Single number  Firm wide summary – Handles futures, options, and other complications  Relatively model free  Easy to explain  Deviations from normal distributions

 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

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

 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

 At 99% level, will exceed 3-4 times per year  Distributions have fat tails  Probability of loss – Not magnitude

 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%

 Portfolio value today = 100  Normal value (mean = 100, std = 10 per month), time horizon = 1 month,  95% VaR = Percentile = 83.5

 Measure initial portfolio value (100)  For 95% confidence level, find 5 th 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

 Increase level to 99%  Portfolio value = 76.5  VaR = = 23.5  With probability 0.99, your losses will be less than 23.5  Increasing confidence level, increases VaR

 Holding period – Risk environment – Portfolio constancy/liquidity  Confidence level – How far into the tail? – VaR use – Data quantity

 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

 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

 A sub-additive risk measure is  Sum of risks is conservative (overestimate)  VaR not sub-additive – Temptation to split up accounts or firms

Sources of Market Risk

 Currency Risk  Fixed-Income Risk  Equity Risk  Commodity Risk