Analytical comments on each stage of the results, including explaining patterns in the results and any unusual features

Welcome to the World of Analytical Commentary!

In the CP2 exam, your model is only as good as your ability to explain it. You could build the most mathematically perfect spreadsheet in history, but if you can’t explain why the numbers look the way they do, you won't earn those crucial communication marks. In this chapter, we focus on analytical comments—the "storytelling" part of your actuarial work where you explain patterns, spot weird results, and prove your model is reliable. Don't worry if this feels a bit like writing an essay; we’re going to break it down into simple, logical steps!

1. Why Do We Need Analytical Comments?

Imagine you go to the doctor for a blood test. If the doctor just hands you a piece of paper that says "Glucose: 105" and walks away, you'd be confused. You need the doctor to say: "This is slightly higher than last time because you had a sugary snack before the test, but it’s still within the normal range."

That is exactly what you are doing for your "client" (the examiner) in CP2. Analytical comments serve three main purposes:

1. Validation: Showing that the results make sense based on the inputs.
2. Verification: Proving that the model is calculating things correctly.
3. Insight: Highlighting the "So what?"—what do these numbers actually mean for the business or the problem at hand?

2. Explaining Patterns in the Results

When you look at your final output table or chart, you should look for trends and relationships. Most actuarial models follow logical patterns. If you see a pattern, point it out and explain the "driver."

Common Patterns to Look For:

• Linear Trends: If the input increases by 10%, the output increases by roughly 10%. Example: Total premiums should increase linearly with the number of policyholders.
• Compounding Patterns: Results that grow faster over time. Example: A savings fund growing at a constant interest rate \( i \) will follow the pattern \( (1+i)^n \).
• Inverse Relationships: When one thing goes up, the other goes down. Example: As the discount rate increases, the Present Value (PV) of future liabilities decreases.

Quick Tip: Always use "Directional Language." Instead of saying "The results changed," say "The results increased significantly as the mortality rate rose."

3. Identifying and Explaining Unusual Features

This is where many students lose marks. If there is a "jump," a "dip," or a "flat line" in your results, you must acknowledge it. If you ignore a weird number, the examiner assumes you didn't notice it or your model is broken.

What counts as "Unusual"?

• Outliers: One data point that is much higher or lower than the rest.
• Step Changes: A sudden jump in values (e.g., when a tax threshold is hit or a policy limit is reached).
• Asymptotic Behavior: When results level off and stop changing even if inputs keep moving.

How to explain them: Use the "Cause and Effect" method.
"There is a sharp spike in claims in Year 5 (Effect). This is due to the one-off maturity of the high-value endowment policies identified in the data (Cause)."

Did you know? In CP2, a "weird" result isn't always a mistake in your formulas. Often, the examiner builds a "quirk" into the data to see if you are brave enough to spot it and explain it!

4. Commenting at Each Stage of the Model

Analytical comments shouldn't just be at the very end of your report. You should provide brief comments at key stages of your modeling process.

Stage A: Data Preparation

When you clean your data, comment on any patterns you saw.
Example: "The data shows a 5% increase in average salaries over the period, which is consistent with the inflation assumptions provided."

Stage B: Calculations/Intermediate Results

Check if the "middle" steps look right.
Example: "The intermediate survival probabilities \( p_x \) decrease with age, which is expected as mortality risk increases for older lives."

Stage C: Final Outputs and Sensitivities

This is the most important part. Explain how sensitive the result is to certain assumptions.
Formula Alert: If you are checking the sensitivity of a result \( R \) to a change in assumption \( A \), you are essentially looking at:
\( \frac{\Delta R}{\Delta A} \)

If a small change in the interest rate causes a massive change in the pension deficit, you must comment on this volatility.

5. The "Reasonableness" Check

Before finalizing your comments, ask yourself: "Does this pass the smell test?"

If your model says a 25-year-old needs to save \$10 million a month for retirement, something is wrong. If the model is correct (based on the bizarre instructions given in the exam), your comment should acknowledge that the result seems high and explain why (e.g., "The required savings are exceptionally high due to the target retirement age being set at 30.").

Common Mistake to Avoid: Don't just describe the table.
Bad: "In Year 1 the value is 10, in Year 2 it is 12." (The examiner can see the table!)
Good: "The values show a steady 20% growth year-on-year, reflecting the compound interest effect."

6. Summary and Key Takeaways

Quick Review Box:
- Patterns: Explain the direction and driver of the trend.
- Anomalies: Don't hide them! Spot them, explain the cause, and state if they are expected.
- Sensitivities: Explain which assumptions have the biggest impact on the final answer.
- Language: Use clear, non-jargon terms so a "non-actuary" could understand your logic.

Key Takeaway: Analytical commentary is about proving you are in control of the model. You aren't just a calculator; you are the interpreter of the data. Keep your comments concise, logical, and always link the "What" (the number) to the "Why" (the model logic or data).

Don't worry if you find it hard to spot patterns at first. The more you practice looking at your output charts instead of just the cells, the more natural it will become. You've got this!