FRM Zvi Wiener 02-588-3049 mswiener/zvi.html Financial Risk Management.

FRM

Zvi Wiener

02-588-3049http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

Financial Risk Management

Zvi Wiener FRM-2 slide 2


Lunch

Breakfast

$2 $4

$5 $7 $9

$11 $13 $15

50% 50%

= $11 = ??

50%

50%


Correlation =+1

$2 $4

$5 $7 $9

$11 $13 $15

Lunch

Breakfast

50%

50%

= $11 = $4

50% 50%


Correlation =-1

$2 $4

$5 $7 $9

$11 $13 $15Lunch

Breakfast

50%

50%

= $11 = $2

50% 50%


Correlation =0

$2 $4

$5 $7 $9

$11 $13 $15Lunch

Breakfast

50%

50%

= $11 = $3.16

50% 50%


Example

We will receive n dollars where n is determined by a die.

What would be a fair price for participation in this game?


Example 1

Score Probability

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

6 1/6

5.36

6

6

5

6

4

6

3

6

2

6

1

Fair price is 3.5 NIS.

Assume that we can play

the game for 3 NIS only.


Example

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

What is the probability to gain $5?


Example

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

All combinations:

36 combinations with equal probabilities


Example

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

All combinations:

4 out of 36 give $5, probability = 1/9


All combinations:


Additional information:the first die gives 4.

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


Example 1

-2 -1 0 1 2 3

%67.166

1


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


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

6 1 2 3 4 5 6


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

0.025

0.05

0.075

0.1

0.125

0.15

Example 1 (2 cubes)


-10-9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9101112131415

0.02

0.04

0.06

0.08

0.1

Example 1 (5 cubes)


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


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%)


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


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


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.


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


G-30 policy recommendations

• Independent risk management

• Practices by end-user

• Measuring credit exposure

• Master agreements

• Credit enhancements

• Promoting enforceability

• Professional expertise


G-30 policy recommendations• Systems

• Authority

• Accounting practices

• Disclosures

• Recognizing netting

• Legal and regulatory uncertainty

• Tax treatment

• Accounting standards


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


1988 BIS Accordrisk 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.


1988 BIS AccordThe Assets-to-capital multiple 20

Bank’s total assets divided by its total capital.

Some off-balance-sheet items, like letters of credit are accounted at nominal.


Weights in Cooke ratioOn-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.


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 =

Assets*W+Credit equivalent*W


Cooke ratio

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


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.


Models

• Standard model.

• Internal models (based on VaR).

(3*marketVaR10d +4*creditVaR10d)*trigger/8

trigger = 8 in North America and between 8 and 25 in the UK


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.


New proposals

• BIS 2000

• VaR based approach to credit risk. CreditMetrics

CreditRisk+

KMV

Merton.


New Approach

Three pillars

A. Minimum Capital Requirement

B. Supervisory Review Process

C. Market Discipline Requirements


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

FRM Zvi Wiener 02-588-3049 mswiener/zvi.html Financial Risk Management.

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