HUJI-03

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Financial Risk Management

• Zvi Wiener
• mswiener_at_mscc.huji.ac.il
• 02-588-3049

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Financial Risk Management

• Zvi Wiener
• Head of Finance Department
• The Hebrew University of Jerusalem
• 02-588-3049, mswiener_at_mscc.huji.ac.il

Arik Perez arikp_at_mof.gov.il tel. [phone],
02-531-7751
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Statistics

• Random variables
• Mean, Standard Deviation, Correlation
• Normal distribution

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Basic Corporate Finance

• NPV, IRR, YTM
• Assets, Liabilities
• Regulators, Bank of Israel, MOF
• ISDA, SEC

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Investments

• Stocks, Indices, ?, CAPM, ?
• Bonds, duration, convexity
• NIS, CPI linked
• callable, puttable, convertible
• Forwards, Futures, Swaps
• Options, ?
• European, American
• Call, Put, BS formula
• Markets prices, volatilites, LIBORs, swap rates

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Financial Risk Management

• Following P. Jorion, Value at Risk, McGraw-Hill
• Chapter 1
• The Need for Risk Management

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Financial Risks

• Risk is the volatility of unexpected outcomes.
• Business Risk
• Financial Risk
• Legal Risk
• Operational Risk

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Analytic Risk Management Tools

• Duration 1938
• Markowitz mean-variance 1952
• Sharpes CAPM 1963
• Multiple factor models 1966
• Black-Merton-Scholes model 1973
• RAROC 1983
• Limits by duration buckets 1986

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Analytic Risk Management Tools

• Risk-weighted assets (banks) 1988
• Stress Testing 1992
• Value-at-Risk, VaR 1993
• RiskMetrics 1994
• CreditMetrics 1997
• Integration of credit and market 1998-
• Enterprisewide RM 2000-

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Derivatives and Risk Management

• Stocks and bonds are securities issued to raise
  capital.
• Derivatives are contracts, agreements used for
  risk transfer.

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Financial Derivatives

• Futures, Forwards, Swaps
• Options
• European, American, Asian, Parisian
• Call, Put
• Cap, Floor
• Credit derivatives

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Types of Financial Risks

• Market Risk
• Credit Risk
• Liquidity Risk
• Operational Risk
• Legal Risk

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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
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Example

• You live in Herzliya and work in Tel-Aviv.
• When do you have to leave your home to be at work
  at 830?

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How much can we lose?

• Everything
• correct, but useless answer.
• How much can we lose realistically?

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Definition

• VaR is defined as the predicted worst-case loss
  at a specific confidence level (e.g. 99) over a
  certain period of time.

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Definition (Jorion)

• VaR is the worst loss over a target horizon with
  a given level of confidence.

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VaR
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Meaning of VaR

• A portfolio manager has a daily VaR equal 1M at
  99 confidence level.
• This means that there is only one chance in 100
  that a daily loss bigger than 1M occurs,

under normal market conditions.
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Returns
year
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Main Ideas

• A few well known risk factors
• Historical data economic views
• Diversification effects
• Testability
• Easy to communicate

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Conventional Analysis

Risk factor
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VaR approach

Risk factor
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Important

• VaR is a necessary, but not sufficient procedure
  for controlling risk.
• It must be supplemented by limits and controls,
  in addition to an independent risk-management
  function.
• Sound risk-management practices.

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Financial Risk Management

• Following P. Jorion, Value at Risk, McGraw-Hill
• Chapter 2
• Lessons from Financial Disasters

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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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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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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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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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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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Daiwa

• 12-th largest bank in Japan
• September 1995
• Hidden loss of 1.1B accumulated over 11 years
• Toshihide Igushi, trader in New York
• Had control of front and back offices
• In 92 and 93 FED warned Daiwa about bad
  management structure.

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Big Losses

• Bank Negara, Malaysia 3B 92
• Banesto (Spains 5th bank) 4.7B 93
• Credit Lyonnais 15B 94
• SL short deposits, long loans 150 80s
• Japan 550 90s

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Responses

• G-30 report
• DPG Derivatives Policy Group, risk.ifci.ch
• JPMorgans RiskMetrics www.riskmetrics.com
• GARP www.garp.com
• PRMIA www.prmia.org
• GAO General Accounting Office,
  www.gao.gov/reports.htm
• FASB FAS 133 www.fas133.com, FAS 107
• IASC, IAS 39 www.iasc.org.uk
• SEC Securities and Exchange Commission
• www.sec.gov/rules/final/33-7386.txt

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Financial Risk Management

• Following P. Jorion, Value at Risk, McGraw-Hill
• Chapter 3
• Regulatory Capital Standards with VaR

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Why regulation?

• Externalities
• Deposit insurance
• Moral hazard less incentives to control risk
• Basel Accord 1988
• measure of solvency Cooke ratio

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Cooke ratio

• The Basel Accord requires capital to be at least
  8 of the total risk-weighted assets of the bank.
• Capital definition is broad
• Tier 1. Stocks, reserves (retained earnings) (?
  50)
• Tier 2. Perpetual securities, undisclosed
  reserves, subordinated debt gt5 years.

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Weights Asset Type

• 0 Cash
• Claims on OECD central government
• local currency claims on central banks
• 20 Cash to be received
• OECD banks and regulated securities firms
• non-OECD banks below 1 year
• multilateral development banks
• foreign OECD public sector entities
• 50 residential mortgage loans

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Weights Asset Type

• 100 Claims on private sector (corp. debt,
  equity)
• Claims on non-OECD banks above 1 year
• Real estate
• Plant and equipment
• At national discretion
• 0-50 Claims on domestic OECD public-sector
  entities
• OECD (Organization for Economic Cooperation and
  Development) Austria, Belgium, Canada, Denmark,
  France, Germany, Greece, Iceland, Ireland, Italy,
  Luxembourg, The Netherlands, Norway, Portugal,
  Spain, Sweden, Switzerland, Turkey, UK, Japan,
  Finland, Australia, New Zealand, Mexico, Czech
  Republic, Hungary, Korea and Poland.

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Credit Risk Charge
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Activity Restrictions

• Restrictions on large risks (over 10 of capital)
• must be reported
• over 25 prohibited
• total of large risks can not exceed 8capital

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Criticism of 1988 Approach

• Regulatory arbitrage (securitization)
• Credit derivatives
• Inadequate differentiation of credit risks
• Non-recognition of term structure effect
• Non-recognition of risk mitigation
• Non-recognition of diversification
• Non-recognition of market risk

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Market Risk Amendment 1996

• Trading book financial instruments that
  intentionally held for short-term resale and are
  typically marked-to-market
• Banking book other instruments, like loans.
• TRC CRC MRC
• Tier 3 capital short-term subordinated debt
  (must be less than 2.5Tier1)

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The Standardized Model

• Maturity bands
• Partial netting
• Duration weights
• No diversification across risks

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The Internal Models Approach

• Quantitative parameters for VaR
• 10 business days or 2 weeks
• 99 confidence level
• at least one year of historical data updated at
  least quarterly
• Treatment of correlations can be recognized

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• 1 day can be scaled by square root of 10
• Typically average times k is used.
• k initially is set to 3, but later it can be
  increased
• Specific Risk Charge SRC is added.

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Basel Rules MRC

• Market Risk Charge MRC
• SRC - specific risk charge, k ?3.

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Backtesting

• Verification of Risk Management models.
• Comparison if the models forecast VaR with the
  actual outcome - PL.
• Exception occurs when actual loss exceeds VaR.
• After exception - explanation and action.

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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?

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Further development

• Basel II
• Better treatment of credit risk
• Operational risk

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Non banks

• Securities Firms
• Insurance companies
• Pension funds
• SEC reporting 7A in 10K
• ???? ???? ???? ????? ??????, ??? ?? ?????

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FRM-99, Question 89

• What is the correct interpretation of a 3
  overnight VaR figure with 99 confidence level?
• A. expect to lose at most 3 in 1 out of next 100
  days
• B. expect to lose at least 3 in 95 out of next
  100 days
• C. expect to lose at least 3 in 1 out of next
  100 days
• D. expect to lose at most 6 in 2 out of next 100
  days

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FRM-99, Question 89

• What is the correct interpretation of a 3
  overnight VaR figure with 99 confidence level?
• A. expect to lose at most 3 in 1 out of next 100
  days
• B. expect to lose at least 3 in 95 out of next
  100 days
• C. expect to lose at least 3 in 1 out of next
  100 days
• D. expect to lose at most 6 in 2 out of next 100
  days

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Properties of Risk Measure

• Monotonicity (XltY, R(X)gtR(Y))
• Translation invariance R(Xk) R(X)-k
• Homogeneity R(aX) a R(X) (liquidity??)
• Subadditivity R(XY) ? R(X) R(Y)
• the last property is violated by VaR!

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No subadditivity of VaR

• Bond has a face value of 100,000, during the
  target period there is a probability of 0.75
  that there will be a default (loss of 100,000).
• Note that VaR99 0 in this case.
• What is VaR99 of a position consisting of 2
  independent bonds?

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FRM-98, Question 22

• Consider arbitrary portfolios A and B and their
  combined portfolio C. Which of the following
  relationships always holds for VaRs of A, B, and
  C?
• A. VaRA VaRB VaRC
• B. VaRA VaRB ? VaRC
• C. VaRA VaRB ? VaRC
• D. None of the above

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FRM-98, Question 22

• Consider arbitrary portfolios A and B and their
  combined portfolio C. Which of the following
  relationships always holds for VaRs of A, B, and
  C?
• A. VaRA VaRB VaRC
• B. VaRA VaRB ? VaRC
• C. VaRA VaRB ? VaRC
• D. None of the above

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Confidence level

• low confidence leads to an imprecise result.
• For example 99.99 and 10 business days will
  require history of
• 10010010 100,000 days in order to have only 1
  point.

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Time horizon

• long time horizon can lead to an imprecise
  result.
• 1 - 10 days means that we will see such a loss
  approximately once in 10010 3 years.
• 5 and 1 day horizon means once in a month.
• Various subportfolios may require various
  horizons.

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Time horizon

• When the distribution is stable one can translate
  VaR over different time periods.

This formula is valid (in particular) for iid
normally distributed returns.
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FRM-97, Question 7

• To convert VaR from a one day holding period to a
  ten day holding period the VaR number is
  generally multiplied by
• A. 2.33
• B. 3.16
• C. 7.25
• D. 10

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FRM-97, Question 7

• To convert VaR from a one day holding period to a
  ten day holding period the VaR number is
  generally multiplied by
• A. 2.33
• B. 3.16
• C. 7.25
• D. 10

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Home assignment

• Read chapters 1-3, pay attention to boxes.

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The end