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Zvi Wiener

[email protected]

02-588-3049

Financial Risk Management

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Zvi Wiener VaR-PJorion-Ch1-3 slide 2


Zvi Wiener

Head of Finance Department

The Hebrew University of Jerusalem

02-588-3049, [email protected]

Arik Perez

[email protected]

tel. 050-412-733, 02-531-7751


Statistics

Random variables

Mean, Standard Deviation, Correlation

Normal distribution

BABA

BABABA 222222


Basic Corporate Finance

NPV, IRR, YTM

Assets, Liabilities

Regulators, Bank of Israel, MOF

ISDA, SEC


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



Following P. Jorion, Value at Risk, McGraw-Hill

Chapter 1

The Need for Risk Management



Financial Risks

Risk is the volatility of unexpected outcomes.

Business Risk

Financial Risk

Legal Risk

Operational Risk


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


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-


Derivatives and Risk Management

Stocks and bonds are securities – issued to raise capital.

Derivatives are contracts, agreements used for risk transfer.


Financial Derivatives

Futures, Forwards, Swaps

Options

European, American, Asian, Parisian

Call, Put

Cap, Floor

Credit derivatives


Types of Financial Risks

Market Risk

Credit Risk

Liquidity Risk

Operational Risk

Legal Risk


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


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?


How much can we lose?

Everything

correct, but useless answer.

How much can we lose realistically?


Definition

VaR is defined as the predicted worst-case

loss at a specific confidence level (e.g. 99%)

over a certain period of time.


Definition (Jorion)

VaR is the worst loss over a target horizon

with a given level of confidence.


-3 -2 -1 1 2 3

0.2

0.4

0.6

0.8

1

Profit/Loss

VaR

1% VaR1%


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.


Returns

year

1% of worst cases


Main Ideas

A few well known risk factors

Historical data + economic views

Diversification effects

Testability

Easy to communicate


Conventional Analysis

Risk factor

$ value

sensitivity

scenarios


VaR approach

Risk factor

$

yield

price


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.




Chapter 2

Lessons from Financial Disasters



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


Public Funds

($ million)

Orange County 1,640

San Diego 357

West Virginia 279

Florida State Treasury 200

Cuyahoga County 137

Texas State 55


Barings

February 26, 1995

233 year old bank

28 year old Nick Leeson

$1,300,000,000 loss

bought by ING for $1.5


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


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


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.


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


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

http://risk.ifci.ch/




http://www.riskmetrics.com/

http://www.garp.com/

http://www.prmia.org/

http://www.gao.gov/reports.htm

http://www.fas133.com/

http://www.iasc.org.uk/

http://www.sec.gov/rules/final/33-7386.txt




Chapter 3

Regulatory Capital Standards with VaR



Why regulation?

Externalities

Deposit insurance

Moral hazard – less incentives to control risk

Basel Accord 1988

measure of solvency = Cooke ratio


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.


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


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.


Credit Risk Charge

iii assetwCRC %8


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


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


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)


The Standardized Model

Maturity bands

Partial netting

Duration weights

No diversification across risks


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


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


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


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.


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?


Further development

Basel II

Better treatment of credit risk

Operational risk


Non banks

Securities Firms

Insurance companies

Pension funds

SEC reporting 7A in 10K

בארץ – ועדת גלאי – דיווח איכותי, אחר כך כמותי


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


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!


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?


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


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.


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.


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.


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


Home assignment

Read chapters 1-3, pay attention to boxes.


The end

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