Exam SRM Study Plan: Balancing Theory and Application

Understanding the Exam Structure

Exam SRM (Statistics for Risk Modeling) tests your ability to apply statistical learning methods to actuarial problems. The exam covers linear models, GLMs, time series, tree-based methods, clustering, principal components, and model assessment. Questions test both conceptual understanding (interpreting output, choosing appropriate methods) and computational skills (fitting models, computing metrics). The exam is multiple choice with a mix of calculation and concept questions.

Based on the syllabus weighting, allocate approximately 25 to 30% of your study time to linear models and GLMs, 20 to 25% to machine learning methods, 15 to 20% to time series, and 20 to 25% to model assessment and selection. The exact weighting may vary slightly from sitting to sitting, so review the current syllabus before beginning your study.

The exam emphasizes understanding over memorization. You will rarely be asked to reproduce a formula from scratch. Instead, expect questions that test your ability to choose the right method for a given problem, interpret model output, diagnose problems, and compare alternatives. Building strong conceptual understanding is more valuable than rote formula memorization.

Building a Strong Foundation: Weeks 1 to 3

Begin with linear regression, which forms the foundation for nearly everything else on the syllabus. Cover simple linear regression (estimation, inference, prediction intervals), then multiple regression (interpretation of coefficients, adjusted R-squared, F-tests, partial F-tests). Practice reading regression output tables until you can quickly extract and interpret coefficients, standard errors, t-statistics, and p-values.

Move to residual analysis and model diagnostics: understanding residual plots, leverage, Cook's distance, and the distinction between outliers and influential observations. Then cover variable selection methods (forward, backward, stepwise) and their limitations. Finish with AIC, BIC, and cross-validation for model comparison.

During these weeks, work through practice problems daily. Aim for 10 to 15 problems per topic, focusing on problems that require interpretation rather than just computation. Keep a formula card for key formulas (S_xx, S_xy, MSE, R-squared, adjusted R-squared), but spend more time understanding what each quantity means.

GLMs and Classification: Weeks 4 to 5

Generalized linear models extend regression to non-normal responses. Cover logistic regression first (binary outcome, logit link, odds ratio interpretation, deviance), then Poisson regression (count outcome, log link, overdispersion), and gamma regression (continuous positive outcome, commonly used for claim severity). Understand the three components of a GLM: random component, systematic component, and link function.

Key topics within GLMs: maximum likelihood estimation (conceptually, not the optimization details), deviance as a measure of fit, analysis of deviance tables, and comparison of nested GLMs using likelihood ratio tests or AIC. In actuarial applications, GLMs are the standard for insurance ratemaking, so understanding their practical use is important.

For classification topics, cover the confusion matrix, sensitivity, specificity, precision, recall, F1 score, ROC curves, and AUC. Understand how the classification threshold affects these metrics and how to choose an appropriate threshold for a given application. Practice computing metrics from a confusion matrix until the calculations are automatic.

Time Series: Weeks 5 to 6

Time series analysis requires a different mindset from cross-sectional regression. Begin with stationarity (what it means, how to test for it, differencing to achieve it). Cover autoregressive (AR) models, moving average (MA) models, and their combination (ARMA and ARIMA). Understanding the autocorrelation function (ACF) and partial autocorrelation function (PACF) is critical for model identification.

The key skill is matching ACF/PACF patterns to model types: AR(p) has exponentially decaying ACF and PACF that cuts off after lag p. MA(q) has ACF that cuts off after lag q and exponentially decaying PACF. ARMA shows exponential decay in both. Practice this pattern matching with multiple examples.

Cover exponential smoothing methods (simple, double, Holt-Winters) and understand when each is appropriate. Be able to compute one-step-ahead forecasts for each method. Seasonal models (SARIMA, seasonal exponential smoothing) may appear on the exam, so ensure you understand the basic concept of seasonal differencing and seasonal components.

Machine Learning Methods: Weeks 7 to 8

This section covers a wide range of methods. Prioritize understanding the concepts, strengths, weaknesses, and tuning parameters for each method rather than memorizing algorithmic details. Decision trees: understand how splits are chosen (Gini impurity, entropy, SSE reduction), pruning (cost-complexity pruning with alpha), and interpretation of tree diagrams.

Random forests: bagging + random feature selection at each split. Understand why this reduces variance compared to a single tree. Know the role of the number of trees and the number of features considered at each split (mtry). Gradient boosting: sequential fitting of shallow trees to residuals. Understand the role of learning rate, number of trees, and tree depth. Know that boosting can overfit if too many trees are used.

Also cover: SVMs (margin, cost parameter C, kernel trick), k-nearest neighbors (choice of k, distance metrics, curse of dimensionality), neural networks (basic architecture, activation functions, backpropagation conceptually), principal component analysis (variance explained, scree plot, choosing the number of components), and clustering (k-means algorithm, hierarchical clustering, choosing k).

Model Assessment and Review: Weeks 9 to 10

Dedicate the final weeks to cross-cutting topics and review. Cross-validation (k-fold, leave-one-out): understand the bias-variance trade-off in choosing k. The bias-variance trade-off itself: underfitting vs. overfitting, how model complexity affects each, and the U-shaped test error curve. Regularization (ridge, LASSO, elastic net): understand the penalty terms, how they shrink coefficients, and why LASSO performs variable selection while ridge does not.

Take at least two full practice exams under timed conditions during these weeks. Review every problem you get wrong and identify the underlying concept you missed. Create a summary sheet of common pitfalls and tricky distinctions (e.g., AIC vs. BIC, sensitivity vs. precision, MCAR vs. MAR, forward selection vs. backward elimination).

For each method on the syllabus, ensure you can answer four questions: (1) when should this method be used? (2) what does the output tell us? (3) what can go wrong? (4) how does it compare to alternatives? If you can answer these four questions for every topic, you are well prepared for the exam.

Study Tips and Common Pitfalls

The most common mistake is spending too much time on mathematical derivations at the expense of conceptual understanding. Exam SRM tests application, not proof writing. Know the formulas well enough to compute quantities from given data, but prioritize understanding what each formula measures and when it is appropriate.

Another pitfall is neglecting the "compare methods" style of question, which is common on SRM. Practice explaining in one or two sentences why you would choose method A over method B for a given scenario. Build a mental comparison table across methods, covering: supervised vs. unsupervised, parametric vs. nonparametric, interpretable vs. flexible, sensitivity to outliers, handling of missing data, and computational cost.

Use practice exams from the SOA as your primary calibration tool. Third-party study materials are useful for learning, but the SOA's own practice problems best reflect the style, difficulty, and emphasis of the actual exam. Plan to complete at least 200 practice problems across all topics before sitting for the exam.