Samenvatting / Summary
Course: Risk Management
Risk Management
and
Financial
Institutions
Fourth Edition
John C. Hull
,Table of Contents
Chapter 1: Introduction..................................................................................5
1.1 Risk vs. Return for investors..................................................................5
1.2 The efficient frontier.............................................................................5
1.3 The capital asset pricing model (CAPM)..................................................6
1.4 Arbitrage Pricing Model.........................................................................6
1.5 Risk vs. Return for companies................................................................6
1.6 Risk management by financial institutions .............................................7
1.7 Credit Rating........................................................................................7
Chapter 2: Banks...........................................................................................8
2.1 Commercial banking..............................................................................8
2.2 The Capital Requirements of a Small Commercial Bank...........................8
2.3 Deposit Insurance.................................................................................8
2.4 Investment banking..............................................................................8
2.5 Securities trading ...............................................................................10
2.6 Potential conflicts of interest in banking..............................................10
2.7 Today’s Large Banks............................................................................11
2.8 Risks facing banks...............................................................................11
Chapter 3: Insurance Companies and Pension Plans ......................................12
3.1 Life insurance.....................................................................................12
3.2 Annuity contracts................................................................................12
3.4. Longevity risk and Mortality Risk........................................................13
3.5 Property-casualty insurance................................................................13
3.6 Health insurance.................................................................................14
3.7 Moral Hazard and Adverse Selection....................................................14
3.8 Reinsurance........................................................................................14
3.9 Capital requirements:..........................................................................14
3.10 The risks facing insurance companies.................................................15
3.11 Regulation........................................................................................15
3.12 Pension plans....................................................................................15
Chapter 4: Mutual funds and Hedge funds.....................................................16
4.1 Mutual funds.......................................................................................16
4.2 Hedge funds.......................................................................................18
Chapter 5: Trading in Financial Markets ........................................................19
5.2. Clearing Houses.................................................................................19
5.3 OTC Market Changes...........................................................................19
5.4 Long and short positions in assets.......................................................20
5.5 Derivative markets..............................................................................20
5.6 Plain vanilla derivatives.......................................................................21
5.7 Non-Traditional Derivatives..................................................................22
5.8 Exotic Options and Structured Products...............................................22
5.9 Risk Management Challenges...............................................................22
Chapter 6: The credit crisis of 2007...............................................................23
6.1 The U.S. housing market......................................................................23
6.2 Securitization......................................................................................24
6.3 The crisis............................................................................................ 25
6.4 What went Wrong?..............................................................................25
6.5 Lessons from the Crisis........................................................................26
2
,Chapter 8: How Traders Manage Their Exposures ..........................................27
8.1 Delta ................................................................................................. 27
8.2 Gamma............................................................................................... 27
8.3 Vega................................................................................................... 28
8.4 Theta.................................................................................................. 28
8.5 Rho..................................................................................................... 28
8.6 Calculating Greek Letters....................................................................29
8.7 Taylor Series Expansions......................................................................29
8.8 The realities of hedging.......................................................................29
8.9 Hedging Exotic Options.......................................................................29
8.10 Scenario Analysis..............................................................................29
Chapter 9: Interest Rate Risk........................................................................30
9.2 Types of Rates ....................................................................................30
9.3 Duration............................................................................................. 31
9.4 Convexity............................................................................................ 31
9.5 Generalization.....................................................................................32
9.6 Nonparallel yield curve shifts...............................................................32
9.7 Interest rate deltas in practice.............................................................32
9.8 Principal Components Analysis.............................................................33
9.9 Gamma and Vega................................................................................33
Chapter 10: Volatility...................................................................................34
10.1 Definition of volatility........................................................................34
10.2 Implied volatilities.............................................................................34
10.4 Are daily percentage changes in financial variables normal?................34
10.5 Monitoring daily volatility..................................................................35
10.6 The exponentially weighted moving average model............................35
Chapter 11: Correlations and copulas............................................................36
11.1 Definition of correlation.....................................................................36
11.2 Monitoring correlation.......................................................................36
11.4 Copulas............................................................................................. 36
Chapter 12: Value at Risk and Expected Shortfall...........................................37
12.1 Definition of VaR...............................................................................37
12.2 Examples of the calculation of VaR.....................................................37
12.4 Expected Shortfall.............................................................................37
12.5 Coherent Risk Measures....................................................................38
12.6 Choice of parameters for VaR and ES..................................................39
12.7 Marginal, incremental, and component Measures................................39
12.8 Euler’s Theorem................................................................................39
12.9 Aggregating VaRs..............................................................................40
12.10 Back-testing....................................................................................40
Chapter 13: Historical Simulation and Extreme Value Theory..........................41
13.1 The methodology ..............................................................................41
13.3 Extensions .......................................................................................41
Chapter 14: Model-Building Approach...........................................................42
14.1 The basic methodology......................................................................42
14.3 Correlation and covariance matrices...................................................42
14.8 Monte Carlo simulation......................................................................42
14.10 Model building vs. historical simulation............................................43
3
,Chapter 15: Basel I, Basel II and Solvency II..................................................44
15.1 Reasons for regulating banks.............................................................44
15.2 Bank Regulation Pre-1988..................................................................44
15.3 The 1988 BIS Accord..........................................................................44
15.5 Netting............................................................................................. 45
15.6 The 1996 Amendment........................................................................45
15.7 Basel II.............................................................................................. 46
15.8 Credit risk capital under Basel II.........................................................46
15.9 Operational risk capital under Basel II................................................47
15.10 Pillar 2 : Supervisory Review............................................................48
15.11 Pillar 3: Market discipline.................................................................48
15.12 Solvency II......................................................................................48
Chapter 16: Basel II.5, Basel III and Dodd-Frank.............................................49
16.1 Basel II.5........................................................................................... 49
16.2 Basel III............................................................................................. 49
16.3 Contingent Convertible Bonds............................................................51
16.4 Dodd-Frank Act.................................................................................51
Chapter 19: Credit Risk: Estimating Default Probabilities...............................52
19.1 Credit ratings....................................................................................52
19.2 Historical default probabilities...........................................................52
19.3 Recovery dates..................................................................................52
19.5 Credit spreads...................................................................................53
19.7 Comparison of default probability estimates.......................................54
19.8 Using equity prices to estimate default probabilities...........................54
Chapter 23: Operational Risk........................................................................55
23.1 Defining operational risk?..................................................................55
23.2 Determination of the regulatory capital..............................................55
23.3 Categorization of Operational Risks....................................................56
23.4 Loss Severity and Loss Frequency......................................................56
23.5 Implementation of AMA.....................................................................57
23.6 Proactive approaches........................................................................58
23.7 Allocation of Operational Risk Capital.................................................58
23.9 Insurance..........................................................................................58
23.10 Sarbanes-Oxley act..........................................................................58
Chapter 24: Liquidity risk.............................................................................59
24.1 Liquidity trading risk.........................................................................59
24.2 Liquidity funding risk ........................................................................60
24.3 Liquidity black holes..........................................................................60
Chapter 25: Model Risk................................................................................61
25.1 Marking to market.............................................................................61
Chapter 26: Economic Capital and RAROC......................................................62
26.1 Definition of Economic Capital............................................................62
26.2 Components of Economic Capital........................................................62
26.3 Shapes of the loss distributions.........................................................63
26.4 The relative importance of risks.........................................................63
26.5 Aggregating economic capital............................................................63
26.6 Allocating of economic capital............................................................64
26.8 RAROC.............................................................................................. 64
Chapter 28: Risk management Mistakes to avoid...........................................65
28.1 Risk limits.........................................................................................65
28.2 Managing the trading rooms..............................................................65
28.3 Liquidity risk.....................................................................................66
28.4 Lessons for nonfinancial corporations.................................................66
28.5 A final point......................................................................................67
4
,Chapter 1: Introduction
The primary responsibility of the risk management function is to
understand the portfolio of risks that the company is currently taking and
the risks it plans to take in the future.
1.1 Risk vs. Return for investors
In risk management it is about the trade-off between risk and expected
return. The higher the risk, the higher the expected return. Companies
must take risk to survive and prosper. Most investors are risk-averse,
meaning that investors want to increase expected return while reducing
the standard deviation of return.
The expected return of a single
stock is a weighted average of the
possible returns, where the weight
applied to a particular return
equals the probability of
occurrence. The risk of a single
stock can be quantified by the
standard deviation:
In a portfolio consisting of two types of investments, the expected return is
the weighted average of the weights applied to a particular investment
and the expected investment returns. Portfolio risk can be measured by
the including the correlation between the investments:
1.2 The efficient frontier
In the case more investments are added to a
portfolio, the efficient frontier represents the limits
of the risk-return trade-off. There are no
investments possible that will dominate the
investment combinations of the efficient frontier
given a certain risk-return trade-off.
5
, When a risk-free investment is considered, the
efficient frontier must be a straight line since there
should be a linear trade-off between the expected
return and the standard deviation of returns.
Hereby, all investors should choose the same
portfolio of risky assets: the market portfolio.
1.3 The capital asset pricing model (CAPM)
The expected return required on an
investment should reflect the extend to
which the investment contributes to the
risks of the market portfolio. There are
two components to the risk in the
investment’s return. Both are captured
in the CAPM:
Systematic risk: the market risk that cannot be diversified by an
investor.
Unsystematic risk: the risk that is unrelated to the return from the
market portfolio.
The a represents the superior the
difference between the actual return
and the expected return on a portfolio.
An alpha can be created by trying to
pick stocks that outperform the market
or by anticipating on market
movements (‘market timing’). The
higher the β, the greater the systematic
risk being taken and the greater the extend to which returns are
dependent on the performance of the market.
1.4 Arbitrage Pricing Model
Arbitrage pricing theory (APT) can be viewed as an extension of the CAPM.
In APT there are several factors affecting investment returns. Each factor is
a separate source of systematic risk. Unsystematic risk in APT is the risk
that is unrelated to all the factors.
1.5 Risk vs. Return for companies
Since the ultimate owners of companies are its shareholders, new projects
undertaken by a company should be seen as an addition to the
shareholder’s portfolio. When the expected return of a project is higher
than the CAPM, a project should be accepted. Otherwise it should be
rejected.
The Lehman Brothers Bankruptcy (2008) is the largest bankruptcy in US
history. When a company faces bankruptcy, shareholder value will be
6
Course: Risk Management
Risk Management
and
Financial
Institutions
Fourth Edition
John C. Hull
,Table of Contents
Chapter 1: Introduction..................................................................................5
1.1 Risk vs. Return for investors..................................................................5
1.2 The efficient frontier.............................................................................5
1.3 The capital asset pricing model (CAPM)..................................................6
1.4 Arbitrage Pricing Model.........................................................................6
1.5 Risk vs. Return for companies................................................................6
1.6 Risk management by financial institutions .............................................7
1.7 Credit Rating........................................................................................7
Chapter 2: Banks...........................................................................................8
2.1 Commercial banking..............................................................................8
2.2 The Capital Requirements of a Small Commercial Bank...........................8
2.3 Deposit Insurance.................................................................................8
2.4 Investment banking..............................................................................8
2.5 Securities trading ...............................................................................10
2.6 Potential conflicts of interest in banking..............................................10
2.7 Today’s Large Banks............................................................................11
2.8 Risks facing banks...............................................................................11
Chapter 3: Insurance Companies and Pension Plans ......................................12
3.1 Life insurance.....................................................................................12
3.2 Annuity contracts................................................................................12
3.4. Longevity risk and Mortality Risk........................................................13
3.5 Property-casualty insurance................................................................13
3.6 Health insurance.................................................................................14
3.7 Moral Hazard and Adverse Selection....................................................14
3.8 Reinsurance........................................................................................14
3.9 Capital requirements:..........................................................................14
3.10 The risks facing insurance companies.................................................15
3.11 Regulation........................................................................................15
3.12 Pension plans....................................................................................15
Chapter 4: Mutual funds and Hedge funds.....................................................16
4.1 Mutual funds.......................................................................................16
4.2 Hedge funds.......................................................................................18
Chapter 5: Trading in Financial Markets ........................................................19
5.2. Clearing Houses.................................................................................19
5.3 OTC Market Changes...........................................................................19
5.4 Long and short positions in assets.......................................................20
5.5 Derivative markets..............................................................................20
5.6 Plain vanilla derivatives.......................................................................21
5.7 Non-Traditional Derivatives..................................................................22
5.8 Exotic Options and Structured Products...............................................22
5.9 Risk Management Challenges...............................................................22
Chapter 6: The credit crisis of 2007...............................................................23
6.1 The U.S. housing market......................................................................23
6.2 Securitization......................................................................................24
6.3 The crisis............................................................................................ 25
6.4 What went Wrong?..............................................................................25
6.5 Lessons from the Crisis........................................................................26
2
,Chapter 8: How Traders Manage Their Exposures ..........................................27
8.1 Delta ................................................................................................. 27
8.2 Gamma............................................................................................... 27
8.3 Vega................................................................................................... 28
8.4 Theta.................................................................................................. 28
8.5 Rho..................................................................................................... 28
8.6 Calculating Greek Letters....................................................................29
8.7 Taylor Series Expansions......................................................................29
8.8 The realities of hedging.......................................................................29
8.9 Hedging Exotic Options.......................................................................29
8.10 Scenario Analysis..............................................................................29
Chapter 9: Interest Rate Risk........................................................................30
9.2 Types of Rates ....................................................................................30
9.3 Duration............................................................................................. 31
9.4 Convexity............................................................................................ 31
9.5 Generalization.....................................................................................32
9.6 Nonparallel yield curve shifts...............................................................32
9.7 Interest rate deltas in practice.............................................................32
9.8 Principal Components Analysis.............................................................33
9.9 Gamma and Vega................................................................................33
Chapter 10: Volatility...................................................................................34
10.1 Definition of volatility........................................................................34
10.2 Implied volatilities.............................................................................34
10.4 Are daily percentage changes in financial variables normal?................34
10.5 Monitoring daily volatility..................................................................35
10.6 The exponentially weighted moving average model............................35
Chapter 11: Correlations and copulas............................................................36
11.1 Definition of correlation.....................................................................36
11.2 Monitoring correlation.......................................................................36
11.4 Copulas............................................................................................. 36
Chapter 12: Value at Risk and Expected Shortfall...........................................37
12.1 Definition of VaR...............................................................................37
12.2 Examples of the calculation of VaR.....................................................37
12.4 Expected Shortfall.............................................................................37
12.5 Coherent Risk Measures....................................................................38
12.6 Choice of parameters for VaR and ES..................................................39
12.7 Marginal, incremental, and component Measures................................39
12.8 Euler’s Theorem................................................................................39
12.9 Aggregating VaRs..............................................................................40
12.10 Back-testing....................................................................................40
Chapter 13: Historical Simulation and Extreme Value Theory..........................41
13.1 The methodology ..............................................................................41
13.3 Extensions .......................................................................................41
Chapter 14: Model-Building Approach...........................................................42
14.1 The basic methodology......................................................................42
14.3 Correlation and covariance matrices...................................................42
14.8 Monte Carlo simulation......................................................................42
14.10 Model building vs. historical simulation............................................43
3
,Chapter 15: Basel I, Basel II and Solvency II..................................................44
15.1 Reasons for regulating banks.............................................................44
15.2 Bank Regulation Pre-1988..................................................................44
15.3 The 1988 BIS Accord..........................................................................44
15.5 Netting............................................................................................. 45
15.6 The 1996 Amendment........................................................................45
15.7 Basel II.............................................................................................. 46
15.8 Credit risk capital under Basel II.........................................................46
15.9 Operational risk capital under Basel II................................................47
15.10 Pillar 2 : Supervisory Review............................................................48
15.11 Pillar 3: Market discipline.................................................................48
15.12 Solvency II......................................................................................48
Chapter 16: Basel II.5, Basel III and Dodd-Frank.............................................49
16.1 Basel II.5........................................................................................... 49
16.2 Basel III............................................................................................. 49
16.3 Contingent Convertible Bonds............................................................51
16.4 Dodd-Frank Act.................................................................................51
Chapter 19: Credit Risk: Estimating Default Probabilities...............................52
19.1 Credit ratings....................................................................................52
19.2 Historical default probabilities...........................................................52
19.3 Recovery dates..................................................................................52
19.5 Credit spreads...................................................................................53
19.7 Comparison of default probability estimates.......................................54
19.8 Using equity prices to estimate default probabilities...........................54
Chapter 23: Operational Risk........................................................................55
23.1 Defining operational risk?..................................................................55
23.2 Determination of the regulatory capital..............................................55
23.3 Categorization of Operational Risks....................................................56
23.4 Loss Severity and Loss Frequency......................................................56
23.5 Implementation of AMA.....................................................................57
23.6 Proactive approaches........................................................................58
23.7 Allocation of Operational Risk Capital.................................................58
23.9 Insurance..........................................................................................58
23.10 Sarbanes-Oxley act..........................................................................58
Chapter 24: Liquidity risk.............................................................................59
24.1 Liquidity trading risk.........................................................................59
24.2 Liquidity funding risk ........................................................................60
24.3 Liquidity black holes..........................................................................60
Chapter 25: Model Risk................................................................................61
25.1 Marking to market.............................................................................61
Chapter 26: Economic Capital and RAROC......................................................62
26.1 Definition of Economic Capital............................................................62
26.2 Components of Economic Capital........................................................62
26.3 Shapes of the loss distributions.........................................................63
26.4 The relative importance of risks.........................................................63
26.5 Aggregating economic capital............................................................63
26.6 Allocating of economic capital............................................................64
26.8 RAROC.............................................................................................. 64
Chapter 28: Risk management Mistakes to avoid...........................................65
28.1 Risk limits.........................................................................................65
28.2 Managing the trading rooms..............................................................65
28.3 Liquidity risk.....................................................................................66
28.4 Lessons for nonfinancial corporations.................................................66
28.5 A final point......................................................................................67
4
,Chapter 1: Introduction
The primary responsibility of the risk management function is to
understand the portfolio of risks that the company is currently taking and
the risks it plans to take in the future.
1.1 Risk vs. Return for investors
In risk management it is about the trade-off between risk and expected
return. The higher the risk, the higher the expected return. Companies
must take risk to survive and prosper. Most investors are risk-averse,
meaning that investors want to increase expected return while reducing
the standard deviation of return.
The expected return of a single
stock is a weighted average of the
possible returns, where the weight
applied to a particular return
equals the probability of
occurrence. The risk of a single
stock can be quantified by the
standard deviation:
In a portfolio consisting of two types of investments, the expected return is
the weighted average of the weights applied to a particular investment
and the expected investment returns. Portfolio risk can be measured by
the including the correlation between the investments:
1.2 The efficient frontier
In the case more investments are added to a
portfolio, the efficient frontier represents the limits
of the risk-return trade-off. There are no
investments possible that will dominate the
investment combinations of the efficient frontier
given a certain risk-return trade-off.
5
, When a risk-free investment is considered, the
efficient frontier must be a straight line since there
should be a linear trade-off between the expected
return and the standard deviation of returns.
Hereby, all investors should choose the same
portfolio of risky assets: the market portfolio.
1.3 The capital asset pricing model (CAPM)
The expected return required on an
investment should reflect the extend to
which the investment contributes to the
risks of the market portfolio. There are
two components to the risk in the
investment’s return. Both are captured
in the CAPM:
Systematic risk: the market risk that cannot be diversified by an
investor.
Unsystematic risk: the risk that is unrelated to the return from the
market portfolio.
The a represents the superior the
difference between the actual return
and the expected return on a portfolio.
An alpha can be created by trying to
pick stocks that outperform the market
or by anticipating on market
movements (‘market timing’). The
higher the β, the greater the systematic
risk being taken and the greater the extend to which returns are
dependent on the performance of the market.
1.4 Arbitrage Pricing Model
Arbitrage pricing theory (APT) can be viewed as an extension of the CAPM.
In APT there are several factors affecting investment returns. Each factor is
a separate source of systematic risk. Unsystematic risk in APT is the risk
that is unrelated to all the factors.
1.5 Risk vs. Return for companies
Since the ultimate owners of companies are its shareholders, new projects
undertaken by a company should be seen as an addition to the
shareholder’s portfolio. When the expected return of a project is higher
than the CAPM, a project should be accepted. Otherwise it should be
rejected.
The Lehman Brothers Bankruptcy (2008) is the largest bankruptcy in US
history. When a company faces bankruptcy, shareholder value will be
6
