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: - calc unpaid	Freq/Sev vs Paid Devlpt: - why Freq/Sev better
E (2019.Spring #15)	counts x severities: - calculate unpaid	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)	counts x severities: - calc ultimate (seasonality)	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)	counts x severities: - calc ultimate (law change)
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	counts x severities: - calc ultimate
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)	counts x severities: - calc IBNR
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, let's go back 1 step and start with the reported count and reported loss triangles. Here are the steps, but you could probably guess them without being told:

• develop counts to ultimate
• calculate the severity triangle as losses/counts
• develop 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 and a couple of practice problems.

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 Your Exam Score: For reserving questions, pay attention to whether they ask for ultimate or IBNR or unpaid amounts.

Comment: If the question asks for the unpaid amount but you stop 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 only doing calculations needed 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 only to years you're not asked about.

I'm going to ask you to look at another exam problem below that also uses the counts x severities idea, but there's a twist because the data triangle is organized by AHYs or Accident Half-Years and you have to take into account seasonality. So instead of rows in the triangle representing 12-month periods January-December, they now represent 6-month periods January-June, July-December. The development method doesn't specifically treat AHY triangles any differently from AY triangles but sometimes the January-June rows develop differently from the July-December rows. And we know from earlier discussions on the development method that changing development patterns can lower the accuracy of the results.

The source text has a very detailed discussion of seasonality, but I think this exam problem demonstrates the idea more clearly. The seasonality twist is this:

• After you calculate the LDF triangles for counts and severities, it's very obvious that the January-June AHYs develop differently from the July-December AHYs. That means you have to make 2 LDF selections for each development period: one based on January-June LDFs, the other based on July-December LDFs. You then get 2 corresponding sets of CDFs. If you don't do that then one half-year will get LDFs that are too high and the other will get LDFs that are too low.

It is not a hard problem but is very good for demonstrating seasonality.

E (2017.Fall #18)

And here's one more. This one requires an adjustment for a new law that will reduce claims by 25% but that's something we've covered in earlier chapters. You just have to make sure you restate older data to take into account the benefit change.

E (2017.Spring #17)

And last one for now, promise. Here, you have to decide whether to use the paid count or reported count triangle to get the ultimate counts. In practice, you might develop both triangles to ultimate then make a selection based on a weighted average of the results, but they don't want you to do that here.

E (2016.Fall #22)