RISK MANAGEMENT IN
FINANCIAL INSTITUTIONS
KU Leuven
Summary Risk Management in Financial Institutions
Extensive summary/overview of the learning materials of the course ‘Risk management in
financial institutions’ taught by Prof. T. Wouters, based on the Professor’s PowerPoint slides.
Academic year: 2020-2021
,Inhoudsopgave
1 INTRODUCTION TO RISK MANAGEMENT ................................................................................................3
1.1 WHAT IS RISK? ..........................................................................................................................................3
1.1.1 Risk is all personal .......................................................................................................................3
1.1.2 Knight: uncertainty versus risk ....................................................................................................3
1.1.3 Risk as a dual concept .................................................................................................................3
1.1.4 Categorizing risk in likelihood and severity .................................................................................3
1.1.5 Volatility and risk ........................................................................................................................4
1.1.6 Multiple dimensions of risk .........................................................................................................4
1.2 RISK MANAGEMENT, RISK MEASUREMENT AND REGULATION ..............................................................................5
1.2.1 Financial institutions ...................................................................................................................5
1.2.2 Banks and risk .............................................................................................................................5
1.2.3 Insurance company and risk........................................................................................................6
1.2.4 The risk management process.....................................................................................................7
1.2.5 The risk management cycle .........................................................................................................7
1.2.6 Measuring risks in financial institutions ......................................................................................7
1.3 RECENT FINANCIAL SCANDALS ......................................................................................................................8
1.4 TYPOLOGY OF RISK EXPOSURES .....................................................................................................................9
1.4.1 Business risk versus non-business risk .........................................................................................9
2 RISK MEASUREMENT ...........................................................................................................................11
2.1 TOOLS FOR MEASURING RISKS ....................................................................................................................11
2.1.1 Need for a formal framework ...................................................................................................11
2.1.2 Measuring unfavorable outcomes ............................................................................................13
2.1.3 Measuring the likelihood of different outcomes: distributional properties ..............................14
2.1.4 Appendix ...................................................................................................................................19
2.2 RISK MEASUREMENT: VOLATILITY AND COMOVEMENT .....................................................................................21
2.2.1 Volatility ....................................................................................................................................21
2.2.2 Comovement .............................................................................................................................24
2.3 VALUE-AT-RISK AND EXPECTED SHORTFALL ...................................................................................................27
2.3.1 Introduction to Value-at-Risk ....................................................................................................27
2.3.2 VaR as a risk measure ...............................................................................................................33
2.3.3 Choice of quantitative factors ...................................................................................................34
2.3.4 Backtesting VaR ........................................................................................................................35
2.3.5 Portfolio tools VaR ....................................................................................................................38
3 MEASURING MARKET RISK...................................................................................................................40
3.1 INTRODUCTION TO MARKET RISK .................................................................................................................40
3.1.1 Market risk ................................................................................................................................40
3.1.2 Fixed income securities .............................................................................................................41
3.1.3 Equity ........................................................................................................................................45
3.1.4 Linear derivative market: forwards, futures and swaps ............................................................46
3.1.5 Options ......................................................................................................................................48
3.2 MARKET VAR .........................................................................................................................................51
3.2.1 Historical simulation .................................................................................................................52
3.2.2 Model-building approach: normal model .................................................................................56
4 MEASURING CREDIT RISK .....................................................................................................................68
4.1 INTRODUCTION TO CREDIT RISK...................................................................................................................68
4.1.1 Credit risk ..................................................................................................................................68
4.1.2 Probability of default ................................................................................................................69
4.1.3 Loss given default ......................................................................................................................78
4.1.4 Credit exposure .........................................................................................................................80
4.1.5 Managing credit risk .................................................................................................................81
4.2 CREDIT VALUE-AT-RISK.............................................................................................................................83
1
, 4.2.1 Credit risk losses and VaR..........................................................................................................83
4.2.2 Credit risk models ......................................................................................................................88
5 RISK MANAGEMENT IN PRACTICE ........................................................................................................94
5.1 STRESS TESTING AND SCENARIO ANALYSIS .....................................................................................................94
5.1.1 Why stress testing? ...................................................................................................................94
5.1.2 Implementation.........................................................................................................................94
5.1.3 Evaluation .................................................................................................................................97
5.2 REGULATION ..........................................................................................................................................98
5.2.1 Pillar 1 .......................................................................................................................................99
5.2.2 Pillar 2 .....................................................................................................................................105
5.2.3 Pillar 3 .....................................................................................................................................106
2
,1 Introduction to risk management
1.1 What is risk?
1.1.1 Risk is all personal
You could have multiple reactions to risk. You could choose to ignore it, to run away from it
or to just go for it without really thinking about it…
à Risk is personal:
• It is a personal feeling (= risk appetite)
• Depending on the type of risk at hand, the impact it could have and the likelihood it
could occur.
1.1.2 Knight: uncertainty versus risk
Knight’s uncertainty vs. risk:
• Uncertainty implies that we observe multiple possible outcomes.
• Risk implies uncertainty where probabilities can be assigned to the possible outcomes.
Critique:
• There is no notion of the loss that could be made…
• E.g., If I flip a coin, there would be uncertainty about the outcome before you flip it.
You can assign probabilities to the possible outcomes. Yet you have no risk in the flip
of the coin, if there is nothing at risk to you.
à Risk implies that you can be harmed.
1.1.3 Risk as a dual concept
Risk= the likelihood of harmful consequence.
• It incorporates the concept of uncertainty/probabilities.
• It also stresses the potential negative consequences deviating from expectations.
This approach also allows us to define opportunity as the related likelihood of favorable
outcome.
Such dual focus is necessary for a successful risk management strategy:
• By limiting risk, you also limit opportunities.
• By exploiting opportunities, you also exploit risk.
1.1.4 Categorizing risk in likelihood and severity
Likelihood: high likelihood = event will most
likely take place
Severity: high severity = if the event takes place,
the impact will be significant
3
,Low likelihood and low severity:
• Non-events
• Not to worry about
High likelihood and low severity:
• Events well known
• Included in pricing of products or mitigated by controls in processes
Low likelihood and high severity:
• Black Swan events: events one could never assume to occur until it occurs with
potential high impact
• The name stems from the fact that initially one thought only white swans to exist, until
the moment of spotting a black swan
• Theory introduced by N. Taleb
• Difficult to approach with normal statistics, Extreme Value Theory is better suited
• E.g., Covid-19 is a Black Swan event. There was the Spanish flu, but no-one foresaw it
realistic to occur again.
Hight likelihood and high severity:
• Grey Rhinos: well-known events, with a potential high impact
• Important point of attention of risk management (in normal times)
• Normal statistics work well here.
1.1.5 Volatility and risk
To have a complete description of risk, we should also account for the utility of each of the
outcomes. Not each outcome is perceived equally harmful and in general people are risk
averse.
E.g., Suppose the following bets are proposed to you:
1. You win €500 for sure.
2. With 50% chance you win €400, and with 50% chance you win €600. The expected
profit is €500.
3. With 10% chance you win €200, and with 90% chance you win €700. The expected
profit is €650.
Even though the expected profit of 3 is higher, most people will choose option 1 (maybe
option 2) because they are risk averse.
1.1.6 Multiple dimensions of risk
The problem with accounting risk aversion is that, in general, it will not give us a unique
ranking: it depends on individual preferences. We thus ignore individual preferences in risk
management.
However, we do account for it in risk management by setting a risk appetite defined on
company level.
4
, 1.2 Risk management, risk measurement and regulation
1.2.1 Financial institutions
There are different kinds of financial institutions:
• Banks: retail, corporate, investment and private banking
• Insurance companies:
o Life, health, property and casualty
o Direct insurance (= an insurance policy directly towards a client/policy holder),
reinsurance (= providing insurance to insurance companies)
• Investment funds
Financial institutions and capital:
• The goal of risk management is to keep a firm solvent, and to this end, a company has
capital that covers for unexpected losses.
• Capital only covers unexpected losses, expected losses are included in pricing and
mitigated by processes.
Risk management is particularly important for financial institutions due to their unique
characteristics:
• Their business model is all about taking risks
• The failure of a financial institution (mainly banks) has high costs because of contagion
effects (externalities)
à Regulation aims at financial stability
1.2.2 Banks and risk
Risk is central to banking: a bank is in the business of taking risks and the bank balance sheet
reflects these risks.
• Loans can be to retail clients, corporates, governments.
• Investment in banking book are investments that the bank will usually keep until
maturity: e.g., corporate or government bonds.
• Investment in trading book are investments to generate trading income: e.g., bonds,
equity (stock)…
• Financial instruments at liability side can be bonds issued, subordinated loans…
The risks in the banking balance sheet are:
• The production of loans creates credit risk
• The investment portfolio has credit risk and market risk
• The transformation of deposits into loans creates liquidity risk (maturity
transformation/maturity mismatch: short-term deposits vs. long-term loans) and
market risk (interest rate risk)
5
FINANCIAL INSTITUTIONS
KU Leuven
Summary Risk Management in Financial Institutions
Extensive summary/overview of the learning materials of the course ‘Risk management in
financial institutions’ taught by Prof. T. Wouters, based on the Professor’s PowerPoint slides.
Academic year: 2020-2021
,Inhoudsopgave
1 INTRODUCTION TO RISK MANAGEMENT ................................................................................................3
1.1 WHAT IS RISK? ..........................................................................................................................................3
1.1.1 Risk is all personal .......................................................................................................................3
1.1.2 Knight: uncertainty versus risk ....................................................................................................3
1.1.3 Risk as a dual concept .................................................................................................................3
1.1.4 Categorizing risk in likelihood and severity .................................................................................3
1.1.5 Volatility and risk ........................................................................................................................4
1.1.6 Multiple dimensions of risk .........................................................................................................4
1.2 RISK MANAGEMENT, RISK MEASUREMENT AND REGULATION ..............................................................................5
1.2.1 Financial institutions ...................................................................................................................5
1.2.2 Banks and risk .............................................................................................................................5
1.2.3 Insurance company and risk........................................................................................................6
1.2.4 The risk management process.....................................................................................................7
1.2.5 The risk management cycle .........................................................................................................7
1.2.6 Measuring risks in financial institutions ......................................................................................7
1.3 RECENT FINANCIAL SCANDALS ......................................................................................................................8
1.4 TYPOLOGY OF RISK EXPOSURES .....................................................................................................................9
1.4.1 Business risk versus non-business risk .........................................................................................9
2 RISK MEASUREMENT ...........................................................................................................................11
2.1 TOOLS FOR MEASURING RISKS ....................................................................................................................11
2.1.1 Need for a formal framework ...................................................................................................11
2.1.2 Measuring unfavorable outcomes ............................................................................................13
2.1.3 Measuring the likelihood of different outcomes: distributional properties ..............................14
2.1.4 Appendix ...................................................................................................................................19
2.2 RISK MEASUREMENT: VOLATILITY AND COMOVEMENT .....................................................................................21
2.2.1 Volatility ....................................................................................................................................21
2.2.2 Comovement .............................................................................................................................24
2.3 VALUE-AT-RISK AND EXPECTED SHORTFALL ...................................................................................................27
2.3.1 Introduction to Value-at-Risk ....................................................................................................27
2.3.2 VaR as a risk measure ...............................................................................................................33
2.3.3 Choice of quantitative factors ...................................................................................................34
2.3.4 Backtesting VaR ........................................................................................................................35
2.3.5 Portfolio tools VaR ....................................................................................................................38
3 MEASURING MARKET RISK...................................................................................................................40
3.1 INTRODUCTION TO MARKET RISK .................................................................................................................40
3.1.1 Market risk ................................................................................................................................40
3.1.2 Fixed income securities .............................................................................................................41
3.1.3 Equity ........................................................................................................................................45
3.1.4 Linear derivative market: forwards, futures and swaps ............................................................46
3.1.5 Options ......................................................................................................................................48
3.2 MARKET VAR .........................................................................................................................................51
3.2.1 Historical simulation .................................................................................................................52
3.2.2 Model-building approach: normal model .................................................................................56
4 MEASURING CREDIT RISK .....................................................................................................................68
4.1 INTRODUCTION TO CREDIT RISK...................................................................................................................68
4.1.1 Credit risk ..................................................................................................................................68
4.1.2 Probability of default ................................................................................................................69
4.1.3 Loss given default ......................................................................................................................78
4.1.4 Credit exposure .........................................................................................................................80
4.1.5 Managing credit risk .................................................................................................................81
4.2 CREDIT VALUE-AT-RISK.............................................................................................................................83
1
, 4.2.1 Credit risk losses and VaR..........................................................................................................83
4.2.2 Credit risk models ......................................................................................................................88
5 RISK MANAGEMENT IN PRACTICE ........................................................................................................94
5.1 STRESS TESTING AND SCENARIO ANALYSIS .....................................................................................................94
5.1.1 Why stress testing? ...................................................................................................................94
5.1.2 Implementation.........................................................................................................................94
5.1.3 Evaluation .................................................................................................................................97
5.2 REGULATION ..........................................................................................................................................98
5.2.1 Pillar 1 .......................................................................................................................................99
5.2.2 Pillar 2 .....................................................................................................................................105
5.2.3 Pillar 3 .....................................................................................................................................106
2
,1 Introduction to risk management
1.1 What is risk?
1.1.1 Risk is all personal
You could have multiple reactions to risk. You could choose to ignore it, to run away from it
or to just go for it without really thinking about it…
à Risk is personal:
• It is a personal feeling (= risk appetite)
• Depending on the type of risk at hand, the impact it could have and the likelihood it
could occur.
1.1.2 Knight: uncertainty versus risk
Knight’s uncertainty vs. risk:
• Uncertainty implies that we observe multiple possible outcomes.
• Risk implies uncertainty where probabilities can be assigned to the possible outcomes.
Critique:
• There is no notion of the loss that could be made…
• E.g., If I flip a coin, there would be uncertainty about the outcome before you flip it.
You can assign probabilities to the possible outcomes. Yet you have no risk in the flip
of the coin, if there is nothing at risk to you.
à Risk implies that you can be harmed.
1.1.3 Risk as a dual concept
Risk= the likelihood of harmful consequence.
• It incorporates the concept of uncertainty/probabilities.
• It also stresses the potential negative consequences deviating from expectations.
This approach also allows us to define opportunity as the related likelihood of favorable
outcome.
Such dual focus is necessary for a successful risk management strategy:
• By limiting risk, you also limit opportunities.
• By exploiting opportunities, you also exploit risk.
1.1.4 Categorizing risk in likelihood and severity
Likelihood: high likelihood = event will most
likely take place
Severity: high severity = if the event takes place,
the impact will be significant
3
,Low likelihood and low severity:
• Non-events
• Not to worry about
High likelihood and low severity:
• Events well known
• Included in pricing of products or mitigated by controls in processes
Low likelihood and high severity:
• Black Swan events: events one could never assume to occur until it occurs with
potential high impact
• The name stems from the fact that initially one thought only white swans to exist, until
the moment of spotting a black swan
• Theory introduced by N. Taleb
• Difficult to approach with normal statistics, Extreme Value Theory is better suited
• E.g., Covid-19 is a Black Swan event. There was the Spanish flu, but no-one foresaw it
realistic to occur again.
Hight likelihood and high severity:
• Grey Rhinos: well-known events, with a potential high impact
• Important point of attention of risk management (in normal times)
• Normal statistics work well here.
1.1.5 Volatility and risk
To have a complete description of risk, we should also account for the utility of each of the
outcomes. Not each outcome is perceived equally harmful and in general people are risk
averse.
E.g., Suppose the following bets are proposed to you:
1. You win €500 for sure.
2. With 50% chance you win €400, and with 50% chance you win €600. The expected
profit is €500.
3. With 10% chance you win €200, and with 90% chance you win €700. The expected
profit is €650.
Even though the expected profit of 3 is higher, most people will choose option 1 (maybe
option 2) because they are risk averse.
1.1.6 Multiple dimensions of risk
The problem with accounting risk aversion is that, in general, it will not give us a unique
ranking: it depends on individual preferences. We thus ignore individual preferences in risk
management.
However, we do account for it in risk management by setting a risk appetite defined on
company level.
4
, 1.2 Risk management, risk measurement and regulation
1.2.1 Financial institutions
There are different kinds of financial institutions:
• Banks: retail, corporate, investment and private banking
• Insurance companies:
o Life, health, property and casualty
o Direct insurance (= an insurance policy directly towards a client/policy holder),
reinsurance (= providing insurance to insurance companies)
• Investment funds
Financial institutions and capital:
• The goal of risk management is to keep a firm solvent, and to this end, a company has
capital that covers for unexpected losses.
• Capital only covers unexpected losses, expected losses are included in pricing and
mitigated by processes.
Risk management is particularly important for financial institutions due to their unique
characteristics:
• Their business model is all about taking risks
• The failure of a financial institution (mainly banks) has high costs because of contagion
effects (externalities)
à Regulation aims at financial stability
1.2.2 Banks and risk
Risk is central to banking: a bank is in the business of taking risks and the bank balance sheet
reflects these risks.
• Loans can be to retail clients, corporates, governments.
• Investment in banking book are investments that the bank will usually keep until
maturity: e.g., corporate or government bonds.
• Investment in trading book are investments to generate trading income: e.g., bonds,
equity (stock)…
• Financial instruments at liability side can be bonds issued, subordinated loans…
The risks in the banking balance sheet are:
• The production of loans creates credit risk
• The investment portfolio has credit risk and market risk
• The transformation of deposits into loans creates liquidity risk (maturity
transformation/maturity mismatch: short-term deposits vs. long-term loans) and
market risk (interest rate risk)
5
