Friedland11.FreqSev

Reading: Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.

Chapter 11: Frequency-Severity Methods

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• fact A...
• disposal rate method - calculate ultimate/unpaid amounts with trending and adjustments for court decisions

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #20)	disposal rate method: - unpaid	Freq/Sev vs Paid Devlpt: - why Freq/Sev better
E (2019.Spring #15)	unpaid claims: - freq-sev method	identify scenario: - rptd claims down
E (2019.Spring #20)	tail severity: - provide an estimate	tail severity: - selection of maturity age
E (2018.Spring #18)
E (2017.Fall #18)	ultimate: - Freq-Sev method	trend in counts: - explain	seasonality: - suggest diagnostic
E (2017.Fall #20)	ultimate frequency: - select & justify	ultimate severity: - select & justify	ultimate: - B-F & Freq-Sev methods
E (2017.Fall #23)	tail severity: - provide an estimate	tail severity: - selection of maturity age
E (2017.Spring #16)	IBNR: - Freq-Sev method	ads/disads: - Freq-Sev method
E (2017.Spring #17)	ultimate: - Freq-Sev method
E (2016.Fall #20)	disposal rates - good: - Freq-Sev method	disposal rates - not good: - Freq-Sev method	adjustments: - to Freq-Sev method
E (2016.Fall #22)	settlement rate change: - provide evidence	ultimate: - Freq-Sev method
E (2016.Spring #19)	does Freq-Sev work?: - long-tailed lines	does Freq-Sev work?: - many reopened claims	does Freq-Sev work?: - spike in high-severity clms	does Freq-Sev work?: - change in case reserving
E (2015.Fall #20)	does Freq-Sev work?: - general liability	does Freq-Sev work?: - reduced deductibles	unpaid claim estimate: - suggest improvement
E (2015.Spring #20)	ultimate: - use several methods	do methods work: - discuss
E (2015.Spring #21)	disposal rate method: - ultimate	disposal rate method: - adjust for severity spike
E (2014.Fall #16)	estimate of counts: - assess reasonableness
E (2014.Fall #17)	disposal rate method: - unpaid	legislative reform: - assess impact
E (2014.Spring #16)	ultimate counts: - reins. attachment points
E (2013.Fall #16)	IBNR: - Freq-Sev method
E (2013.Spring #19)	IBNR: - Freq-Sev method

In Plain English!

Example A: Intro to FS Methods

Alice likes to use "FS" as an abbreviation for Frequency-Severity so we'll follow her lead. The concept behind FS methods is super-simple. Recall:

frequency = counts /exposures

severity = losses / counts

I'm going to use the term "losses" in this chapter, not "claims". (The reason is that it's too easy to get "claims" confused with "counts") So, we'll refer to losses and counts. Recall also that in practice paid counts usually means the same thing as closed counts. That ignores the possibility of partial payments where a claim could be paid but not technically closed, but let's agree for our purposes here that paid & closed mean the same thing.

The simplest possible example of the FS method is this:

• ultimate counts for AY 2025 = 100
• ultimate severity for AY 2025 = $2,000

Then,

• ultimate loss for AY 2025 = 100 x $2,000 = $200,000.

This is because if you multiply the counts by the severity, the counts cancel out and the result is losses.

Example B: FS Methods - Developing Counts and Severities

Let's build on the idea from the previous section. Instead of being given the ultimate count and ultimate severity directly, you have to go back 1 step and start with the reported count and reported loss triangles. Here are the steps, but you could probably guess without being told:

• develop counts to ultimate
• calculate the severity triangle as losses/counts
• develop the severities to ultimate
• calculate the ultimate loss as (ultimate count) x (ultimate severity)

That's all there is to it. There's really nothing new - it's just an application of the development method to a triangle of severities. Here's an exam problem based on this idea along with Alice's solution.

E (2019.Spring #15)

Solution: 2019.Spring #15

Practice: 2 problems like 2019.Spring #15

Since Alice has been through all of this before, she has a couple of pro tips for you:

Alice's Pro Tip for Maximizing Exam Score: For reserving questions, pay attention to whether they ask for ultimate or unpaid amounts.

Comment: If the question asks for the unpaid amount but you stopped after calculating the ultimate, you would likely lose 0.25 pts. This is obviously an unnecessary loss of points but under the pressure of the exam it's very easy to miss details like this. Train yourself to take 5 seconds and check that you gave them what they asked for.

Alice's Pro Tip for Optimal Time Management: You are usually asked about 1 specific AY. Save time by doing only the calculations you need for that AY.

Comment: This pro tip is a little trickier to apply but can save you oodles of time. In real reserving work, you would calculate the ultimate loss for all years but on the exam they usually only ask for 1 year, often the most recent year. If you are observant you'll notice there are calculations you can skip because they pertain to years you're not asked about.