The book provides an engaging account of theoretical, empirical, and practical aspects of various statistical methods in measuring risks of financial institutions, especially banks. In this book, the author demonstrates how banks can apply many simple but effective statistical techniques to
analyze risks they face in business and safeguard themselves from potential vulnerability. It covers three primary areas of banking; risks-credit, market, and operational risk and in a uniquely intuitive, step-by-step manner the author provides hands-on details on the primary statistical tools that
can be applied for financial risk measurement and management.
The book lucidly introduces concepts of various well-known statistical methods such as correlations, regression, matrix approach, probability and distribution theorem, hypothesis testing, value at risk, and Monte Carlo simulation techniques and provides a hands-on estimation and interpretation of
these tests in measuring risks of the financial institutions. The book strikes a fine balance between concepts and mathematics to tell a rich story of thoughtful use of statistical methods.
Author(s): Arindam Bandyopadhyay
Edition: 1
Publisher: Oxford University Press
Year: 2022
Language: English
Pages: 320
Tags: Statistics; Risk Management; Banks; Financial Institutions; Hypotheses Testing; Probability; Distribution Theorems; Matrix Algebra; Multivariate Analysis; Monte Carlo Simulation Techniques; Statistical Tools; Time-Series Forecasting Techniques
Cover
Basic Statistics for Risk Management in Banks and Financial Institutions
Copyright
Dedication
Contents
Book Summary
1. Introduction to Risk Management: Basics of Statistics
What is Risk?
Essence of Financial Risk Management
Evolution of Basel Regulation
What is Risk Management?
Benefits of Risk Management
Types of Risks in a Financial Institution/Organization
Measurement of Operational Risk
Need for Liquidity Risk Management
Difference in Nature of Bank Risks
Integration of Risks
What is the Role of Statistical Approach to Manage Risk?
Summary
Review Questions
References
2. Description of Data and Summary Statistics for Measurement of Risk
Data Description and Presentation
Summary Statistics
Coefficient of Variation (CV) = SD/Mean
Quartiles and Percentiles
Gini and Lorenz Curve
Other Statistical Indices of Loan Inequality/Concentration
Summary
Review Questions
References
3. Probability and Distribution Theorems and Their Applications in Risk Management
Probability Theorems
Probability Properties
Probability Rules
Conditional Probability
Joint Dependence
Mutually Exclusive vs. Non-Exclusive Events
Independent Events
Bayes’ Probability Theorem
Repeated Trials—Draws with Replacement
Probability and Expectations
Probability Distribution
Discrete Distributions
Binomial Distribution
Poisson Distribution
Continuous Distribution
Standard Normal Distribution
Non-Normal Distributions
Concept of Confidence Interval
Summary
Review Questions
References
4. Hypotheses Testing in Banking Risk Analysis
Hypothesis Testing Procedure
Statistical Concept behind Hypothesis Testing
Power of Test
One-Tailed vs. Two-Tailed Test
Illustration of the Concept with Examples
Statistical Significance through t-Statistic
Example of One-Tailed Test
Solution
Analyse the Sample Data
Statistical Test Results Interpretation
Mean Comparison Test (t-Test)
Non-Parametric Wilcoxon Rank-Sum Test
Test Procedure
Analysis of Variance (ANOVA)
Summary
Review Questions
References
5. Matrix Algebra and their Application in Risk Prediction and Risk Monitoring
Transition Matrix Analysis—Computation of Probability of Default
Matrix Multiplication and Estimation of PD for Different Time Horizons
Statistical Test on Significant Increase in Credit Risk (SICR)
Inverse of Matrix and Solution of Equations
Summary
Review Questions
References
6. Correlation Theorem and Portfolio Management Techniques
Portfolio Measure of Credit Risk
Example
Correlation Measures
Steps for Computation of the Spearman Rank Correlation
Measurement of Portfolio Market Risk
Portfolio Optimization
Integration of Risk and Estimation of Bank Capital
Summary
Review Questions
References
7. Multivariate Analysis to Understand Functional Relationship and Scenario Building
Regression Basics
Interpretation
Applications of Multiple Regressions in Risk Analysis
Multiple Discriminant Analysis (MDA)
Diagnostic Checks
Application of MDA Technique
Non-Linear Probability Models-Logistic Regression
Application of Logit Model in Risk Management
Validation of Predictive Power of Logit Models
Panel Regression Methods
The Fixed Effect Model
LSDV Model
Limitations of Fixed Effect Approach
Random Effect Model
Fixed Effect vs. Random Effect Specification
Example of Panel Regression in STATA: Factors Determine Refinancing by Housing Finance Companies (HFCs)
Heteroskedasticity and Multicollinearity Tests
Summary
Review Questions
References
8. Monte Carlo Simulation Techniques and Value at Risk
Types of VaR Techniques
Steps in HS
Steps in VCVaR
Steps in MCS
Value at Risk as a Measure of Market Risk
VaR for Interest Rate Instruments
Stressed VaR
Credit VaR (C-VaR) for Loan Portfolio
Operational Risk VaR: Loss Distribution Approach
Methodology
Kolmogorov–Smirnov Test (K–S)
Anderson–Darling (A–D) Test
P–P & Q–Q Plot
Exercise-Operational Risk VaR Method
VaR Back Testing
Summary
Review Questions
References
9. Statistical Tools for Model Validation and Back Testing
Power Curve
Kolmogorov–Sminrov (K–S) Test
Information Value (IV)
Hosmer–Lemeshow (HL) test
Goodness-of-Fit Test
Steps in HL Test
STATA Example
ROC Curve Generated from Retail Logit PD Model
Akaike Information Criterion
Bayesian Information Criterion (BIC) or Schwarz Criterion
Summary
Review Questions
References
10. Time-Series Forecasting Techniques for Banking Variables
Analysis of Trend: Polynomial Trend
Application of Trend Forecasting
Time Series: AR and MA Process
Stationarity
Seasonality
ARMA Model
Autoregressive Model
Stationarity Condition
Autocorrelation Function and Partial Autocorrelation Function
Unit Root Test
Autoregressive Integrated Moving Average Model
ARIMA Model Identification
Detecting Trend and Seasonality in a Series
Estimating the ARIMA Model-Box-Jenkins Approach
Forecasting with ARIMA Model
Key Steps in Building ARIMA Forecasting Model
ARIMA Forecast Example
Multivariate Time-Series Model
Summary
Review Questions
References
Appendix: Statistical Tables
Index
