Risk Management

1
Value-at-Risk (VaR)

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

2
Risk

• Business Risk
• Financial Risk
• market risk
• credit risk
• liquidity risk
• Operational Risk
• Legal Risk

3
How much can we lose?

• Everything
• correct, but useless answer.
• How much can we lose realistically?

4
Derivatives 1993-1995

• ( million)
• Shova Shell, Japan 1,580
• Kashima Oil, Japan 1,450
• Metallgesellschaft 1,340
• Barings, U.K. 1,330
• Codelco, Chile 200
• Procter Gamble, US 157

5
Barings

• February 26, 1995
• 233 year old bank
• 28 year old Nick Leeson
• 1,300,000,000 loss
• bought by ING for 1.5

6
Public Funds

• ( million)
• Orange County 1,640
• San Diego 357
• West Virginia 279
• Florida State Treasury 200
• Cuyahoga County 137
• Texas State 55

7
Orange County

• Bob Citron, the county treasures
• 7.5B portfolio (schools, cities)
• borrowed 12.5B, invested in 5yr. notes
• interest rates increased
• reported at cost - big mistake!
• realized loss of 1.64B

8
Financial Losses

• Barings 1.3B
• Bank Negara, Malaysia 92 3B
• Banesto, Spain 4.7B
• Credit Lyonnais 10B
• SL, U.S.A. 150B
• Japan 500B

9
Metallgesellshaft

• 14th largest industrial group
• 58,000 employees
• offered long term oil contracts
• hedge by long-term forward contracts
• short term contracts were used (rolling hedge)
• 1993 price fell from 20 to 15
• 1B margin call in cash

10
(No Transcript)
11
What is the current Risk?

• duration, convexity
• volatility
• delta, gamma, vega
• rating
• target zone

• Bonds
• Stocks
• Options
• Credit
• Forex

• Total ?

12
Standard Approach
13
Modern Approach
Financial Institution
14
Risk Management

• Risk measurement
• Reporting to board
• Limits monitoring
• Diversification, reinsurance
• Vetting
• Reporting to regulators
• Decision making based on risk

15
Who manages risk?
AIG General Re Swiss Re Aetna Zurich
Nike Sony Dell Computers Philip Morris Ford
Motor

• Citibank
• Bank of England
• CIBC
• J. P. Morgan
• Bankers Trust

16
Regulators

• BIS
• FSA
• SEC
• ISDA
• FASB
• Bank of Israel
• Galais committee

17
Basic Steps in RM process

• Identify risks
• Data base (market position)
• Risk measurement
• Regulators
• Risk Management
• Reporting
• Strategic decisions

18
Building a RM system

• Initial study of risks
• Decision, Risk Manager
• Risk measurement system
• Responsibilities and structure
• Testing
• Active Risk Management
• Staff training and maintenance

19
Risk Management andRisk Measurement
20
Risk Management System
Can NOT

• Predict future
• Identify business opportunities
• Be always right!

Risk Management System Can

• Predict loss, given event
• Identify most dangerous scenarios
• Recommend how to change risk profile

21
Tool, not rule!
22
Definition

• VaR is defined as the predicted worst-case loss
  at a specific confidence level (e.g. 99) over a
  certain period of time.

23
VaR
24
Meaning of VaR

• A portfolio manager has a daily VaR equal 1M at
  99 confidence level.
• This means that there is only one chance in 100
  that a daily loss bigger than 1M occurs,

under normal market conditions.
25
History of VaR

• 80s - major US banks - proprietary
• 93 G-30 recommendations
• 94 - RiskMetrics by J.P.Morgan
• 98 - Basel
• SEC, FSA, ISDA, pension funds, dealers
• Widely used and misused!

26
Risk Management Structure
27
Value
dollar
Interest Rate
interest rates and dollar are NOT independent
28
Risk Measuring Software

• CATS, CARMA
• Algorithmics, Risk Watch
• Infinity
• J.P. Morgan, FourFifteen
• FEA, Outlook
• Reuters, Sailfish
• Kamacura
• Bankers Trust, RAROC
• INSSINC, Orchestra

29
Qualitative Requirements

• An independent risk management unit
• Board of directors involvement
• Internal model as an integral part
• Internal controller and risk model
• Backtesting
• Stress test

30
Quantitative Requirements

• 99 confidence interval
• 10 business days horizon
• At least one year of historic data
• Data base revised at least every quarter
• All types of risk exposure
• Derivatives

31
Types of Assets and Risks

• Real projects - cashflow versus financing
• Fixed Income
• Optionality
• Credit exposure
• Legal, operational, authorities

32
Risk Factors

• There are many bonds, stocks and currencies.
• The idea is to choose a small set of relevant
  economic factors and to map everything on these
  factors.
• Exchange rates
• Interest rates (for each maturity and
  indexation)
• Spreads
• Stock indices

33
How to measure VaR

• Historical Simulations
• Variance-Covariance
• Monte Carlo
• Analytical Methods

34
Historical Simulations

• Fix current portfolio.
• Pretend that market changes are similar to those
  observed in the past.
• Calculate PL (profit-loss).
• Find the lowest quantile.

35
Example
Assume we have 1 and our main currency is
SHEKEL. Today 14.30. Historical data
PL 0.215 0 -0.112 0.052

• 4.00
• 4.20
• 4.20
• 4.10
• 4.15

4.304.20/4.00 4.515 4.304.20/4.20
4.30 4.104.10/4.20 4.198 4.154.15/4.10 4.352
36
USD NIS 2000 100 -120 2001 200
100 2002 -300 -20 2003 20 30
today
37
today
Changes in IR
USD 1 1 1 1 NIS 1 0
-1 -1
38
Returns
year
39
VaR
40
Weights

• Since old observations can be less relevant,
  there is a technique that assigns decreasing
  weights to older observations. Typically the
  decrease is exponential.
• See RiskMetrics Technical Document for details.

41
Variance Covariance

• Means and covariances of market factors
• Mean and standard deviation of the portfolio
• Delta or Delta-Gamma approximation
• VaR1 ?P 2.33 ?P
• Based on the normality assumption!

42
Variance-Covariance
?-2.33?
43
Monte Carlo
44
Monte Carlo

• Distribution of market factors
• Simulation of a large number of events
• PL for each scenario
• Order the results
• VaR lowest quantile

45
Monte Carlo Simulation
46
Real Projects

• Most daily returns are invisible.
• Proper financing should be based on risk exposure
  of each specific project.
• Note that accounting standards not always reflect
  financial risk properly.

47
Example

• You are going to invest in Japan.
• Take a loan in Yen.
• Financial statements will reflect your
  investment according to the exchange rate at the
  day of investment and your liability will be
  linked to yen.
• Actually there is no currency risk.

48
Airline company

• fuel - oil prices and
• purchasing airplanes - and Euro
• salaries - NIS, some
• tickets
• marketing - different currencies
• payments to airports for services

49
Airline company

• loans
• equity
• callable bonds

50
Airline company

• Base currency - by major stockholder.
• Time horizon - by time of possible price change.
• Earnings at risk, not value at risk, since there
  is too much optionality in setting prices.
• One can create a one year cashflow forecast and
  measure its sensitivity to different market
  events.

51
Reporting

• Division of VaR by business units, areas of
  activity, counterparty, currency.
• Performance measurement - RAROC (Risk Adjusted
  Return On Capital).

52
How VaR is used

• Internal Risk Management
• Reporting
• Regulators

53
Backtesting

• Verification of Risk Management models.
• Comparison if the models forecast VaR with the
  actual outcome - PL.
• Exception occurs when actual loss exceeds VaR.
• After exception - explanation and action.

54
Backtesting
OK increasing k intervention

• Green zone - up to 4 exceptions
• Yellow zone - 5-9 exceptions
• Red zone - 10 exceptions or more

55
Stress

• Designed to estimate potential losses in abnormal
  markets.
• Extreme events
• Fat tails
• Central questions
• How much we can lose in a certain scenario?
• What event could cause a big loss?

56
Unifying Approach

• One number
• Based on Statistics
• Portfolio Theory
• Verification
• Widely Accepted
• Easy Comparison

57
Board of Directors(Basle, September 1998)

• periodic discussions with management concerning
  the effectiveness of the internal control system
• a timely review of evaluations of internal
  controls made by management, internal and
  external auditors
• periodic efforts to ensure that management has
  promptly followed up on recommendations and
  concerns expressed by auditors and supervisory
  authorities on internal control weaknesses
• a periodic review of the appropriateness of the
  banks strategy and risk limits.

58
Open Questions

• Risks related to cashflow
• Non-traded assets
• Credit information
• Global Database
• Liquidity problem

59
Issues Specific to Israel

• Indexation
• Exchange Band
• Shallow Markets