may-00 risk management zvi wiener 02-588-3049 mswiener/zvi.html value-at-risk (var)
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May-00 Risk Management
Zvi Wiener
02-588-3049http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Value-at-Risk (VaR)
May-2000 slide 2VaR
Risk
Business Risk
Financial Risk
– market risk
– credit risk
– liquidity risk
Operational Risk
Legal Risk
May-2000 slide 3VaR
How much can we lose?
Everything
correct, but useless answer.
How much can we lose realistically?
May-2000 slide 4VaR
Derivatives 1993-1995
($ million)Shova Shell, Japan 1,580Kashima Oil, Japan 1,450Metallgesellschaft 1,340Barings, U.K. 1,330Codelco, Chile 200Procter & Gamble, US 157
May-2000 slide 5VaR
Barings
February 26, 1995
233 year old bank
28 year old Nick Leeson
$1,300,000,000 loss
bought by ING for $1.5
May-2000 slide 6VaR
Public Funds
($ million) Orange County 1,640 San Diego 357 West Virginia 279 Florida State Treasury 200 Cuyahoga County 137 Texas State 55
May-2000 slide 7VaR
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
May-2000 slide 8VaR
Barings $1.3B Bank Negara, Malaysia 92 $3B Banesto, Spain $4.7B Credit Lyonnais $10B S&L, U.S.A. $150B Japan $500B
Financial Losses
May-2000 slide 9VaR
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
May-2000 slide 10VaR
May-2000 slide 11VaR
What is the current Risk?
duration, convexity
volatility
delta, gamma, vega
rating
target zone
Bonds Stocks Options Credit Forex Total ?
May-2000 slide 12VaR
Standard Approach
May-2000 slide 13VaR
Modern Approach
Financial Institution
May-2000 slide 14VaR
Risk Management
Risk measurement
Reporting to board
Limits monitoring
Diversification, reinsurance
Vetting
Reporting to regulators
Decision making based on risk
May-2000 slide 15VaR
Who manages risk?
Citibank
Bank of England
CIBC
J. P. Morgan
Bankers Trust
AIG
General Re
Swiss Re
Aetna
Zurich
Nike
Sony
Dell Computers
Philip Morris
Ford Motor
May-2000 slide 16VaR
Regulators
BIS
FSA
SEC
ISDA
FASB
Bank of Israel
Galai’s committee
May-2000 slide 17VaR
Basic Steps in RM process
Identify risks
Data base (market + position)
Risk measurement
Regulators
Risk Management
Reporting
Strategic decisions
May-2000 slide 18VaR
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
May-2000 slide 19VaR
Risk Management and
Risk Measurement
May-2000 slide 20VaR
Risk Management System 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
Can NOT
May-2000 slide 21VaR
Tool, not rule!
May-2000 slide 22VaR
Definition
VaR is defined as the predicted worst-case
loss at a specific confidence level (e.g. 99%)
over a certain period of time.
May-2000 slide 23VaR
-3 -2 -1 1 2 3
0.2
0.4
0.6
0.8
1
Profit/Loss
VaR
1% VaR1%
May-2000 slide 24VaR
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,
1%VaR
under normal market conditions.
May-2000 slide 25VaR
History of VaR
80’s - 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!
May-2000 slide 26VaR
Risk Management Structure
Market data Current position
Risk Mapping
Valuation
Value-at-Risk
Reporting and Risk Management
May-2000 slide 27VaR
1011
1213
14 4.1
4.15
4.2
4.25
4.3
7.257.5
7.758
8.25
1011
1213
14
interest rates and dollar areNOT independent
Value
Interest Ratedollar
May-2000 slide 28VaR
Risk Measuring Software CATS, CARMA Algorithmics, Risk Watch Infinity J.P. Morgan, FourFifteen FEA, Outlook Reuters, Sailfish Kamacura Bankers Trust, RAROC INSSINC, Orchestra
May-2000 slide 29VaR
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
May-2000 slide 30VaR
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
May-2000 slide 31VaR
Types of Assets and Risks
Real projects - cashflow versus financing
Fixed Income
Optionality
Credit exposure
Legal, operational, authorities
May-2000 slide 32VaR
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
May-2000 slide 33VaR
How to measure VaR
Historical Simulations
Variance-Covariance
Monte Carlo
Analytical Methods
May-2000 slide 34VaR
Historical Simulations
Fix current portfolio.
Pretend that market changes are
similar to those observed in the past.
Calculate P&L (profit-loss).
Find the lowest quantile.
May-2000 slide 35VaR
Example
4.00
4.20
4.20
4.10
4.15
Assume we have $1 and our main currency is SHEKEL. Today $1=4.30.
Historical data:
4.30*4.20/4.00 = 4.515
4.30*4.20/4.20 = 4.30
4.10*4.10/4.20 = 4.198
4.15*4.15/4.10 = 4.352
P&L
0.215
0
-0.112
0.052
May-2000 slide 36VaR
432 )063.01(
20
)062.01(
300
)061.01(
200
06.01
100
432 )13.01(
30
)12.01(
20
)11.01(
100
1.01
120
today
USD NIS
2000 100 -120
2001 200 100
2002 -300 -20
2003 20 30
May-2000 slide 37VaR
today
432 )073.01(
20
)072.01(
300
)071.01(
200
07.01
100
432 )12.01(
30
)11.01(
20
)11.01(
100
11.01
120
Changesin IR
USD: +1% +1% +1% +1%NIS: +1% 0% -1% -1%
432 )063.01(
20
)062.01(
300
)061.01(
200
06.01
100
432 )13.01(
30
)12.01(
20
)11.01(
100
1.01
120
May-2000 slide 38VaR
Returns
year
1% of worst cases
May-2000 slide 39VaR
-3 -2 -1 1 2 3
0.2
0.4
0.6
0.8
1
Profit/Loss
VaR
1% VaR1%
May-2000 slide 40VaR
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.
May-2000 slide 41VaR
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!
May-2000 slide 42VaR
Variance-Covariance VVVaR 33.2%1
2.33
-2.33
1%
May-2000 slide 43VaR
Monte Carlo
-1 -0.5 0.5 1
-1
-0.5
0.5
1
May-2000 slide 44VaR
Monte Carlo
Distribution of market factors
Simulation of a large number of events
P&L for each scenario
Order the results
VaR = lowest quantile
May-2000 slide 45VaR
Monte Carlo Simulation
10 20 30 40
-15
-10
-5
5
10
15
May-2000 slide 46VaR
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.
May-2000 slide 47VaR
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.
May-2000 slide 48VaR
Airline company
fuel - oil prices and $ purchasing airplanes - $ and Euro salaries - NIS, some $ tickets $ marketing - different currencies payments to airports for services
May-2000 slide 49VaR
Airline company
loans
equity
callable bonds
May-2000 slide 50VaR
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.
May-2000 slide 51VaR
Reporting
Division of VaR by business units, areas of
activity, counterparty, currency.
Performance measurement - RAROC (Risk
Adjusted Return On Capital).
May-2000 slide 52VaR
How VaR is used
Internal Risk Management
Reporting
Regulators
May-2000 slide 53VaR
Backtesting
Verification of Risk Management models.
Comparison if the model’s forecast VaR with
the actual outcome - P&L.
Exception occurs when actual loss exceeds
VaR.After exception - explanation and action.
May-2000 slide 54VaR
Backtesting
Green zone - up to 4 exceptions
Yellow zone - 5-9 exceptions
Red zone - 10 exceptions or more
OK
increasing k
intervention
May-2000 slide 55VaR
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?
May-2000 slide 56VaR
Unifying Approach
One number
Based on Statistics
Portfolio Theory
Verification
Widely Accepted
Easy Comparison
May-2000 slide 57VaR
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 bank’s strategy and risk limits.
May-2000 slide 58VaR
Open Questions
Risks related to cashflow
Non-traded assets
Credit information
Global Database
Liquidity problem
May-2000 slide 59VaR
Issues Specific to Israel
Indexation
Exchange Band
Shallow Markets
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