FIN 685: Risk Management

Larry Schrenk, Instructor

TOPICS

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

Course Details

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

PREREQUISITES

MSF, not MBA, Course Statistics Finance– Derivatives

Mathematics Economics Accounting

BOOK

Philippe Jorion, Financial Risk Manager Handbook (FRMH)

SCHEDULEPART 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 RISK3. Dependencies TBA4.  The World of Monte Carlo–Simulation, not Gambling FRMH 4

  5. The Hot Techniques: Value at Risk (VaR), etc. FRMH 14, 15Exam 1 (through Topic 4)

 PART III: SPECIFIC APPLICATIONS6. 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

REVIEW/EXCEL SCHEDULE1. Probability Measures FRMH 22. Linear Regression FRMH 33. Time Value of Money and Bonds FRMH 14. Stocks, FX, Commodities FRMH 95. Exam 1, No Review6. Derivatives: Introduction FRMH 57. Derivatives: Black-Scholes FRMH 68. Derivatives: Binomial Model FRMH 69. Exam 2, No Review 10. Fixed-Income FRMH 711. Fixed-Income Derivatives FRMH 812. Exam 3, No Review

PROFESSIONAL ORGANIZATIONS Global Association of Risk

Professionals (GARP)– Financial Risk Manager Certificate

Professional Risk Managers’ International Association (PRMIA)– Professional Risk Manager Certificat

e

What is Risk?

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

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.

RISK DEFINITION

Different Risks; Different Possibilities

Greater/Lesser Risk; Greater/Lesser Deviation

Upside and Downside Risk

RISK ANALYSIS

Stages of Risk Analysis

1. Identify Exposure

2. Measure Amount

3. Price

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.

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.

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

OVER-SIMPLIFIED EXAMPLE

1. Risk Exposure: Return Volatility

2. Risk Measure: Standard Deviation

3. Risk Price: 1% risk premium per 2% Standard Deviation

• Alternate: CAPM

THE QUANTIFICATION OF RISK• Past Data– Historical prices – Forward-looking data– Assumption: Future behaves like

past

• Statistical Distribution– Distribution, –Mean, – Variance, etc.

QUANTIFICATION EXAMPLE

• Historical Data:– Normally distributed, m = 10%, s = 20%

• Forecast– E[r] = 10%– Confidence intervals, standard error, etc.

-84%-71%-59%-46%-34%-21% -9% 3% 16% 28% 41% 53% 65% 78% 90%0

50

100

150

200

250

300

350

0%

20%

40%

60%

80%

100%

120%

Return DistributionNormal, m = 10%, s = 25%

Bin

Fre

quency

COHERENT RISK MEASURE Criteria–Monotonicity– Sub-additivity– Positive homogeneity– Translation invariance

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.

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.

POSITIVE HOMOGENEITY Expression

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

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.

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

What is Risk Management?

RISK PROFILE

Natural▪

Engineered▪

TYPES OF RISK

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

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.

MARKET RISK

Capital Asset Pricing Model (CAPM)– Diversification

–Market versus Non-Market Risks

– Beta

POSSIBLE BETAS

Market (b =1)▪

b >1

b < 1

BUILDING THE SML

Beta

Retu

rnR

etu

rn

rM

rf

0 1

Risk Free Asset

Market

WHAT HAPPENS IN STOCK DIVERSIFICATION?▪

Number of Stocks

Vola

tilit

y o

f Po

rtfo

lio

Market Risk

Non-Market Risk

SOME APPROACHES TO RISK Notional Amount

Sensitivity Analysis– Inputs– VaR

Scenario Analysis– Events

Value-at-Risk (VaR)

VAR OVERVIEW

Sensitivity Measure

‘Worst-Case-Scenario’

Downside Risk Only

Lower Tail

1/100 Year Flood Level

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).

VAR ADVANTAGES

• Risk -> Single number• Firm wide summary– Handles futures, options, and other

complications• Relatively model free• Easy to explain• Deviations from normal

distributions

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

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

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

POSSIBLE PROBLEMS

At 99% level, will exceed 3-4 times per year

Distributions have fat tails

Probability of loss – Not magnitude

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%

VAR EXAMPLE 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

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

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

CHOOSING VAR PARAMETERS

• Holding period– Risk environment– Portfolio constancy/liquidity

• Confidence level– How far into the tail?– VaR use– Data quantity

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

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

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

Risk(A B)Risk(A)Risk(B)

Sources of Market Risk

SOURCES OF MARKET RISK Currency Risk

Fixed-Income Risk

Equity Risk

Commodity Risk