Welcome to Data Assumptions!
In your CP2 journey, you will quickly realize that real-world data is rarely perfect. It can be messy, incomplete, or just plain weird. This is where assumptions come in. Think of assumptions as the "bridge" that connects the imperfect data you are given to the working model you need to build. In this chapter, we will learn how to make smart, professional choices when the data doesn't give us the full story.
Don't worry if this seems a bit like guesswork at first. Actuarial assumptions aren't just random stabs in the dark; they are reasoned justifications based on the information we have. By the end of this note, you'll feel much more confident in handling "ugly" data!
1. Why do we need to make assumptions?
When you receive a dataset for a CP2 project, you might find gaps. Maybe some policyholders forgot to list their age, or perhaps a column of numbers has a few obvious typos. If we simply ignore these issues, our model might crash or produce wrong results.
We make assumptions to:
• Fill in missing information.
• Correct obvious errors (anomalies).
• Simplify complex data so the model runs efficiently.
• Create a proxy when the specific data we want isn't available.
The Everyday Analogy: Imagine you are following a recipe to bake a cake, but the page is torn and you can't see how much sugar to use. Based on your experience with other cakes, you assume one cup is about right. That is exactly what we do with data—we use what we know to fill in the blanks.
2. Dealing with Missing Data
Missing data is the most common hurdle. You have two main ways to handle it, and the choice you make depends on how much data is missing.
A. Removing the Data (The "Delete" Approach)
If only a tiny fraction of the data is missing (e.g., 2 records out of 10,000), it might be safest to simply exclude them. You assume that these few records won't change the overall result.
B. Imputing the Data (The "Fill-in" Approach)
If a lot of data is missing, deleting it might bias your results. Instead, you make an assumption to fill it in. For example:
• Averages: If the "Entry Age" is missing, you might assume the person is the mean or median age of the rest of the group.
• Prudence: In some cases, you might assume a "worst-case" scenario to be safe (e.g., assuming a missing smoker status is "Smoker" for a life insurance model).
Quick Review: Always ask yourself—"Will my assumption materially change the final answer?" If the answer is yes, you must explain your choice very carefully in your audit trail!
3. Handling Outliers and Anomalies
An outlier is a data point that is so far away from the rest that it looks wrong. For example, if you see a policyholder whose age is listed as 150, or a monthly premium of \$-5,000.
How to handle these?
1. Cap and Floor: You might assume the age is actually 100 (capping it) or 18 (flooring it) if those are the policy limits.
2. Correction: If a value is clearly a typo (e.g., 202.3 instead of 2023), you might assume the intended value based on the surrounding context.
3. Removal: If the data point is physically impossible and you can't guess the right value, exclude it.
Did you know? In the CP2 exam, markers care less about which assumption you made and more about why you made it. There is often no single "right" answer, only a "well-justified" one.
4. Using Proxies
Sometimes, the data you need simply doesn't exist. In these cases, you use a proxy—a substitute that behaves similarly to the missing data.
Example: You are modeling car insurance claims for electric vehicles (EVs), but you only have data for petrol cars. You might assume that EV drivers behave similarly to petrol car drivers, perhaps adding a small percentage increase to repair costs because EV parts are more expensive.
Memory Aid: The P.A.R. Test
When making an assumption, check if it is:
• Practical (Can it be easily modeled?)
• Appropriate (Does it make sense for this specific problem?)
• Reasonable (Would another actuary agree with you?)
5. The Audit Trail: Documenting Your Assumptions
In CP2, if it isn't documented, it didn't happen! This is the most important part of the "Preparation and analysis of data" section. You must write down every assumption you make about the data provided.
What to include in your documentation:
• What the assumption is (e.g., "Assumed missing ages are 45").
• Why you made it (e.g., "45 is the average age of the valid records").
• The Impact (e.g., "Since only 1% of data was missing, the impact on the final premium is expected to be minimal").
Common Mistake to Avoid: Don't just say "I assumed the missing values were 0." You must explain why 0 is a sensible choice. If it's not sensible, don't do it!
Summary Checklist
Before you move on to the modeling phase, ensure you have:
• Identified all missing or inconsistent data points.
• Decided whether to exclude or adjust those points.
• Check if your assumptions are consistent with the overall objectives of the task.
• Written a clear justification for each assumption in your summary document.
Key Takeaway: Assumptions are not "cheating"—they are a necessary tool to make a model work. Just be honest about what you've done and explain your logic clearly!