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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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
5
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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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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Value
dollar
Interest Rate
interest rates and dollar are NOT independent
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Regulation of Financial Intermediaries

• take deposits, give loans
• very small equity capital, big leverage
• FDIC, CDIC, Israel - implicit
• domino effect
• Minimal capital requirements (8-9)

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Banks

• major increase of off-balance sheet in 80s
• 1988 Basle accord (88 BIS Accord) -
  international minimum capital guidelines (credit
  risk).
• 1996 Amendment - market risk VaR.
• Amendment BIS 98

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Accord Amendment

• assets to capital ? 20
• eligible capital/risk weighted assets ? 8
• minimal capital charge for market risk
• concentration risk
• positions of 10 must be reported
• positions of 25 need special permission

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Accord Amendment

• regulators encourage banks to develop models.
• Banks must implement a RM infrastructure in
  their daily RM - limits, monitoring, etc.
• G-30 report, 1993.

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G-30 policy recommendations

• The Role of senior management
• Marking to market
• Market valuation methods
• Identifying revenue sources
• Measuring market risk (VaR)
• Stress simulation
• Investing and funding forecasts

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G-30 policy recommendations

• Independent risk management
• Practices by end-user
• Measuring credit exposure
• Master agreements
• Credit enhancements
• Promoting enforceability
• Professional expertise

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G-30 policy recommendations

• Systems
• Authority
• Accounting practices
• Disclosures
• Recognizing netting
• Legal and regulatory uncertainty
• Tax treatment
• Accounting standards

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1988 BIS Accord

• Developed by Basle committee
• Accepted by G-10 Belgium, Canada, France,
  Germany, Italy, Japan, Netherlands, Sweden, UK,
  USA.
• minimum asset to capital multiple
• risk based capital ratio

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1988 BIS Accord

• risk based capital ratio - solvency ratio (Cooke
  ratio).
• Capital divided by risk weighted on-balance-sheet
  assets plus off-balance-sheet exposures.
• Weights are based on credit risk.
• No netting or portfolio effects!
• No market risk.

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1988 BIS Accord

• The Assets-to-capital multiple ? 20
• Banks total assets divided by its total capital.
• Some off-balance-sheet items, like letters of
  credit are accounted at nominal.

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Weights in Cooke ratio

• On-balance-sheet items
• 0 Cash, gold, OECD government
• claims, insured mortgages.
• 20 OECD banks, OECD public sector
• entities.
• 50 Uninsured residential mortgages.
• 100 All other claims.

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Cooke ratio

• Off-balance-sheet credit equivalent.
• 1. Nonderivative exposure - conversion factor is
  set by regulators between 0 and 1.
• 2. Derivative exposure Current replacement cost
  Add-on amount

Risk weighted amount ?AssetsW?Credit
equivalentW
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Cooke ratio

• Banks are required to maintain capital equal to
  at least 8 of their total risk weighted assets.
  (In Israel 9.)

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Capital

• Tier 1. Stock equity, preferred stock, minority
  equity interest in consolidated subsidiaries,
  less goodwill and other deductions.
• Tier 2. Cumulative perpetual preferred shares,
  99 year debentures, some subordinated debt (?5y).
• Tier 3. Can be used to cover market risk only.
  Short term subordinated debt (?2y).
• Tier 1 Tier 2 ? 8, and Tier 1 must be at
  least 50 of this amount.

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Models

• Standard model.
• Internal models (based on VaR).
• (3marketVaR10d 4creditVaR10d)trigger/8
• trigger 8 in North America and between 8 and 25
  in the UK

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Problems with the current approach

• No distinction between a loan of 100 and 100
  loans of 1 each one.
• Turkish bank has lower capital requirements than
  General Electric.
• A loan to AA rated firm is treated as a loan to
  a B rated firm.
• Some similar contracts are treated differently.

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New proposals

• BIS 2000
• VaR based approach to credit risk.
• CreditMetrics
• CreditRisk
• KMV
• Merton.

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New Approach

• Three pillars
• A. Minimum Capital Requirement
• B. Supervisory Review Process
• C. Market Discipline Requirements

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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