Financial Risk Management Zvi Wiener 02 588 3049

Financial Risk Management Zvi Wiener 02 -588 -3049 http: //pluto. mscc. huji. ac. il/~mswiener/zvi. html FRM

Zvi Wiener FRM-2 2

Breakfast Lunch $2 $4 $5 $7 $9 50% $11 $13 $15 50% = $11 Zvi Wiener FRM-2 50% = ? ? 3

Correlation =+1 Breakfast Lunch $5 $11 $2 $4 $7 $9 $13 $15 50% = $11 Zvi Wiener FRM-2 50% = $4 4

Correlation =-1 Breakfast $2 $4 $5 $7 $9 50% $11 $13 $15 50% 50% Lunch = $11 Zvi Wiener FRM-2 = $2 5

Correlation =0 Breakfast $2 $4 $5 $7 $9 50% $11 $13 $15 50% 50% Lunch = $11 Zvi Wiener FRM-2 = $3. 16 6

Example We will receive n dollars where n is determined by a die. What would be a fair price for participation in this game? Zvi Wiener FRM-2 7

Example 1 Score 1 2 3 4 5 6 Probability 1/6 1/6 1/6 Fair price is 3. 5 NIS. 1/6 Assume that we can play the game for 3 NIS only. Zvi Wiener FRM-2 8

Example If there is a pair of dice the mean is doubled. What is the probability to gain $5? Zvi Wiener FRM-2 9

Example All combinations: 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 36 combinations with equal probabilities Zvi Wiener FRM-2 10

Example All combinations: 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 4 out of 36 give $5, probability = 1/9 Zvi Wiener FRM-2 11

Additional information: the first die gives 4. All combinations: 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 1 out of 9 give $5, probability = 1/9 Zvi Wiener FRM-2 12

Additional information: the first die gives 4. All combinations: 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 4 out of 24 give $5, probability = 1/6 Zvi Wiener FRM-2 13

Example 1 -2 Zvi Wiener -1 0 FRM-2 1 2 3 14

Example 1 1 2 3 4 5 6 Zvi Wiener 1 2 3 4 5 6 7 8 9 10 FRM-2 5 6 7 8 9 10 11 12 we pay 6 NIS. 15

P&L 1 2 3 4 5 6 Zvi Wiener 1 -4 -3 -2 -1 0 1 2 3 4 FRM-2 5 0 1 2 3 4 5 6 16

Example 1 (2 cubes) Zvi Wiener FRM-2 17

Example 1 (5 cubes) Zvi Wiener FRM-2 18

Value Interest Rate dollar interest rates and dollar are NOT independent Zvi Wiener FRM-2 19

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%) Zvi Wiener FRM-2 20

Banks • major increase of off-balance sheet in 80 s • 1988 Basle accord (88 BIS Accord) international minimum capital guidelines (credit risk). • 1996 Amendment - market risk + Va. R. • Amendment = BIS 98 Zvi Wiener FRM-2 21

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 Zvi Wiener FRM-2 22

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. Zvi Wiener FRM-2 23

G-30 policy recommendations • The Role of senior management • Marking to market • Market valuation methods • Identifying revenue sources • Measuring market risk (Va. R) • Stress simulation • Investing and funding forecasts Zvi Wiener FRM-2 24

G-30 policy recommendations • Independent risk management • Practices by end-user • Measuring credit exposure • Master agreements • Credit enhancements • Promoting enforceability • Professional expertise Zvi Wiener FRM-2 25

G-30 policy recommendations • Systems • Authority • Accounting practices • Disclosures • Recognizing netting • Legal and regulatory uncertainty • Tax treatment • Accounting standards Zvi Wiener FRM-2 26

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 Zvi Wiener FRM-2 27

1988 BIS Accord risk based capital ratio - solvency ratio (Cooke ratio). Capital divided by risk weighted onbalance-sheet assets plus off-balancesheet exposures. Weights are based on credit risk. No netting or portfolio effects! No market risk. Zvi Wiener FRM-2 28

1988 BIS Accord The 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. Zvi Wiener FRM-2 29

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. Zvi Wiener FRM-2 30

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 Zvi Wiener FRM-2 31

Cooke ratio • Banks are required to maintain capital equal to at least 8% of their total risk weighted assets. (In Israel 9%. ) Zvi Wiener FRM-2 32

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 ( 5 y). • Tier 3. Can be used to cover market risk only. Short term subordinated debt ( 2 y). • Tier 1 + Tier 2 8%, and Tier 1 must be at least 50% of this amount. Zvi Wiener FRM-2 33

Models • Standard model. • Internal models (based on Va. R). (3*market. Va. R 10 d +4*credit. Va. R 10 d)*trigger/8 trigger = 8 in North America and between 8 and 25 in the UK Zvi Wiener FRM-2 34

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. Zvi Wiener FRM-2 35

New proposals • BIS 2000 • Va. R based approach to credit risk. § Credit. Metrics §Credit. Risk+ § KMV § Merton. Zvi Wiener FRM-2 36

New Approach Three pillars A. Minimum Capital Requirement B. Supervisory Review Process C. Market Discipline Requirements Zvi Wiener FRM-2 37

What is the current Risk? • Bonds • Stocks • Options • Credit • Forex • Total Zvi Wiener duration, convexity volatility delta, gamma, vega rating target zone ? FRM-2 38

Standard Approach Zvi Wiener FRM-2 39

Modern Approach Financial Institution Zvi Wiener FRM-2 40