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FRMhttp://pluto.mscc.huji.ac.il/
~mswiener/zvi.htmlHUJI-03
Zvi Wiener
mswiener@mscc.huji.ac.il
02-588-3049
Financial Risk Management
Zvi Wiener VaR-PJorion-Ch1-3 slide 2
Financial Risk Management
Zvi Wiener
Head of Finance Department
The Hebrew University of Jerusalem
02-588-3049, mswiener@mscc.huji.ac.il
Arik Perez
arikp@mof.gov.il
tel. 050-412-733, 02-531-7751
Zvi Wiener VaR-PJorion-Ch1-3 slide 3
Statistics
Random variables
Mean, Standard Deviation, Correlation
Normal distribution
BABA
BABABA 222222
Zvi Wiener VaR-PJorion-Ch1-3 slide 4
Basic Corporate Finance
NPV, IRR, YTM
Assets, Liabilities
Regulators, Bank of Israel, MOF
ISDA, SEC
Zvi Wiener VaR-PJorion-Ch1-3 slide 5
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
FRMhttp://pluto.mscc.huji.ac.il/
~mswiener/zvi.htmlHUJI-03
Following P. Jorion, Value at Risk, McGraw-Hill
Chapter 1
The Need for Risk Management
Financial Risk Management
Zvi Wiener VaR-PJorion-Ch1-3 slide 7
Financial Risks
Risk is the volatility of unexpected outcomes.
Business Risk
Financial Risk
Legal Risk
Operational Risk
Zvi Wiener VaR-PJorion-Ch1-3 slide 8
Analytic Risk Management Tools
Duration 1938
Markowitz mean-variance 1952
Sharpe’s CAPM 1963
Multiple factor models 1966
Black-Merton-Scholes model 1973
RAROC 1983
Limits by duration buckets 1986
Zvi Wiener VaR-PJorion-Ch1-3 slide 9
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-
Zvi Wiener VaR-PJorion-Ch1-3 slide 10
Derivatives and Risk Management
Stocks and bonds are securities – issued to raise capital.
Derivatives are contracts, agreements used for risk transfer.
Zvi Wiener VaR-PJorion-Ch1-3 slide 11
Financial Derivatives
Futures, Forwards, Swaps
Options
European, American, Asian, Parisian
Call, Put
Cap, Floor
Credit derivatives
Zvi Wiener VaR-PJorion-Ch1-3 slide 12
Types of Financial Risks
Market Risk
Credit Risk
Liquidity Risk
Operational Risk
Legal Risk
Zvi Wiener VaR-PJorion-Ch1-3 slide 13
What is the current Risk?
duration, convexity
volatility
delta, gamma, vega
rating
target zone
Bonds
Stocks
Options
Credit
Forex
Total ?
Zvi Wiener VaR-PJorion-Ch1-3 slide 16
Example
You live in Herzliya and work in Tel-Aviv.
When do you have to leave your home to be at work at 8:30?
Zvi Wiener VaR-PJorion-Ch1-3 slide 17
How much can we lose?
Everything
correct, but useless answer.
How much can we lose realistically?
Zvi Wiener VaR-PJorion-Ch1-3 slide 18
Definition
VaR is defined as the predicted worst-case
loss at a specific confidence level (e.g. 99%)
over a certain period of time.
Zvi Wiener VaR-PJorion-Ch1-3 slide 19
Definition (Jorion)
VaR is the worst loss over a target horizon
with a given level of confidence.
Zvi Wiener VaR-PJorion-Ch1-3 slide 21
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,
1%VaR
under normal market conditions.
Zvi Wiener VaR-PJorion-Ch1-3 slide 23
Main Ideas
A few well known risk factors
Historical data + economic views
Diversification effects
Testability
Easy to communicate
Zvi Wiener VaR-PJorion-Ch1-3 slide 24
Conventional Analysis
Risk factor
$ value
sensitivity
scenarios
Zvi Wiener VaR-PJorion-Ch1-3 slide 26
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.
FRMhttp://pluto.mscc.huji.ac.il/
~mswiener/zvi.htmlHUJI-03
Following P. Jorion, Value at Risk, McGraw-Hill
Chapter 2
Lessons from Financial Disasters
Financial Risk Management
Zvi Wiener VaR-PJorion-Ch1-3 slide 28
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 29
Public Funds
($ million)
Orange County 1,640
San Diego 357
West Virginia 279
Florida State Treasury 200
Cuyahoga County 137
Texas State 55
Zvi Wiener VaR-PJorion-Ch1-3 slide 30
Barings
February 26, 1995
233 year old bank
28 year old Nick Leeson
$1,300,000,000 loss
bought by ING for $1.5
Zvi Wiener VaR-PJorion-Ch1-3 slide 31
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 32
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 33
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.
Zvi Wiener VaR-PJorion-Ch1-3 slide 35
Big Losses
Bank Negara, Malaysia $3B 92
Banesto (Spain’s 5th bank) $4.7B 93
Credit Lyonnais $15B 94
S&L short deposits, long loans $150 80s
Japan $550 90s
Zvi Wiener VaR-PJorion-Ch1-3 slide 36
ResponsesG-30 reportDPG = Derivatives Policy Group, risk.ifci.ch
JPMorgan’s 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
FRMhttp://pluto.mscc.huji.ac.il/
~mswiener/zvi.htmlHUJI-03
Following P. Jorion, Value at Risk, McGraw-Hill
Chapter 3
Regulatory Capital Standards with VaR
Financial Risk Management
Zvi Wiener VaR-PJorion-Ch1-3 slide 38
Why regulation?
Externalities
Deposit insurance
Moral hazard – less incentives to control risk
Basel Accord 1988
measure of solvency = Cooke ratio
Zvi Wiener VaR-PJorion-Ch1-3 slide 39
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 >5 years.
Zvi Wiener VaR-PJorion-Ch1-3 slide 40
Weights Asset Type
0% CashClaims on OECD central governmentlocal currency claims on central banks
20% Cash to be receivedOECD banks and regulated securities firmsnon-OECD banks below 1 yearmultilateral development banksforeign OECD public sector entities
50% residential mortgage loans
Zvi Wiener VaR-PJorion-Ch1-3 slide 41
Weights Asset Type
100% Claims on private sector (corp. debt, equity…)Claims on non-OECD banks above 1 yearReal estatePlant and equipment
At national discretion0-50% 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.
Zvi Wiener VaR-PJorion-Ch1-3 slide 43
Activity Restrictions
Restrictions on large risks (over 10% of capital)
must be reported
over 25% prohibited
total of large risks can not exceed 8*capital
Zvi Wiener VaR-PJorion-Ch1-3 slide 44
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 45
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 2.5*Tier1)
Zvi Wiener VaR-PJorion-Ch1-3 slide 46
The Standardized Model
Maturity bands
Partial netting
Duration weights
No diversification across risks
Zvi Wiener VaR-PJorion-Ch1-3 slide 47
The Internal Models Approach
Quantitative parameters for VaR10 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
Zvi Wiener VaR-PJorion-Ch1-3 slide 48
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.
ti
titt SRCVaRVaRk
MaxMRC
60
11,
60
Zvi Wiener VaR-PJorion-Ch1-3 slide 49
Basel Rules MRC
Market Risk Charge = MRC
SRC - specific risk charge, k 3.
tti
itt SRCVaRVaRk
MaxMRC
1
60
1
,60
10%)99,1( dVaRVaR tt
Zvi Wiener VaR-PJorion-Ch1-3 slide 50
Backtesting
Verification of Risk Management models.
Comparison if the model’s forecast VaR with
the actual outcome - P&L.
Exception occurs when actual loss exceeds
VaR.After exception - explanation and action.
Zvi Wiener VaR-PJorion-Ch1-3 slide 51
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 VaR-PJorion-Ch1-3 slide 52
Further development
Basel II
Better treatment of credit risk
Operational risk
Zvi Wiener VaR-PJorion-Ch1-3 slide 53
Non banks
Securities Firms
Insurance companies
Pension funds
SEC reporting 7A in 10K
בארץ – ועדת גלאי – דיווח איכותי, אחר כך כמותי
Zvi Wiener VaR-PJorion-Ch1-3 slide 54
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 55
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 56
Properties of Risk Measure
Monotonicity (X<Y, R(X)>R(Y))
Translation invariance R(X+k) = R(X)-k
Homogeneity R(aX) = a R(X) (liquidity??)
Subadditivity R(X+Y) R(X) + R(Y)
the last property is violated by VaR!
Zvi Wiener VaR-PJorion-Ch1-3 slide 57
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?
Zvi Wiener VaR-PJorion-Ch1-3 slide 58
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 59
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 60
Confidence level
low confidence leads to an imprecise result.
For example 99.99% and 10 business days will require history of
100*100*10 = 100,000 days in order to have only 1 point.
Zvi Wiener VaR-PJorion-Ch1-3 slide 61
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 100*10 = 3 years.
5% and 1 day horizon means once in a month.
Various subportfolios may require various horizons.
Zvi Wiener VaR-PJorion-Ch1-3 slide 62
Time horizon
When the distribution is stable one can translate VaR
over different time periods.
TdayVaRdaysTVaR )1()(
This formula is valid (in particular) for iid
normally distributed returns.
Zvi Wiener VaR-PJorion-Ch1-3 slide 63
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
Zvi Wiener VaR-PJorion-Ch1-3 slide 64
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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