Download FIN 685: Risk Management

FIN 685: Risk Management
Topic 1: What is Risk? How Do We
Measure It?
Larry Schrenk, Instructor
Course Details
 What is Risk?
 What is Risk Management?
 Introduction to VaR
 Sources of Market Risk

Course Details

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
MSF, not MBA, Course
 Statistics
 Finance

– Derivatives
Mathematics
 Economics
 Accounting


Philippe Jorion, Financial Risk Manager
Handbook (FRMH)
PART I: RISK IN GENERAL
1. What is Risk? How Do We Measure It?
PART II: DEALING WITH RISK
2. How Do We Deal with Risk? Why Should We Care?
3. Dependencies
4. The World of Monte Carlo–Simulation, not Gambling
5. The Hot Techniques: Value at Risk (VaR), etc.
Exam 1 (through Topic 4)
PART III: SPECIFIC APPLICATIONS
6. Credit Risk I
7. Credit Risk II
8. Credit Risk III
9. Operational Risk
Exam 2 (through Topic 8)
10. Liquidity Risk
11. Managing Risk across the Firm
12. Our Friends in Basel
Exam 3 (through Topic 12); Case and Projects Due
FRMH 10, 11
FRMH 12, 13
TBA
FRMH 4
FRMH 14, 15
FRMH 18, 19
FRMH 20, 21
FRMH 22, 23
FRMH 24
FRMH 25
FRMH 16, 26
FRMH 29, 30
1. Probability Measures
2. Linear Regression
3. Time Value of Money and Bonds
4. Stocks, FX, Commodities
5. Exam 1, No Review
6. Derivatives: Introduction
7. Derivatives: Black-Scholes
8. Derivatives: Binomial Model
9. Exam 2, No Review
10. Fixed-Income
11. Fixed-Income Derivatives
12. Exam 3, No Review
FRMH 2
FRMH 3
FRMH 1
FRMH 9
FRMH 5
FRMH 6
FRMH 6
FRMH 7
FRMH 8

Global Association of Risk Professionals
(GARP)
– Financial Risk Manager Certificate

Professional Risk Managers’ International
Association (PRMIA)
– 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 50-50 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] – rf
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, m = 10%, s = 20%
–
Return Distribution
Normal, m = 10%, s = 25%
350
100%
250
80%
200
60%
150
40%
100
50
20%
0
0%
-84%
-76%
-69%
-62%
-55%
-48%
-41%
-34%
-27%
-20%
-13%
-5%
2%
9%
16%
23%
30%
37%
44%
51%
58%
65%
73%
80%
87%
More
Frequency
300
Bin
Forecast

–
–
120%
E[r] = 10%
Confidence intervals, standard error, etc.

Criteria
– Monotonicity
– Sub-additivity
– Positive homogeneity
– Translation invariance

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.

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, 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?

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
b >1
Market (b =1)▪
b<1
Return
rM
Market
rf
Risk Free Asset
0
1
Beta
Volatility of Portfolio
Non-Market Risk
Market Risk
Number of Stocks

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 99th 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 =
16.5
0.05 Percentile = 83.5
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
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


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
Risk(A  B)  Risk(A)  Risk(B)
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