Moodys Analytics Risk Practitioner Conference 2014 Quantitative - PowerPoint PPT Presentation

Moody’s Analytics Risk Practitioner Conference ‐ 2014 Quantitative Modeling Approaches for Mid ‐ size Institutions Thomas L Thomas Quantitative Portfolio Manager City National Bank

Development of Commercial Stress Testing Process We chose to take an incremental Credit Manager Worst Case Transition Matrix approach: 1. There are many stress testing techniques Migration Analysis Spreadsheet +/ ‐ PD % (TARP Stress Testing) including: • Shock Testing Proxy Analysis • “Breakage Points” ‐ General Sensitivity Analysis (Shock Testing) in CreditManager • Scenario Analysis • Econometric Modeling 2. Staring with simpler models first and then moving to Scenario Analysis Specific Shock Testing more complex econometric models Macroeconomic Scenario – “Fed Test " • Helps understand your data Bottom Up Industry Segment Top Down Macro Scenario and loss behavior Macro Scenario – Moody’s CSUN • Sets parameters (boundaries' for later modeling) CRE PPR Model Acts as a challenge and • Investor Properties Owner Occupied Properties – Land & Construction – Under Development Under Development reasonableness check – tested CNB Idiosyncratic Scenarios – Under Development 1/20/2015 2

Important to Map DFAST Process Flow As the graphic above illustrates, the credit capital stress testing modeling process consists of the following three main steps: • Data extraction and preparation • Applying stress test models • Export results to Fed reporting templates Helps understand potential data issues and explain the process and data flow to both regulators as well as senior management. 3

Econometric Approach ‐ Regression Analysis • Econometrics is a branch of economics that uses the “science and art of building models which utilizes a set of quantitative tools to construct and test mathematical representations of the real world.” • More specifically the branch attempts to unify economics with math and statistics to make forecasts and empirically test economic theory. • While the analyst may employ several different mathematical and statistical techniques to build his or her econometric model, regression is often the starting point. The regression is represented through a modification of the formula for a straight line by adding • an error term (e): � = a+B 1 X 1 + e

Regression Approaches Two general regression approaches: Introspective Counterfactual Queries and Prospective Counterfactual Queries. • Introspective Counterfactual Queries ‐ The goal in this case is to determine the values that are driving the dependent variable or imply casual relationships. • Here statistical methods are used to estimate the strength of the causal relationships. • The independent variables are said to be efficient when exhibiting good fit via statistical measures like the adjusted R ‐ squared and statistically significant “F” and “t” tests. • Prospective Counterfactual Queries ‐ T ake the form what value would the dependent variable take if the independent variable X were set to a specific value. Such models are simply conditional expectation models that are more in the line of traditional curve fitting techniques. • If the question we are trying to answer is one of conditional expectations, and not causal, then we do not have to be as concerned whether other causal factors are present. • Measurements of goodness of fit, like R ‐ squared, Adjusted R ‐ squared, F and t statistics are sufficient to estimate the best fit line given a specific value of “X. • Due to feedback issues in the independent variables – we believe a Prospective Counterfactual or “curve fitting” approach is best.

Issues to Consider Multicollinearity – • • In causal models is an implicit assumption in many regression models that the relationship between the independent (exogenous regression variables) are assumed to be independent. • In addition, the relationship between the independent variables and errors between predicted values and the actual values are also assumed to be independent. • These can be checked by looking at the sings in the regression coefficients and through test like variance inflation factor test (VIF) to diagnose potential multicollinear variables. • Stationarity – • That is the independent variables do not change dramatically over time thereby skewing the regression forecast. • Plotting trends and using histograms to view the independent variable’s distribution help identify if the data is stationary. • If the data is not stationary – utilizing transposition techniques like “Tuckey’s Ladder” can be used – the simplest is using the period ‐ over ‐ period change in the data for your regression.

Choosing the Appropriate Horizon  It is important to choose the correct time horizon to model the behavior you are interested in examining.  The model above illustrates a regression analysis of predicted charge ‐ off rates using Federal Reserve data to proxy the impact to LGD during a stress event.  Note the first analysis includes a long ‐ time horizon incorporating an expansionary period between 2000 and 2005. This pulls the regression downward as a result the actual charge ‐ off rates exceed the regressions upper 95% confidence level.  When we only model the stressed recessionary period – the actual charge off rates and forecast now fit within our confidence level and mimic the correct expected behavior.

Picking Independent Variables Correlation Matrix Real Dow Jones Disposable CPI 3-Month Total Stock Market Commercial Ln 3-Month Ln 10-Year Ln BBB Comm. Nominal Income Unemployment Inflation Treasury 10-Year Treasury BBB Corporate Market Volatility House Price Real Estate Treasury Treasury Corporate Delinquency GDP Growth Growth Rate Rate Yield Yield Yield Index Index (VIX) Index Price Index Yield Yield Yield Comm. Delinquency 1 Nominal GDP Growth -0.3433 1 Real Disposable Income Growth -0.3306 0.4913 1 Unemployment Rate 0.9555 -0.19 -0.3141 1 CPI Inflation Rate -0.2171 0.5125 0.3789 -0.1835 1 3-Month Treasury Yield -0.6818 0.2487 0.2423 -0.7253 0.1623 1 10-Year Treasury Yield -0.7184 0.1802 0.3042 -0.7955 0.1258 0.6355 1 BBB Corporate Yield 0.0195 -0.7384 -0.3239 -0.145 -0.465 -0.0165 0.3292 1 Dow Jones Total Stock Market Index -0.0962 0.3358 0.2813 -0.1503 0.411 0.342 0.0198 -0.4909 1 Market Volatility Index (VIX) 0.4638 -0.8034 -0.5257 0.3412 -0.5521 -0.4333 -0.3286 0.6681 -0.5194 1 House Price Index -0.4465 0.2791 0.2096 -0.4167 0.2098 0.4702 0.1687 -0.2929 0.6338 -0.5115 1 Commercial Real Estate Price Index -0.0423 -0.1383 0.0235 -0.1451 0.1392 0.235 -0.1253 -0.0576 0.7393 -0.0585 0.7206 1 Ln 3-Month Treasury Yield -0.8974 0.219 0.313 -0.9431 0.1868 0.8337 0.8313 0.1412 0.1587 -0.4135 0.4425 0.1316 1 Ln 10-Year Treasury Yield -0.7054 0.1626 0.3002 -0.7822 0.1224 0.6156 0.9901 0.3322 0.0125 -0.3351 0.2018 -0.1078 0.8318 1 Ln BBB Corporate Yield -0.0207 -0.695 -0.2822 -0.1893 -0.4156 0.0247 0.389 0.9952 -0.4733 0.6251 -0.2745 -0.0554 0.1946 0.3929 1 We chose to utilize only the Fed Scenario Variables – This kept it more manageable • and reduced the need for additional forecasts. • Use common sense when picking variables. For example if you are modeling commercial loan defaults, one would expect the house price index to add little value. Indeed, the housing index exhibited a low correlation 45% compared to 10 ‐ year treasury which exhibited 72% correlation. • Use a correlation matrix (something easily created in Microsoft Excel) to help choose relevant variables and confirm which variables to exclude.  Keep in mid the signs to make sure the are institutively correct with expected economic behavior.

Example Stepwise Regression R 2 Commercial Factors 3 ‐ Month Treasury 68.39% 10 ‐ Year Treasury 58.24% VIX Index Only 26.78% Nominal GDP Growth 14.66% CPI Inflation Rate 10.24% Dow Jones Total Index Only 4.89% BBB Corporate Yield 3.35% R 2 Consumer Factors Unemployment Only 93.56% Real Disposable Income Only 14.90% Change R 2 Multi ‐ Factor Regression Change to Base 3 ‐ Month, 10 ‐ Year Treasury (BASE) 70.70% 3 ‐ Month, 10 ‐ Year Treasury, VIX 72.28% 1.58% 1.58% 3 ‐ Month, 10 ‐ Year Treasury, VIX,GDP 71.87% ‐ 0.40% 1.18% 3 ‐ Month, 10 ‐ Year Treasury, VIX,GDP, DowJones 74.70% 2.82% 4.00% 3 ‐ Month, 10 ‐ Year Treasury, VIX,GDP, DowJones,BBB 74.77% 0.07% 4.07% 3 ‐ Month, 10 ‐ Year Treasury, VIX,GDP, DowJones,BBB, Comml RE 79.38% 4.62% 8.68% 3 ‐ Month, 10 ‐ Year Treasury, VIX, Unemployment 96.33% 16.95% 25.64% 3 ‐ Month, 10 ‐ Year Treasury, VIX, Unemployment, Dow Jones 97.27% 0.93% 26.57% 10 ‐ Year Treasury, VIX, Unemployment, Dow Jones 97.34% 0.07% 26.64% All Factors 97.97% 1.64% 27.27% This is an example of stepwise regression utilizing Federal Reserve delinquency data as a proxy for PD behavior • Note in this process we first begin by regressing each of the individual “Fed” scenario factors against delinquencies. • We then go through a process of combining various factors to obtain the “Best Fitting Regression Line.”