Zvi Wiener

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Financial Risk Management

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

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Risk

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

3

• Crouhy, Galai, Mark, Risk Management, McGraw
  Hill, 2000.
• Golub, Tilman, Risk Management Approaches for
  Fixed Income Markets, Wiley, 2000.
• Jorion, Value at Risk, McGraw Hill, 1997.
• http//www.gloriamundi.org
• http//www.riskmetrics.com
• http//www.bis.org
• http//www.garp.com

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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

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Barings

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

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Public Funds

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

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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

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Financial Losses

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

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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

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Risk Management andRisk Measurement
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Basic Statistics

• Certainty and uncertainty
• Probabilities, distribution, PDF, CDF
• Mean, variance
• Multivariable distributions
• Covariance, correlation, beta
• Quantile

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1 100 2 50 3 50
(1005050)/3 66.67 km/hr.
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• 1. 40
• 2. 10
• 3. -50
• 4. 20

• 1. -2
• 2. 1
• 3. -1
• 4. 1

1.41.10.51.2 0.924
0.981.010.991.01 0.9897
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Probabilities

• Certainty
• Uncertainty
• Probabilities

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Probabilities

• Mean
• Variance

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Probabilities
0.3
0.2
0.1
1 2 3 4 5
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Probabilities
0.3
0.2
0.1
1 2 3 4 5
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Probabilities
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Probabilities
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Sample Estimates
Sometimes one can use weights
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Normal Distribution N(?, ?)
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Normal Distribution N(?, ?)
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Normal Distribution
quantile
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Lognormal Distribution
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Covariance

• Shows how two random variables are connected
• For example
• independent
• move together
• move in opposite directions
• covariance(X,Y)

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Correlation

• -1 ? ? ? 1
• ? 0 independent
• ? 1 perfectly positively correlated
• ? -1 perfectly negatively correlated

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Properties
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Time Aggregation
Assuming normality
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Time Aggregation

• Assume that yearly parameters of CPI are
• mean 5, standard deviation (SD) 2.
• Then daily mean and SD of CPI changes are

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Portfolio

• ?2(AB) ?2(A) ?2(B) 2?(A)?(B)?

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?


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?12
?2
?
John Zerolis "Triangulating Risk", Risk v.9
n.12, Dec. 1996
?1
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Useful Books

• Duffie D., Dynamic Asset Pricing Theory.
• Duffie D., Security Markets, Stochastic Models.
• Shimko D. Finance in Continuous Time, A Primer.
  Kolb Publishing Company, 1992.

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Binomial Tree
1.0
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Example

• We will receive n dollars where n is determined
  by a die.
• What would be a fair price for participation in
  this game?

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Example 1

• Score Probability
• 1 1/6
• 2 1/6
• 3 1/6
• 4 1/6
• 5 1/6
• 6 1/6

Fair price is 3.5 NIS. Assume that we can
play the game for 3 NIS only.
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Example

• If there is a pair of dice the mean is doubled.
• What is the probability to gain 5?

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Example
All combinations

• 1,1 2,1 3,1 4,1 5,1 6,1
• 1,2 2,2 3,2 4,2 5,2 6,2
• 1,3 2,3 3,3 4,3 5,3 6,3
• 1,4 2,4 3,4 4,4 5,4 6,4
• 1,5 2,5 3,5 4,5 5,5 6,5
• 1,6 2,6 3,6 4,6 5,6 6,6

36 combinations with equal probabilities
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Example
All combinations

• 1,1 2,1 3,1 4,1 5,1 6,1
• 1,2 2,2 3,2 4,2 5,2 6,2
• 1,3 2,3 3,3 4,3 5,3 6,3
• 1,4 2,4 3,4 4,4 5,4 6,4
• 1,5 2,5 3,5 4,5 5,5 6,5
• 1,6 2,6 3,6 4,6 5,6 6,6

4 out of 36 give 5, probability 1/9
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Additional information the first die gives 4.
All combinations
1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,
3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5
2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6
1 out of 9 give 5, probability 1/9
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Additional information the first die gives ?4.
All combinations
1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,
3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5
2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6
4 out of 24 give 5, probability 1/6
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Example 1
-2 -1 0 1 2 3
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Example 1

• 1 2 3 4 5 6 we pay
• 1 2 3 4 5 6 7 6 NIS.
• 2 3 4 5 6 7 8
• 3 4 5 6 7 8 9
• 4 5 6 7 8 9 10
• 5 6 7 8 9 10 11
• 6 7 8 9 10 11 12

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PL

• 1 2 3 4 5 6
• 1 -4 -3 -2 -1 0 1
• 2 -3 -2 -1 0 1 2
• 3 -2 -1 0 1 2 3
• 4 -1 0 1 2 3 4
• 5 0 1 2 3 4 5
• 6 1 2 3 4 5 6

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Example 1 (2 cubes)
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Example 1 (5 cubes)
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Breakfast
50 50
50
Lunch
50 50
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Breakfast
2 4 5 7 9 11 13 15
50 50
Lunch
50 50
? 11 ? ??
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Correlation ?1
Breakfast

• 2 4
• 5 7 9
• 11 13 15

50 50
Lunch
50 50
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Correlation ?-1
Breakfast

• 2 4
• 5 7 9
• 11 13 15

50 50
Lunch
50 50
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Correlation ?0
Breakfast

• 2 4
• 5 7 9
• 11 13 15

50 50
Lunch
50 50
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How much can we lose?

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

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What is the current Risk?

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

• Bonds
• Stocks
• Options
• Credit
• Forex

• Total ?

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Standard Approach
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Modern Approach
Financial Institution
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Value
dollar
Interest Rate
interest rates and dollar are NOT independent