1. Prof Ian Giddy Stern School of Business New York University
LIB
Market Risk Analysis
Prof Ian Giddy
Stern School of Business
New York University

2. Risk Management is a Process
Define
Measure
Manage
Monitor

3. Risk Management is a Process
Define
Measure
Manage
Monitor

4. Risk Management is a Process
Define
Measure
Manage
Monitor

5. Risk Management is a Process
Define
Measure
Manage
Monitor

6. Market Risk Measurement
Where are we now? Where do we need to be?
Option Sensitivity Measures
Value at Risk
Duration/ PVof01
Volumetric
Simulations
Notional Amounts
Linear risk measures
Swap/ bond equivalents
Non-linear risk measures
Delta, gamma, vega, theta, rho
No aggregation of risk measures across asset classes or instruments
Limited market scenarios that could include market correlations
Reprice portfolio
Parallel and non-parallel curve shifts
Aggregate portfolio risk per scenario
Distribution of market moves and portfolio values
Includes market correlations
Aggregate risk measures within confidence interval

7. An Overview of Corporate VAR
Transactional Database
Business 1
Portfolio
Database
Business 2
Business 3
Projected Revenues
Projected Operating Costs
Estimates of Cash Flow Distribution
Volatilities
Correlations
Base rates/ Currency market conditions
Historical rates/ Discrete scenarios
Model 1
Model 2
Model 3
Model 4
Interest Rates
Currencies
Equities
Commodities
Mean
Impact on Earnings

8. Summary of “Value at Risk” Reporting
“At close of business each day tell me what the market risks are across all businesses and locations.”
Dennis Weatherstone, JP Morgan
Logical steps:
Economic-value accounting (need market prices or models)
Volatilities and correlations of market prices
Measurement of Risk Exposure
Management of risk
Market-price based performance measurement

9. Portfolio Diversification
DM position
A$ position
S$ position
FIM position
Net effect?

10. Currency Volatility: Start with the Data

11. Calculate Daily % Changes

12. (exponential smoothing) (rolling historicals)
Predict Volatilities
RiskMetrics
(exponential smoothing)
BIS
(rolling historicals)

13. RiskMetrics Method Compared

14. RiskMetrics Method Compared
Other methods include:
Implied volatility from option prices
Structured volatility models (ARCH, GARCH, EGARCH)
Stochastic volatility
The task of most models is to find
some historical pattern of volatility
and to use this to forecast volatility,
which seems to “cluster

15. http://www.jpmorgan.com and http://www.riskmetrics.reuters.com
Get Volatility and Correlation Estimates...eg from RiskMetrics
On the World Wide Web, RiskMetrics publications and data may be found at:
and

16. RiskMetrics Coverage ...plus about a dozen commodities,term structure
of yields, more exotics...
each day, about 450
volatilities and 100,000
correlations.

17. Now More...(and Later, Customizable)

18. Estimated Volatilities

19. Single-Asset Value-at-Risk
Potential loss (5% probability)
=Amount at risk * Adverse price/rate move per period (1.65SD)
Probability
68%
95%
> 99%
– 3
– 2
– 1
+ 1
+ 2
+ 3
Percentage change in exchange rate

20. Single-Asset Value-at-Risk: Example
A Single Position
(Example: $100,000 AUD)
Volatility

21. Estimated Correlations

22. A Correlation Matrix

23. Measuring Portfolio Exposure: Two Assets
The variance of a 2-asset portfolio, :
where wA and wB are the weights of A and B in the portfolio.
To evaluate the gains and structure of a portfolio, we need a variance-covariance matrix:
$ AT RISK VOL. AUD BEF
AUD $50, % 1
BEF $50, %

24. Two-Asset Value-at-Risk: Example
Two Positions
(Example: $100,000 AUD & BEF)
Volatility &
Correlation

25. Return and Risk, Generalized
Portfolio return:
where wi are the weights of each asset in the portfolio. (Expected return is simply the weighted sum of the individual asset returns.)
Portfolio variance:
When i = j, the term wiwj becomes wi2

26. Portfolio Value at Risk+ =
Value-at-Risk
Mean

27. A Management-Friendly Report
An example is FourFifteen™, named after J.P. Morgan's market risk report produced at 4:15 p.m. each day.
The "4:15 Report," a single sheet of paper, summarizes the Daily Earnings at Risk for J.P. Morgan worldwide. 
Portfolio Risk Simulation
USD Base. Vols. & correls. as of May 04, 1995.
AUD
BEF
CAD
DKK
FFR
DEM
ITL
JPY
NLG
ESB
SEK
CHF
GBP
XEU
USD
Total
1 Mo 15 22 37
3 Mo
-200 20
-30
160
- 50
6 Mo 25 -5
12 Mo
-105
- 105
2 Yr
3 Yr
4 Yr
5 Yr
7 Yr
9 Yr
10 Yr
15 Yr
20 Yr
30 Yr
Equity
Implied 59
-29 54
-145
Spot 23
Net 82
-122
Int.
502
262 5
139
400
740
Eq. Fx
5,048
4265
1383
1820
8516
divers.
-347 -6
-83
-451
5,350
4181
1876
8805
RISK
($000)
RiskMetricsª
Gov't Bonds Zero Cashflow FX

28. Exposure Report: Example

29. The Next Step: Efficient Hedging
30% HEDGE
(VAR $25M,
COST $0.8M)
NO HEDGE
(VAR $46M, COST $0)

30. Efficient Hedging, Constrained

31. Efficient Hedging, Constrained

32. The VaR Management Cycle
This process can be undertaken on a monthly cycle basis, as the institution revises its estimates of future business and as new data on volatilities and correlations are acquired.

33. Value at Risk: Assessment
Value at Risk and RiskMetrics:
A method for quantifying risk in dynamic, uncertain environments
Based on the observation that volatilities and correlations are somewhat persistent
The RiskMetrics estimates are in the ballpark of other, more sophisticated, methods

34. Value at Risk: Assessment

35. Value at Risk: Assessment

36. Is VAR Valid?
Are we measuring the right thing for our purpose?
Since we are measuring deviations from expected, do we have a good approximation of the distribution of changes?
How good are our forecasts of volatilities and correlations?
How good are our exposure measures?
How good are our valuation models?

37. Alternatives
Worst-case analysis
Scenario analysis
Historical simulation
Monte-Carlo simulation
Sensitivity measures

38. What Happens in the Tails?
For credit and capital purposes, we want to know about the probability, size and impact of extreme events.
Worst-Case Analysis:
How skewed?
How many?
How large?
Probability of extreme events?
Mean

39. EMU Scenario Analysis for Publicorp
Baseline Scenario
This scenario assumes that current predictions of volatilities and correlations are valid for Publicorp’s
FX risk management horizon. As is shown in the table below, the monthly volatility -- defined as
the standard deviation of percentage changes in the dollar value of foreign currencies -- ranges
from 1.69% for the Canadian dollar to 2.55%% for the Swedish Krona. The correlations between
the DM and the core European currencies are very high - for example, the French franc has a 98%
correlation with the DM - while the other European currencies have a positive but lower
correlation coefficient. In particular, the British pound’s correlation with the DM is 55%. The
table shows that the Value-at-Risk (VaR) for Publicorp’s existing, unhedged positions is $1.222
million.
EMS Crisis Scenario
Under this scenario, we assume that the “inner core” European currencies, the mark, guilder and
Austrian schilling, remain closely linked, but that the correlations between German mark and the
Belgian franc, the French franc, Finnish markka, Spanish peseta and Portuguese escudo all fall to
65%. The result of this is to increase the VaR to $1.291 million -- not a dramatic increase.
EMS Convergence Scenario
The third scenario is one in which the correlations among all the major European Union
currencies rise to 100%. This could be regarded as the “single currency in Europe” scenario.
Because of Publicorp’s offsetting long and short positions in these currencies, the result is a
reduction
in currency exposure: the monthly VaR drops to below $1 million.

40. Scenario Analysis Has its Limitations, Too

41. The Alternative: Full-Valuation Methods
Prices, rates, and
estimated variances
and covariances
Simulation
Monte Carlo
Scenarios
Generate
Delta-Gamma
Valuation
Full
Valuation
MODELS
Estimated value
changes
Distribution of
Values

42. Using a VaR Measure for Trading-Portfolio Performance Evaluation
The Sharpe ratio.
(actual return relative to actual risk)
The risk ratio.
(actual return relative to prospective risk)
The efficiency ratio.
(actual risk relative to prospective risk)
Use risk-return performance measures to evaluate individual trader performance.

43. Performance Evaluation: Example

44. Performance Evaluation: Example

45. Performance Evaluation: Example

46. Performance Evaluation: Example

47. Performance Measurement: Roadmap
Map exposures
Map risks
Manage risks
Measure performance
Take actions to improve performance
FINANCIAL SIDE
EXPOSURES
Known
Anticipated
OPERATIONAL SIDE
MARKET PRICES
RISK MEASUREMENT
VaR
Worst-case scenario, etc.
MARKET VOL & CORR.
RISK MANAGEMENT
Hedging
Investment or trading
PERFORMANCE MEASUREMENT
Relative return
Relative risk.
INCENTIVES
ALLOCATION OF RESOURCES.

48. Treasury Performance Measurement: Conclusion
Performance evaluation: “the science of attribution”
Why did we make/lose money?
The market; the FX manager; my lousy instructions?
How much should I tip this FX manager?
Would I use this method again?
How good is my performance measurement system?

49. Summary: Market Risk Management is a Process
Define
Measure
Manage
Monitor

55. Ian H. Giddy Professor of Finance Stern School of Business
New York University
44 West 4th Street, New York, NY 10012, USA
Tel ; Fax
World Wide Web: