Basic Statistics for Risk Management in Banks and Financial Institutions

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