Summary Risk Management in
Financial Institutions
,Table of Contents
Chapter 1: Introduction to Risk Management ....................................................... 6
What is risk? ............................................................................................................... 6
Knight's Distinction: Risk vs. Uncertainty...................................................................................... 6
Risk as a Dual Concept ............................................................................................................... 6
Risk categories (Severity vs. likelihood matrix) .............................................................................. 6
Risk Aversion .............................................................................................................................. 6
Risk Management, Measurement and Regulation ......................................................... 7
Types of Financial Institutions ..................................................................................................... 7
Why risk management matters for financial institutions................................................................ 7
Banks' Business Model ............................................................................................................... 7
Banks' Leverage .......................................................................................................................... 7
Insurance Companies' Business Model ........................................................................ 8
Linking Management Options to the Risk Matrix ............................................................ 9
Historical Risk Management Failures ........................................................................... 9
Key Lessons from Failures ........................................................................................................... 9
Typology of Risk Exposures ........................................................................................ 10
Business Risk vs. Financial Risk..................................................................................................10
Market Risk................................................................................................................................10
Credit Risk .................................................................................................................................10
Liquidity Risk .............................................................................................................................10
Underwriting Risk.......................................................................................................................11
Operational Risk ........................................................................................................................11
Strategic Risk.............................................................................................................................11
Reputational Risk.......................................................................................................................11
Sustainability Risk (ESG) ............................................................................................................11
Other Risks ................................................................................................................................11
Chapter 2: Tools for measuring risk .................................................................... 12
Need for a normal framework .................................................................................... 12
Two different approaches can be used to deal with uncertainty ...................................................12
Two approaches to deal with probabilities ..................................................................................13
Measuring unfavorable outcomes .............................................................................. 13
Logreturns .................................................................................................................................14
Measuring the likelihood of different outcomes: distributional properties ................... 14
Refresher probability theory .......................................................................................................14
Random nature of returns ..........................................................................................................15
Normal logreturns......................................................................................................................17
Probability theory – updating our beliefs in the presence of new information.................................18
Chapter 3: Volatility and Comovement ............................................................... 19
Volatility ................................................................................................................... 19
Historical measures of volatility..................................................................................................19
Implied volatility ........................................................................................................................23
Comovement ............................................................................................................ 24
Pearson Correlation ...................................................................................................................24
Rank correlation – Spearman correlation ....................................................................................26
Rank correlation – Kendall τ correlation ......................................................................................26
Chapter 4: Value-at-risk and Expected Shortfall .................................................. 27
2
, Value at Risk ............................................................................................................. 27
Definition ..................................................................................................................................27
Types of VaR: absolute vs relative VaR ........................................................................................27
Distributional assumptions ........................................................................................................28
Model-based solutions ..............................................................................................................28
VaR as a Risk Measure: Coherence .............................................................................................30
Expected shortfall ..................................................................................................... 30
Choice of quantitative factors .................................................................................... 31
Parameters: horizon T and confidence level c..............................................................................31
Time Aggregation .......................................................................................................................32
Backtesting VaR ........................................................................................................ 32
Bernoulli Test (one-tailed) ..........................................................................................................33
Backtesting with clustered breaches ..........................................................................................33
Trade-offs in Backtesting ............................................................................................................34
Portfolio VaR tools .....................................................................................................................34
Chapter 5: Market risk........................................................................................ 36
Market risk Definition ................................................................................................ 36
Exchange rate risk ......................................................................................................................36
Interest Rate Risk .......................................................................................................................36
Fixed Income Securities definition ............................................................................. 37
Bond Pricing ..............................................................................................................................37
Equity ....................................................................................................................... 40
Definition ..................................................................................................................................40
Derivatives market .....................................................................................................................41
Lineair derivatives: Forwards, Futures and Swaps....................................................... 41
Forward Contract.......................................................................................................................41
Futures Contract .......................................................................................................................41
Swap Contract ...........................................................................................................................42
Risk for lineair derivatives ...........................................................................................................42
Pricing Linear Derivatives (No-Arbitrage) .....................................................................................42
Non-lineair derivatives: options ................................................................................. 42
Option Payoffs ...........................................................................................................................43
Option Risks ..............................................................................................................................43
Option Value Components .........................................................................................................43
Pricing options ...........................................................................................................................44
Basis Risk ..................................................................................................................................45
Chapter 6: Market Value-at-Risk ......................................................................... 46
Historical simulation ................................................................................................. 46
Non stationarity .........................................................................................................................47
Smoothing tails – extreme value theory .......................................................................................48
Model-Based approach - normal model ...................................................................... 51
Normal VaR (when combining a normal distribution with a full valuation) .....................................51
Mapping approach .....................................................................................................................52
Delta-normal VaR (when combining a normal distribution with a local valuation) ..........................53
Delta-gamma normal VaR (for options) .......................................................................................57
Precision normal VaR .................................................................................................................57
Portfolio tools normal VaR..........................................................................................................58
Evaluation of delta normal VaR ...................................................................................................59
Chapter 7: Credit Risk ........................................................................................ 60
3
, Credit risk ................................................................................................................. 60
Credit loss formula ....................................................................................................................60
Probability of default ................................................................................................. 61
Historical methods: Altman Z-score ...........................................................................................61
Historical methods: Ratings-based PD........................................................................................62
Market price methods: Bond prices ............................................................................................64
Market price methods: Equity prices (Merton model) ...................................................................64
KMV model ................................................................................................................................65
Loss given default ..................................................................................................... 66
Factors affecting recovery ..........................................................................................................66
Amplifier effect ..........................................................................................................................67
PD-LGD interaction ....................................................................................................................67
Credit exposure ........................................................................................................ 67
CE by instrument type ................................................................................................................67
CE for different instruments .......................................................................................................67
Managing credit risk .................................................................................................. 68
Credit risk lifecycle ....................................................................................................................68
Chapter 8: Credit Value-at-Risk .......................................................................... 70
Credit risk losses and VaR ......................................................................................... 70
Diversification of credit risk (portfolio of instruments) ..................................................................71
Credit Value at Risk....................................................................................................................72
Credit risk models ..................................................................................................... 72
CreditMetrics (JPMorgan) ...........................................................................................................73
Chapter 9: Stress Testing and Scenario Analysis ................................................. 76
Why Stress Testing? .................................................................................................. 76
Implementation ........................................................................................................ 76
Uni- vs. Multidimensional Analysis .............................................................................................77
Evaluation................................................................................................................. 79
Chapter 10: Regulation ...................................................................................... 80
Regulatory frameworks ............................................................................................. 80
Basel III for banks ......................................................................................................................80
Solvency II for insurance companies ...........................................................................................80
Three pillars structure ................................................................................................................80
Pillar 1: Basel III capital requirements ........................................................................ 80
Risk Weighted Assets (RWA) .......................................................................................................81
Approaches to estimate PD, EaD, LGD........................................................................................82
Market risk ................................................................................................................................82
Operational risk .........................................................................................................................83
Leverage ratio ............................................................................................................................83
Liquidity ratios ...........................................................................................................................83
Pillar 1: Solvency II capital requirements.................................................................... 83
Key concepts .............................................................................................................................83
Ways to calculate SCR ...............................................................................................................84
Standard Formula SCR tree ........................................................................................................84
Stressed balance sheet calculation ............................................................................................85
Volatility of Solvency II ratio ........................................................................................................85
Pillar 2: Risk assessment and governance .................................................................. 86
4
Financial Institutions
,Table of Contents
Chapter 1: Introduction to Risk Management ....................................................... 6
What is risk? ............................................................................................................... 6
Knight's Distinction: Risk vs. Uncertainty...................................................................................... 6
Risk as a Dual Concept ............................................................................................................... 6
Risk categories (Severity vs. likelihood matrix) .............................................................................. 6
Risk Aversion .............................................................................................................................. 6
Risk Management, Measurement and Regulation ......................................................... 7
Types of Financial Institutions ..................................................................................................... 7
Why risk management matters for financial institutions................................................................ 7
Banks' Business Model ............................................................................................................... 7
Banks' Leverage .......................................................................................................................... 7
Insurance Companies' Business Model ........................................................................ 8
Linking Management Options to the Risk Matrix ............................................................ 9
Historical Risk Management Failures ........................................................................... 9
Key Lessons from Failures ........................................................................................................... 9
Typology of Risk Exposures ........................................................................................ 10
Business Risk vs. Financial Risk..................................................................................................10
Market Risk................................................................................................................................10
Credit Risk .................................................................................................................................10
Liquidity Risk .............................................................................................................................10
Underwriting Risk.......................................................................................................................11
Operational Risk ........................................................................................................................11
Strategic Risk.............................................................................................................................11
Reputational Risk.......................................................................................................................11
Sustainability Risk (ESG) ............................................................................................................11
Other Risks ................................................................................................................................11
Chapter 2: Tools for measuring risk .................................................................... 12
Need for a normal framework .................................................................................... 12
Two different approaches can be used to deal with uncertainty ...................................................12
Two approaches to deal with probabilities ..................................................................................13
Measuring unfavorable outcomes .............................................................................. 13
Logreturns .................................................................................................................................14
Measuring the likelihood of different outcomes: distributional properties ................... 14
Refresher probability theory .......................................................................................................14
Random nature of returns ..........................................................................................................15
Normal logreturns......................................................................................................................17
Probability theory – updating our beliefs in the presence of new information.................................18
Chapter 3: Volatility and Comovement ............................................................... 19
Volatility ................................................................................................................... 19
Historical measures of volatility..................................................................................................19
Implied volatility ........................................................................................................................23
Comovement ............................................................................................................ 24
Pearson Correlation ...................................................................................................................24
Rank correlation – Spearman correlation ....................................................................................26
Rank correlation – Kendall τ correlation ......................................................................................26
Chapter 4: Value-at-risk and Expected Shortfall .................................................. 27
2
, Value at Risk ............................................................................................................. 27
Definition ..................................................................................................................................27
Types of VaR: absolute vs relative VaR ........................................................................................27
Distributional assumptions ........................................................................................................28
Model-based solutions ..............................................................................................................28
VaR as a Risk Measure: Coherence .............................................................................................30
Expected shortfall ..................................................................................................... 30
Choice of quantitative factors .................................................................................... 31
Parameters: horizon T and confidence level c..............................................................................31
Time Aggregation .......................................................................................................................32
Backtesting VaR ........................................................................................................ 32
Bernoulli Test (one-tailed) ..........................................................................................................33
Backtesting with clustered breaches ..........................................................................................33
Trade-offs in Backtesting ............................................................................................................34
Portfolio VaR tools .....................................................................................................................34
Chapter 5: Market risk........................................................................................ 36
Market risk Definition ................................................................................................ 36
Exchange rate risk ......................................................................................................................36
Interest Rate Risk .......................................................................................................................36
Fixed Income Securities definition ............................................................................. 37
Bond Pricing ..............................................................................................................................37
Equity ....................................................................................................................... 40
Definition ..................................................................................................................................40
Derivatives market .....................................................................................................................41
Lineair derivatives: Forwards, Futures and Swaps....................................................... 41
Forward Contract.......................................................................................................................41
Futures Contract .......................................................................................................................41
Swap Contract ...........................................................................................................................42
Risk for lineair derivatives ...........................................................................................................42
Pricing Linear Derivatives (No-Arbitrage) .....................................................................................42
Non-lineair derivatives: options ................................................................................. 42
Option Payoffs ...........................................................................................................................43
Option Risks ..............................................................................................................................43
Option Value Components .........................................................................................................43
Pricing options ...........................................................................................................................44
Basis Risk ..................................................................................................................................45
Chapter 6: Market Value-at-Risk ......................................................................... 46
Historical simulation ................................................................................................. 46
Non stationarity .........................................................................................................................47
Smoothing tails – extreme value theory .......................................................................................48
Model-Based approach - normal model ...................................................................... 51
Normal VaR (when combining a normal distribution with a full valuation) .....................................51
Mapping approach .....................................................................................................................52
Delta-normal VaR (when combining a normal distribution with a local valuation) ..........................53
Delta-gamma normal VaR (for options) .......................................................................................57
Precision normal VaR .................................................................................................................57
Portfolio tools normal VaR..........................................................................................................58
Evaluation of delta normal VaR ...................................................................................................59
Chapter 7: Credit Risk ........................................................................................ 60
3
, Credit risk ................................................................................................................. 60
Credit loss formula ....................................................................................................................60
Probability of default ................................................................................................. 61
Historical methods: Altman Z-score ...........................................................................................61
Historical methods: Ratings-based PD........................................................................................62
Market price methods: Bond prices ............................................................................................64
Market price methods: Equity prices (Merton model) ...................................................................64
KMV model ................................................................................................................................65
Loss given default ..................................................................................................... 66
Factors affecting recovery ..........................................................................................................66
Amplifier effect ..........................................................................................................................67
PD-LGD interaction ....................................................................................................................67
Credit exposure ........................................................................................................ 67
CE by instrument type ................................................................................................................67
CE for different instruments .......................................................................................................67
Managing credit risk .................................................................................................. 68
Credit risk lifecycle ....................................................................................................................68
Chapter 8: Credit Value-at-Risk .......................................................................... 70
Credit risk losses and VaR ......................................................................................... 70
Diversification of credit risk (portfolio of instruments) ..................................................................71
Credit Value at Risk....................................................................................................................72
Credit risk models ..................................................................................................... 72
CreditMetrics (JPMorgan) ...........................................................................................................73
Chapter 9: Stress Testing and Scenario Analysis ................................................. 76
Why Stress Testing? .................................................................................................. 76
Implementation ........................................................................................................ 76
Uni- vs. Multidimensional Analysis .............................................................................................77
Evaluation................................................................................................................. 79
Chapter 10: Regulation ...................................................................................... 80
Regulatory frameworks ............................................................................................. 80
Basel III for banks ......................................................................................................................80
Solvency II for insurance companies ...........................................................................................80
Three pillars structure ................................................................................................................80
Pillar 1: Basel III capital requirements ........................................................................ 80
Risk Weighted Assets (RWA) .......................................................................................................81
Approaches to estimate PD, EaD, LGD........................................................................................82
Market risk ................................................................................................................................82
Operational risk .........................................................................................................................83
Leverage ratio ............................................................................................................................83
Liquidity ratios ...........................................................................................................................83
Pillar 1: Solvency II capital requirements.................................................................... 83
Key concepts .............................................................................................................................83
Ways to calculate SCR ...............................................................................................................84
Standard Formula SCR tree ........................................................................................................84
Stressed balance sheet calculation ............................................................................................85
Volatility of Solvency II ratio ........................................................................................................85
Pillar 2: Risk assessment and governance .................................................................. 86
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