Basic Statistics for Risk Management in Banks and Financial Institutions

Description

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. 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