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Some project templates on the NEAS web site use actual data, such as sports won-loss records. Some project templates use simulated data, such as paid loss triangles.
The project templates provide ideas and suggestions for student projects. You can follow a project template exactly, as some candidates do.
You are not restricted to the formats in the templates. If you have data from your actuarial work, you can use it for the student project. This offers several advantages.
~ Instead of compiling data from web sites, you use figures you already have in Excel worksheets. This saves time.
~ You know the data and its attributes from your actuarial work. You may know that the data follow a multiplicative pattern, so you take logarithms before fitting the regression equation. You may know that the error terms are not normally distributed, so you can test for heteroscedasticity. You may know that the regression coefficients differ for two sub-groups, such as males vs females, so you can include a dummy variable in the regression equation. You may know that a slope coefficient increases or decreases as an independent variable increases, so you use the square of the independent variable as an additional explanatory variable.
Your student project may prove valuable for your actuarial work. Some reserving actuaries quantify separate age-to-age factors for each development period. In fact:
~ Much of the variation they observe in these factors is random fluctuation.
~ A statistical model may uncover patterns that improve the reserve estimates.
If you use actual data, keep the following principles in mind.
(1) Choose a line of business or practice area with low stochasticity.
~ This candidate uses a 12 month by 12 month loss triangle for medical insurance. The payment patterns are steady, so he can optimize his model and get significant results.
~ If you work for a property-casualty insurer, you can use quarterly data for automobile liability. Use five years of data (= 20 quarters), so you avoid the long-term claims with a more skewed size-of-loss distribution. Most insurers keep quarterly data.
~ Avoid lines of business with highly stochastic losses, such as medical malpractice and property-liability.
Statistical models are most important for stochastic lines. But stochasticity makes it hard to interpret results. We focus on your use of statistical techniques, not the importance of your findings.
(2) Test basic relations, even if they are obvious. We are not judging if your student project is an important contribution to actuarial science. Use F tests, tests for serial correlation and heteroscedasticity, and analysis of multicollinearity and forecast variance.
(3) You can use the statistical tests in the project templates, even if you use other data for your student project.
This student project is a good illustration.
The candidate converts cumulative losses to incremental losses, following the procedure in the background posting to paid loss triangles.
He has a loss matrix of 12 months by 12 months, for 144 data points. Of these points, ½ × 12 × 13 = 78 are observed and ½ × 11 × 12 = 66 will be forecast.
He first fits a linear relation to the loss dollars. The fit is poor, since the loss dollars have a multiplicative relation, not an additive relation. So he takes logarithms of the loss dollars and re-fits the model, getting a higher R2. This conclusion is expected, which is fine. His student project shows how he arrived at the conclusion.
He examines whether the decay is geometric by examining the residual plots. He observes a parabolic curve, so he examines if a continuous change to the slope parameter improves the regression. If you use actual data, random fluctuation obscures the shape of the residual plot, so try to use data with relatively low stochasticity.
He uses the square of the development age as another independent variable, which greatly improves the R2 of the regression. You can apply this technique to many actuarial projects.
~ If you regress the logarithm of bond price changes on the logarithms of interest rate changes and bond durations, your regression improves if you also use the square of the bond duration.
~ If you regress the logarithm of European (call or put) option price changes on the logarithms of stock price changes and the option delta, your regression improves if you also use the square of the option delta.
The candidate examines if the change in the slope parameter might better be modeled with a dummy variable. We use dummy variables when the changes are discrete. If we model disability payments for a mix of short-term (less than 6 months) and long-term policies (more than 6 months), with different replacement ratios for the two types, we might use a dummy variable for development before and after six months.
He examines the forecasts from his regression model, showing high accuracy for most months but a high error for the twelfth month. (Health insurance payments are often high in December, since insurers want to close their books on settled claims.)
student projects and actuarial work
A good statistical model improves actuarial practice. Many insurers examine development period decay year by year (or month by month, or quarter by quarter), instead of using a statistical model. The reserving actuary may think that using a separate decay rate for each month, quarter, or year provides greater flexibility.
More often, the opposite is true. Using separate decay rates for each development period gives undue weight to outliers and makes the forecasts less accurate. Reserving actuaries now examine various types of decay rates (exponential, inverse power curve) and fit regression models to them.
Some candidates worry that if they choose their own data, they may not get reasonable results, and the student project will not be accepted. They worry that the NEAS faculty member reviewing the student project may say: "This is a silly hypothesis," or "This is not the proper test for this hypothesis."
The contrary is true. Our faculty know that it is hard to form a student project from scratch. A hypothesis that seems silly to an experienced actuary may seem reasonable to a new candidate. We do not test if you choose the optimal statistical test for each hypothesis. We check if you apply the statistical techniques learned in the course.
Our faculty grades more leniently if you design your own student project. If you have an idea, check on the web for data or take something from the NEAS web site. Data is prolific on the web, and you can find data for almost any project. If surfing the web is difficult for you, you can simulate data, using the methods in the project template for loss reserving.
Form a hypothesis and test it with the statistical procedures from the course. You might find that you can’t validate the hypothesis, or that the stochasticity of the data obscures your results. That is fine; many statistical research projects conclude that the data are inconclusive. Document your work in the write-up and send it in.