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Value-at-Risk (Va. R) Zvi Wiener 02 -588 -3049 http: //pluto. mscc. huji. ac. il/~mswiener/zvi. Value-at-Risk (Va. R) Zvi Wiener 02 -588 -3049 http: //pluto. mscc. huji. ac. il/~mswiener/zvi. html FRM 5

Risk • Business Risk • Financial Risk • market risk • credit risk • Risk • Business Risk • Financial Risk • market risk • credit risk • liquidity risk • Operational Risk • Legal Risk Zvi Wiener FRM 5 -Va. R 2

How much can we lose? Everything correct, but useless answer. How much can we How much can we lose? Everything correct, but useless answer. How much can we lose realistically? Zvi Wiener FRM 5 -Va. R 3

What is the current Risk? • Bonds • Stocks • Options • Credit • What is the current Risk? • Bonds • Stocks • Options • Credit • Forex • Total Zvi Wiener duration, convexity volatility delta, gamma, vega rating target zone ? FRM 5 -Va. R 4

Standard Approach Zvi Wiener FRM 5 -Va. R 5 Standard Approach Zvi Wiener FRM 5 -Va. R 5

Modern Approach Financial Institution Zvi Wiener FRM 5 -Va. R 6 Modern Approach Financial Institution Zvi Wiener FRM 5 -Va. R 6

Definition Va. R is defined as the predicted worst-case loss at a specific confidence Definition Va. R is defined as the predicted worst-case loss at a specific confidence level (e. g. 99%) over a certain period of time. Zvi Wiener FRM 5 -Va. R 7

Va. R 1% Profit/Loss Zvi Wiener FRM 5 -Va. R 8 Va. R 1% Profit/Loss Zvi Wiener FRM 5 -Va. R 8

Meaning of Va. R A portfolio manager has a daily Va. R equal $1 Meaning of Va. R A portfolio manager has a daily Va. R equal $1 M at 99% confidence level. This means that there is only one chance in 100 that a daily loss bigger than $1 M occurs, under normal market conditions. Va. R 1% Zvi Wiener 9

Main Ideas • A few well known risk factors • Historical data + economic Main Ideas • A few well known risk factors • Historical data + economic views • Diversification effects • Testability • Easy to communicate Zvi Wiener FRM 5 -Va. R 10

History of Va. R • 80’s - major US banks - proprietary • 93 History of Va. R • 80’s - major US banks - proprietary • 93 G-30 recommendations • 94 - Risk. Metrics by J. P. Morgan • 98 - Basel • SEC, FSA, ISDA, pension funds, dealers • Widely used and misused! Zvi Wiener FRM 5 -Va. R 11

Risk Management Structure Market data Current position Risk Mapping Valuation Value-at-Risk Reporting and Risk Risk Management Structure Market data Current position Risk Mapping Valuation Value-at-Risk Reporting and Risk Management Zvi Wiener FRM 5 -Va. R 12

Value Interest Rate dollar interest rates and dollar are NOT independent Zvi Wiener FRM Value Interest Rate dollar interest rates and dollar are NOT independent Zvi Wiener FRM 5 -Va. R 13

Risk Measuring Programs • CATS, CARMA • Algorithmics, Risk Watch • Infinity • J. Risk Measuring Programs • CATS, CARMA • Algorithmics, Risk Watch • Infinity • J. P. Morgan, Four. Fifteen • FEA, Outlook • Reuters, Sailfish • Theoretics, TARGA • Bankers Trust, RAROC • INSSINC, Orchestra Zvi Wiener FRM 5 -Va. R $400 K/yr >$1 M $25 K/yr $18 K ? $75 K $50 K/run $25 -75 K 14

Why Capital Requirements • Government Protection • Debt financing • In Israel this is Why Capital Requirements • Government Protection • Debt financing • In Israel this is not binding! • But it will be!! • Traded assets constitute a small portion • 339 -9, 339 -10 defines who must use Va. R Zvi Wiener FRM 5 -Va. R 15

Unifying Approach • One number • Based on Statistics • Portfolio Theory • Verification Unifying Approach • One number • Based on Statistics • Portfolio Theory • Verification • Widely Accepted • Easy Comparison Zvi Wiener FRM 5 -Va. R 16

Capital Requirements Minimal required capital Supervision factor, 3 k 4 Zvi Wiener FRM 5 Capital Requirements Minimal required capital Supervision factor, 3 k 4 Zvi Wiener FRM 5 -Va. R 17

Qualitative Requirements • An independent risk management unit • Board of directors involvement • Qualitative Requirements • An independent risk management unit • Board of directors involvement • Internal model as an integral part • Internal controller and risk model • Backtesting • Stress test Zvi Wiener FRM 5 -Va. R 18

Quantitative Requirements • 99% confidence interval • 10 business days horizon • At least Quantitative Requirements • 99% confidence interval • 10 business days horizon • At least one year of historic data • Data base revised at least every quarter • All types of risk exposure • Derivatives Zvi Wiener FRM 5 -Va. R 19

Types of Assets and Risks • Real projects - cashflow versus financing • Fixed Types of Assets and Risks • Real projects - cashflow versus financing • Fixed Income • Optionality • Credit exposure • Legal, operational, authorities Zvi Wiener FRM 5 -Va. R 20

Risk Factors There are many bonds, stocks and currencies. The idea is to choose Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. • Exchange rates • Interest rates (for each maturity and indexation) • Spreads • Stock indices Zvi Wiener FRM 5 -Va. R 21

How to measure Va. R • Historical Simulations • Variance-Covariance • Monte Carlo • How to measure Va. R • Historical Simulations • Variance-Covariance • Monte Carlo • Analytical Methods • Parametric versus non-parametric approaches Zvi Wiener FRM 5 -Va. R 22

Historical Simulations • Fix current portfolio. • Pretend that market changes are similar to Historical Simulations • Fix current portfolio. • Pretend that market changes are similar to those observed in the past. • Calculate P&L (profit-loss). • Find the lowest quantile. Zvi Wiener FRM 5 -Va. R 23

Example Assume we have $1 and our main currency is SHEKEL. Today $1=4. 30. Example Assume we have $1 and our main currency is SHEKEL. Today $1=4. 30. Historical data: P&L 4. 00 4. 20 4. 30*4. 20/4. 00 = 4. 515 0. 215 4. 20 4. 30*4. 20/4. 20 = 4. 30 0 4. 10 4. 30*4. 10/4. 20 = 4. 198 -0. 112 4. 15 4. 30*4. 15/4. 10 = 4. 352 0. 052 Zvi Wiener FRM 5 -Va. R 24

USD NIS 2000 100 -120 2001 200 100 2002 -300 -20 2003 20 30 USD NIS 2000 100 -120 2001 200 100 2002 -300 -20 2003 20 30 today Zvi Wiener FRM 5 -Va. R 25

today Changes in IR Zvi Wiener USD: NIS: +1% +1% 0% FRM 5 -Va. today Changes in IR Zvi Wiener USD: NIS: +1% +1% 0% FRM 5 -Va. R +1% -1% 26

Returns year 1% of worst cases Zvi Wiener FRM 5 -Va. R 27 Returns year 1% of worst cases Zvi Wiener FRM 5 -Va. R 27

Va. R 1% Profit/Loss Zvi Wiener FRM 5 -Va. R 28 Va. R 1% Profit/Loss Zvi Wiener FRM 5 -Va. R 28

Variance Covariance • Means and covariances of market factors • Mean and standard deviation Variance Covariance • Means and covariances of market factors • Mean and standard deviation of the portfolio • Delta or Delta-Gamma approximation • Va. R 1%= P – 2. 33 P • Based on the normality assumption! Zvi Wiener FRM 5 -Va. R 29

Variance-Covariance 1% 2. 33 -2. 33 Zvi Wiener FRM 5 -Va. R 30 Variance-Covariance 1% 2. 33 -2. 33 Zvi Wiener FRM 5 -Va. R 30

Monte Carlo Zvi Wiener FRM 5 -Va. R 31 Monte Carlo Zvi Wiener FRM 5 -Va. R 31

Monte Carlo • Distribution of market factors • Simulation of a large number of Monte Carlo • Distribution of market factors • Simulation of a large number of events • P&L for each scenario • Order the results • Va. R = lowest quantile Zvi Wiener FRM 5 -Va. R 32

Monte Carlo Simulation Zvi Wiener FRM 5 -Va. R 33 Monte Carlo Simulation Zvi Wiener FRM 5 -Va. R 33

Weights Since old observations can be less relevant, there is a technique that assigns Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See Risk. Metrics Technical Document for details. Zvi Wiener FRM 5 -Va. R 34

Stock Portfolio • Single risk factor or multiple factors • Degree of diversification • Stock Portfolio • Single risk factor or multiple factors • Degree of diversification • Tracking error • Rare events Zvi Wiener FRM 5 -Va. R 35

Bond Portfolio • Duration • Convexity • Partial duration • Key rate duration • Bond Portfolio • Duration • Convexity • Partial duration • Key rate duration • OAS, OAD • Principal component analysis Zvi Wiener FRM 5 -Va. R 36

Options and other derivatives • Greeks • Full valuation • Credit and legal aspects Options and other derivatives • Greeks • Full valuation • Credit and legal aspects • Collateral as a cushion • Hedging strategies • Liquidity aspects Zvi Wiener FRM 5 -Va. R 37

Credit Portfolio • rating, scoring • credit derivatives • reinsurance • probability of default Credit Portfolio • rating, scoring • credit derivatives • reinsurance • probability of default • recovery ratio Zvi Wiener FRM 5 -Va. R 38

Reporting Division of Va. R by business units, areas of activity, counterparty, currency. Performance Reporting Division of Va. R by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital). Zvi Wiener FRM 5 -Va. R 39

How Va. R is used • Internal Risk Management • Reporting • Regulators Zvi How Va. R is used • Internal Risk Management • Reporting • Regulators Zvi Wiener FRM 5 -Va. R 40

Backtesting Verification of Risk Management models. Comparison if the model’s forecast Va. R with Backtesting Verification of Risk Management models. Comparison if the model’s forecast Va. R with the actual outcome - P&L. Exception occurs when actual loss exceeds Va. R. After exception - explanation and action. Zvi Wiener FRM 5 -Va. R 41

Backtesting Green zone - up to 4 exceptions OK Yellow zone - 5 -9 Backtesting Green zone - up to 4 exceptions OK Yellow zone - 5 -9 exceptions increasing k Red zone - 10 exceptions or more intervention Zvi Wiener FRM 5 -Va. R 42

Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss? Zvi Wiener FRM 5 -Va. R 43

Risk Management • Risk measurement • Reporting to board • Limits monitoring • Diversification, Risk Management • Risk measurement • Reporting to board • Limits monitoring • Diversification, reinsurance • Vetting • Reporting to regulators • Decision making based on risk Zvi Wiener FRM 5 -Va. R 44

Tool, not rule! Zvi Wiener FRM 5 -Va. R 45 Tool, not rule! Zvi Wiener FRM 5 -Va. R 45

pluto. mscc. huji. ac. il/~mswiener/ Risk Management resources • Useful Internet sites • Regulators pluto. mscc. huji. ac. il/~mswiener/ Risk Management resources • Useful Internet sites • Regulators • Insurance Companies • Risk Management in SEC reports Zvi Wiener FRM 5 -Va. R 46

How to hedge financial risk? • Static hedge Forwards agreements that fix the price How to hedge financial risk? • Static hedge Forwards agreements that fix the price Futures Options static hedge • Dynamic delta or vega hedge, with a variable amount of options held. It is applicable if there is a very liquid market and low transaction costs. Zvi Wiener FRM 5 -Va. R 47

RMG • http: //www. riskmetrics. com/ • http: //www. pictureofrisk. com/ • http: //www. RMG • http: //www. riskmetrics. com/ • http: //www. pictureofrisk. com/ • http: //www. riskmetrics. com/rm/splash. html • rmgaccess Zvi Wiener FRM 5 -Va. R 48

Who manages risk? Citibank AIG Nike Bank of England General Re Sony CIBC Swiss Who manages risk? Citibank AIG Nike Bank of England General Re Sony CIBC Swiss Re Dell Computers J. P. Morgan Aetna Philip Morris Bankers Trust Zurich Ford Motor Zvi Wiener FRM 5 -Va. R 49

Consulting • Oliver, Wyman and Co. • Willis Corroon • Richard Scora • Ernst Consulting • Oliver, Wyman and Co. • Willis Corroon • Richard Scora • Ernst and Young • Enterprise Advisors • Kamakura Zvi Wiener FRM 5 -Va. R 50

Examples of Risk Reports http: //www. pictureofrisk. com http: //www. mbrm. com/ http: //www. Examples of Risk Reports http: //www. pictureofrisk. com http: //www. mbrm. com/ http: //www. riskmetrics. com/rm/splash. html Zvi Wiener FRM 5 -Va. R 51

Real Projects Most daily returns are invisible. Proper financing should be based on risk Real Projects Most daily returns are invisible. Proper financing should be based on risk exposure of each specific project. Note that accounting standards not always reflect financial risk properly. Zvi Wiener FRM 5 -Va. R 52

Example • You are going to invest in Japan. • Take a loan in Example • You are going to invest in Japan. • Take a loan in Yen. • Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. • Actually there is no currency risk. Zvi Wiener FRM 5 -Va. R 53

Airline company • fuel - oil prices and $ • purchasing airplanes - $ Airline company • fuel - oil prices and $ • purchasing airplanes - $ and Euro • salaries - NIS, some $ • tickets $ • marketing - different currencies • payments to airports for services Zvi Wiener FRM 5 -Va. R 54

Airline company • loans • equity • callable bonds Zvi Wiener FRM 5 -Va. Airline company • loans • equity • callable bonds Zvi Wiener FRM 5 -Va. R 55

Airline company Base currency - by major stockholder. Time horizon - by time of Airline company Base currency - by major stockholder. Time horizon - by time of possible price change. Earnings at risk, not value at risk, since there is too much optionality in setting prices. One can create a one year cashflow forecast and measure its sensitivity to different market events. Zvi Wiener FRM 5 -Va. R 56

Issues Specific to Israel • Indexation • Exchange Band • Shallow Markets Zvi Wiener Issues Specific to Israel • Indexation • Exchange Band • Shallow Markets Zvi Wiener FRM 5 -Va. R 57

Home assignment • Calculate your personal Va. R Zvi Wiener FRM 5 -Va. R Home assignment • Calculate your personal Va. R Zvi Wiener FRM 5 -Va. R 58