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Financial Risk Management. Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html. Risk. Business Risk Operational Risk Financial Risk credit risk market risk liquidity risk Legal Risk. Crouhy, Galai, Mark, Risk Management, McGraw Hill, 2000.

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financial risk management

Financial Risk Management

Zvi Wiener

02-588-3049

http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

slide2
Risk
  • Business Risk
  • Operational Risk
  • Financial Risk
    • credit risk
    • market risk
    • liquidity risk
  • Legal Risk

FRM-1

slide3
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
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
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
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
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
Financial Losses
  • Barings $1.3B
  • Bank Negara, Malaysia 92 $3B
  • Banesto, Spain $4.7B
  • Credit Lyonnais $10B
  • S&L, U.S.A. $150B
  • Japan $500B

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metallgesellshaft
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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basic statistics
Basic Statistics
  • Certainty and uncertainty
  • Probabilities, distribution, PDF, CDF
  • Mean, variance
  • Multivariable distributions
  • Covariance, correlation, beta
  • Quantile

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slide13

A 100 km. B

100 km/hr

50 km/hr

1 – 100 2 – 50 3 – 50

(100+50+50)/3 = 66.67 km/hr.

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slide14
1. +40%

2. +10%

3. -50%

4. +20%

1. -2%

2. +1%

3. -1%

4. +1%

0.98*1.01*0.99*1.01 =

0.9897

1.4*1.1*0.5*1.2 =

0.924

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probabilities
Probabilities

Certainty

Uncertainty

Probabilities

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probabilities1
Probabilities

Mean

Variance

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probabilities2

30%

30%

10%

10%

20%

Probabilities

0.3

0.2

0.1

1 2 3 4 5

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probabilities3
Probabilities

0.3

0.2

0.1

1 2 3 4 5

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sample estimates
Sample Estimates

Sometimes one can use weights

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slide24

Normal Distribution

1%

quantile

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covariance
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
Correlation

-1    1

 = 0 independent

 = 1 perfectly positively correlated

 = -1 perfectly negatively correlated

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time aggregation
Time Aggregation

Assuming normality

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time aggregation1
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

A

rf

B

Portfolio

2(A+B) = 2(A) + 2(B) + 2(A)(B)

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slide32

¥$£

£¥

$¥

£$¥

$£¥

£$

£

$

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slide33

2

12

John Zerolis

"Triangulating Risk",

Risk v.9 n.12, Dec. 1996

1

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useful books
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

0.125

0.25

0.5

0.375

0.5

0.5

0.375

0.25

0.125

Binomial Tree

1.0

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example
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
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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example1
Example

If there is a pair of dice the mean is doubled.

What is the probability to gain $5?

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example2
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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example3
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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slide42

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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slide43

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 11
Example 1

-2 -1 0 1 2 3

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example 12
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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slide46
P&L

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

61 2 3 4 5 6

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breakfast

$4

$2

Breakfast

50% 50%

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lunch

$11

$5

Lunch

50% 50%

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slide52

Breakfast

$2 $4

$5 $7 $9 $11 $13 $15

50%

50%

Lunch

50% 50%

 = $11  = ??

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correlation 1

 = $11  = $4

Correlation =+1

Breakfast

$2 $4

$5 $7 $9

$11 $13 $15

50%

50%

Lunch

50% 50%

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correlation 11

 = $11  = $2

Correlation =-1

Breakfast

$2 $4

$5 $7 $9

$11 $13 $15

50%

50%

Lunch

50% 50%

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correlation 0

 = $11  = $3.16

Correlation =0

Breakfast

$2 $4

$5 $7$9

$11 $13$15

50%

50%

Lunch

50% 50%

FRM-1

how much can we lose
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

What is the current Risk?
  • Bonds
  • Stocks
  • Options
  • Credit
  • Forex
  • Total ?

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modern approach
Modern Approach

Financial Institution

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slide60

Value

dollar

Interest Rate

interest rates and dollar are

NOT independent

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