Friedland10.CapeCod

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

Chapter 10: Cape Cod Method

BattleTable

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

• fact A...
• fact B...

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #19)	ultimate claims: - reported Cape Cod
E (2019.Spring #18)	ultimate claims: - reported Cape Cod	identify scenario: - paid CC works better
E (2018.Spring #8)
E (2017.Fall #21)	ultimate: - Cape Cod
E (2017.Spring #23)	ultimate: - paid devlpt	ultimate: - Cape Cod
E (2016.Spring #18)	Cape Cod vs B-F: - compare	Cape Cod vs B-F: - adjustments to rptd loss	Cape Cod vs B-F: - adjustments to EP	court decision: - identify best method
E (2015.Spring #17)	IBNR: - Cape Code adjustments
E (2014.Spring #15)	IBNR: - B-F	IBNR: - Cape Cod	B-F vs Cape Cod: - rising claims, thin data
E (2013.Fall #20)	IBNR: - Cape Cod

In Plain English!

Example A: Intro to the CC Method

Great news! You can cover the CC method pretty quickly because it's very similar to the BF method. The formulas for Ult_r-BF and Ult_r-CC look exactly the same as you can see below:

Ultr-BF    =   (reported claims) + %unreported x UltECR   =   (reported claims) + (1 – 1/CDF) x UltECR Ultr-CC   =   (reported claims) + %unreported x UltECR   =   (reported claims) + (1 – 1/CDF) x UltECR

The difference is in how Ult_ECR is calculated.

BF: You calculate Ult_ECR using the ECR method. The ECR method does adjust for trend and tort reform but the final ECR selection is judgmental. For a quick refresher, see: ECR Method Trend Adjustment and ECR Method Tort Reform Adjustment.

CC: You calculate Ult_ECR using a formula. There is no judgment involved. The formula makes adjustments the losses for trends and tort reform but also makes adjustments to the EP.

Before we look at an easy example of the CC method, you need to understand the concept of used-up premium or UUP for short. Suppose you're given the data set below. Normally if you wanted an overall loss ratio, you'd first multiply the reported claims by the CDF, take the sum, then divide by the sum of the EP. If you check you'll see that works out to 110.4%. But now we're going to do it kinda backwards: Instead of multiplying the reported claims by their CDF, we divide the EP by the CDF as an alternate way of putting the claims and EP on the same level. This is shown in the table.

CY/AY	reported claims	CDF to ult	EP	UUP = EP / CDF
2023	750	1.5	1,000	667 = 1,000 / 1.5
2024	475	2.5	1,000	400 = 1,000 / 2.5
2025	250	4.0	1,000	250 = 1,000 / 4.0
total	1,475	--		1,317

The CC method then uses 1,475 / 1,317 = 112.0% as the ECR. No judgment, it's just a formula. Note that that it doesn't match the 110.4% calculated above. It's close, but algebraically they are not equal. Friedland describes the concept of used-up premium as follows:

The used-up premium represents the premium corresponding to the claims that are expected to be reported through the valuation date.

Further down, there are a couple of relatively easy practice problems. Note there is 1 extra step in these problems because you have to apply the pure premium trend to the losses before calculating the ECR. Be careful: If you're given a pure premium trend, remember that it applies to losses not premiums. Without digressing too much, we learned (or will learn) from pricing that:

• frequency = counts / exposures
• severity = dollars / counts

Then if

• pure premium = dollars / exposures

by simple algebra we have

• pure premium = frequency x severity

(It's a common mistake to apply the pure premium trend to the premiums instead of the losses.)

Practice: 2 problems on the basic CC method

Example B: Apply CC to Specific Years

We're going to revisit the practice problems from the previous section but instead of calculating the ultimate for the most recent AY, we're going to do it for earlier AYs and that requires an extra adjustment. We had 3 AYs: 2023, 2024, 2025. In both, you were asked to calculate the ultimate for AY 2025 which was the most recent AY. The first two practice problems below are the same except in the first one you have to instead calculate the ultimate for AY 2024; and in the second, for AY 2023.

CC method for earlier AYs: To calculate the ultimate for a particular AY, you have to restate the ECR to be at the level of that AY

The reason for this extra adjustment is that the way we applied to CC method, the calculated ECR was at the level of the most recent AY. But if we want the ultimate for a different AY, we have to put the ECR at the level appropriate for that AY. For this problem, that means detrending the ECR by an appropriate number of years. (There are potentially other adjustments as well but we'll get to those in the next section.)

Practice: 2 problems on CC method with detrending

Example B: A Hard CC Problem

Once you understand the basic version of the CC method, here's a harder problem for you to try. It's harder for 2 reasons:

• they don't give you the rate level adjustment factors directly – you need knowledge of the pricing material to calculate them yourself
• they don't give the CDFs (Cumulative Development Factors) – you have to calculate them yourself from the data triangle but it's very tricky because you first have to adjust the triangle to take into account the tort reform

Give it a try before you watch the video. Part (a) is an application of the paid development method but you have to that before you do the CC method in part (b)

E (2017.Spring #23)

CC Method Concepts

• similar to BF - difference is in how ECR is chosen
  • BF uses results of ECR method (incorporates judgment)
  • CC uses a formula (no judgment involved)
• often use in reinsurance (why?)
• assumption: unreported claims will develop based on expected claims
• ads:
  • uses reported claims in the calculation of the ECR, therefore it will respond (at least partially) to changes in claims ratios
  • (note that if the CR changes over time, increases or decreases, then this trend may not be reflected in the CC formula for ECR)
• disads:
  • dependent on the availability and accuracy of the rate level adjustment factor (can use without adjusting for CRL but then lose accuracy)
  • thin data increases volatility (should then use BF because we can incorporate judgment)