may-00 risk management zvi wiener 02-588-3049 mswiener/zvi.html value-at-risk (var)

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


What is the current Risk?

duration, convexity

volatility

delta, gamma, vega

rating

target zone

Bonds Stocks Options Credit Forex Total ?


Standard Approach


Modern Approach

Financial Institution


Risk Management

Risk measurement

Reporting to board

Limits monitoring

Diversification, reinsurance

Vetting

Reporting to regulators

Decision making based on risk


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


Regulators

BIS

FSA

SEC

ISDA

FASB

Bank of Israel

Galai’s committee


Basic Steps in RM process

Identify risks

Data base (market + position)

Risk measurement

Regulators

Risk Management

Reporting

Strategic decisions


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


Risk Management and

Risk Measurement


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


Tool, not rule!


Definition

VaR is defined as the predicted worst-case

loss at a specific confidence level (e.g. 99%)

over a certain period of time.


-3 -2 -1 1 2 3

0.2

0.4

0.6

0.8

1

Profit/Loss

VaR

1% VaR1%


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.


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!


Risk Management Structure

Market data Current position

Risk Mapping

Valuation

Value-at-Risk

Reporting and Risk Management


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


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


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


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


Types of Assets and Risks

Real projects - cashflow versus financing

Fixed Income

Optionality

Credit exposure

Legal, operational, authorities


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


How to measure VaR

Historical Simulations

Variance-Covariance

Monte Carlo

Analytical Methods


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.


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


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


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


Returns

year

1% of worst cases


-3 -2 -1 1 2 3

0.2

0.4

0.6

0.8

1

Profit/Loss

VaR

1% VaR1%


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.


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!


Variance-Covariance VVVaR 33.2%1

2.33

-2.33

1%


Monte Carlo

-1 -0.5 0.5 1

-1

-0.5

0.5

1


Monte Carlo

Distribution of market factors

Simulation of a large number of events

P&L for each scenario

Order the results

VaR = lowest quantile


Monte Carlo Simulation

10 20 30 40

-15

-10

-5

5

10

15


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.


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.


Airline company

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


Airline company

loans

equity

callable bonds


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.


Reporting

Division of VaR by business units, areas of

activity, counterparty, currency.

Performance measurement - RAROC (Risk

Adjusted Return On Capital).


How VaR is used

Internal Risk Management

Reporting

Regulators


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.


Backtesting

Green zone - up to 4 exceptions

Yellow zone - 5-9 exceptions

Red zone - 10 exceptions or more

OK

increasing k

intervention


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?


Unifying Approach

One number

Based on Statistics

Portfolio Theory

Verification

Widely Accepted

Easy Comparison


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.


Open Questions

Risks related to cashflow

Non-traded assets

Credit information

Global Database

Liquidity problem


Issues Specific to Israel

Indexation

Exchange Band

Shallow Markets

may-00 risk management zvi wiener 02-588-3049 mswiener/zvi.html value-at-risk (var)

Documents

loss f

f barings

barings f

employees f

future f

f codelco

metallgesellshaft f

event f