CAS Exam Errata

Study Guide & Review Videos

There are no fixes to announce for Spring 2025.

Cookbook

There are no fixes to announce for Spring 2025.

Practice Problems

There are no fixes to announce for Spring 2025.

The Exam 6 (US) Course is currently on pause.

Study Guide & Review Videos

Brosius (12/2/24) – Typo on pages 24 and 26. The formula for the slope “b” should show bar(x^2) – bar(x)^2 in the denominator.

Mack Chain-Ladder (12/7/24) – Two typos on page 129 in the AY 2023 SE calculation. The ultimate loss (C_4,4) should say 322, not 403. Also, in the final term, it should be 1/304 + 1/260. The calculated SE is correct as shown.

Meyers (12/11/24) – On page 317, all of the “5” subscripts should be replaced with “10.” The calculations are correct as shown.

Shapland (12/20/24) – See typos below:

• Page 188 – Last cell of hat matrix should say f_1,3, not f_3,1
• Page 192 – In Step 11, central estimates should be called point estimates
• Page 206 – Final bullet under GLM bootstrap model should say that each parameter set is used to calculate future incremental values
• Page 224 – Under normality plot, theoretical quantiles are on x-axis and observed data are on y-axis. Also, Shapland’s plot is not a 45-degree line (just a diagonal line) since axes on different scales

Hurlimann (12/20/24) – On page 9, S_ik should be labeled as incremental losses.

Verrall (12/20/24) – On page 363, when describing the impact of beta, it should low/high confidence in prior mean, not parameter estimates.

Clark (12/20/24) – On pages 111-113, the expected losses should say 3,541, not 3,451. All calculations are correct as shown.

Cookbook

There are no fixes to announce for Spring 2025.

Practice Problems

There are no fixes to announce for Spring 2025.

Study Guide & Review Videos

Fisher Ch. 3 (10/3/24) – Just a quick clarification for the hybrid approach on page 238. The words “aggregate loss ratio” are misleading. This is not an actual loss ratio. It’s the aggregate losses divided by the expected losses as noted in parentheses.

Bahnemann Ch. 6 (10/3/24) – On the bottom of page 299, the AL premium should say $888, not $666.

Mahler (9/9/24) – On the top of page 25, the Method 4 probability should be 3/3, not 4/4.

Fisher Ch. 3 (8/30/24) – In the second step on page 230, the second balance equation should show “367.5k – H” in the numerator, not “336k – H.” Since making this correction leads to a non-sensical basic premium, we had to revise a few inputs to the example. The minimum premium was revised to $250,000. The 1.65 – 1.69 entry ratios were revised to 1.55 – 1.59 with charges of (0.176, 0.173, 0.171, 0.168, 0.167). This leads to a revised net insurance charge of -$2,100 and a revised basic premium of $17,690. We have reposted the guide with these changes.

Fisher Ch. 3 (8/30/24) – At the top of page 250, the excess ratio should be 0.79, not 0.21.

Bahnemann Ch. 5 (8/30/24) – On page 295, the reference to the Poisson distribution in the example at the bottom should be removed. On page 293, the “1.10”s in the numerator of the average untended claim size should not be there. On page 289, the example should say “attachment point of 3,000 and a layer limit of $5,000.”

Bahnemann Ch. 6 (8/30/24) – At top of page 308, the first bullet should say “with non-risk-loaded ILFs.”

Fisher Ch. 1 (8/19/24) – On pages 162 and 164, the claim 1 value should be $1,500 instead of $1,150. We will upload a corrected video soon.

Fisher Ch. 3 (8/19/24) – At the bottom of page 226, the second property should say phi(r) approaches 0 as r approaches infinity.

Bahnemann Ch. 6 (8/19/24) – Per the text’s official errata, the following formulas need to be adjusted: 1) the numerators at the bottom of page 304 should not include the (1+u) factors and 2) the risk load formula at the top of page 308 should not include include (1-F_X(a)) in the denominator. We will upload a corrected video soon.

NCCI Circular – Retro Rating Plan (8/10/24) – The updated study kit was made available by the CAS in the last few weeks. Material changes were made to the NCCI Circular – Retro Rating Plan. The informational exhibits and plan updates were removed, and a bit more detail was added regarding the retrospective development premium. The video has been updated as well.

NCCI – Experience Rating Plan (8/5/24) – The video’s description of interstate vs. intrastate risks was flip-flopped. It has been corrected and reposted.

NCCI – Experience Rating Plan (7/29/24) – On page 180, the final calculation for the manual rate is incorrect. The manual rate should be based on the estimated payroll for the policy period (2.5M for class 005 and 10M for class 2589). This changes the solution of the standard premium to $186,698. This video has been corrected as well.

GLM 2 (7/25/24) – On page 50, the formula for the fitted value of the 35-year-old unmarried driver has a typo. It should say “330.30 x 33.115 x 1 = $10,938.”

GLM 5 (7/25/24) – On page 87, there is a typo in the first paragraph. It should say “The linear fit over-predicts for low building ages, under-predicts for middle building ages, and over-predicts for high building ages.”

GLM 6 (7/25/24) – On page 100, under the formula for the scaled deviance, it should say “where ll_saturated and ll_model are the log-likelihoods for the saturated model and the model being evaluated, respectively.” The video has been corrected as well.

Fisher 3 (7/25/24) – On page 226, there is a typo in the third property of the “five important properties of phi(r) and psi(r).” It should say “psi(r) goes to infinity as r goes to infinity.”

Mahler (7/21/24) – At the bottom of page 14, the total EP should be $54M, not $56M. This changes the final chi-squared test statistic to 2.60824. The conclusion is the same. The video has been corrected.

GLM 6 (7/21/24) – On page 105, the “negatives” in front of the AIC & BIC figures should not be there. The video has been corrected.

Couret & Venter (7/17/24) – On page 33, in the second sentence, it should say “Under WC coverage, insureds retain losses…”

Mahler (7/17/24) – At the top of page 29, for the second scenario, the 2024 estimate should be 0.50(0.023) + 0.10(0.062) + (0.40)(0.0345) = 0.0315. The video has been corrected.

Fisher Ch. 3 (7/15/24) – On pages 229 & 243, there is a typo in the first balance equation. The numerator should say “(e + E)T – H” instead of “(e – E)T – H.” The videos have been corrected.

Cookbook

NCCI – Experience Mod (8/26/24) – For claim 4, both the primary and excess loss portion need to be reduced by 70% (multiplied by 0.3). This wasn’t done for the primary loss (Cell E90).

ISO – Experience Rating (8/23/24) – The formulas for ISO Rule 15.C are updated for clarity in the discussion section and some more detail is included to explain how the adjustments work.

NCCI Circular – NCCI Retro Prem (8/10/24) – We updated this for the 2024 study kit to include the Retro Development Premium.

Fisher Retro – LDD Premium (7/24/24) – I noticed an error in the LDD Premium formula in the Excel version. The step 5 formula should use the same formula from step 4 for the LDD loss cost. We fixed and re-posted an updated version. The PDF version and formula summary are correct.

Problem Bank

GLM 2-4 #11 (10/15/24) – As a note of clarification, see GLM (pg. 38):
For a GLM, model complexity is measured in terms of degrees of freedom, or the number of parameters estimated by the model-fitting procedure.

RF Bahnemann – 17 (9/24/24) – The total loss and claim count numbers weren’t internally consistent with the claim size ranges. We fixed the data in the table. The methodology and approach is the same.

RF Couret & Venter – 3 (9/12/24) – The ELF was incorrectly multiplied by the expected ground-up loss. ELFs should be multiplied by the Standard Premium (unless a problem states otherwise).

RF GLM 2-4 – 12 (9/3/24) – I modified the question for part a to exclude the intercept in the design matrix, similar to how it’s shown in the paper (pg. 13). Technically, the design matrix that the GLM fits to includes a column for the intercept (with a 1 for all records).

For part b, the number of parameters is 8. The intercept is itself a parameter.

RF GLM 2-4 – 9 (9/3/24) – For part b, the paper (pg. 33) seems to conflate the response variable and explanatory variables. In statistical modeling, the response variable is the dependent variable, which is the target variable.

RF Bahnemann – 20 (8/29/24) – The v in the denominator of the pricing formula incorporates the variable expenses plus the load for profit and risk (see page 164 of the text). The risk-loaded ILFs reflect the different amounts of risk load for different limits, with higher limits having higher risk loads.

I modified the problem slightly to break out the variable expenses from the profit load and risk load in the basic limits premium for clarity.

RF Bahnemann – 17 (8/29/24) – The total loss for the 5000-10,000 group should be 168,400.

RF Bahnemann – 10b (8/22/24) – The formula shown in text to the right of the answer should have E[X; a + L] – E[X;a] in the denominator. The answers are correct as shown.

RF Fisher Exper – 6 (8/20/24) – Minor: Given the evaluation date, policy period 2024 shouldn’t have been in the table. We modified the problem slightly to change the evaluation date and adjusted the LDF headers to correspond.

RF ISO – 4 (8/20/24) – I modified the wording of the part a prompt for clarity. Also, there was a mistake in the ARULL calculation. The calculation missed the first year by mistake.

Secondly, the BLEL calculations referenced the wrong Sales years and the new policy was meant to be an occurrence policy. I fixed that. I also added some more clarity in the wording/discussion since we’re solving for the standard premium for the policy being priced, so at policy limits.

RF Bahnemann – 10c (8/10/24) – Part c is faulty. You can’t state definitively one way or the other. We do know that the inflation rate for the excess layer would be larger than either the ground-up severity (5%) or the capped insured layer (3.3%).

NCCI Circular Problems (8/10/24) – We updated these problems for the 2024 study kit to include the Retro Development Premium.

RF Bailey – 4  (8/7/24) – We updated the problem prompt and discussion for clarity and to explain how this problem relates to Table 3 in the paper.

Flashcards

Bahnemann Ch. 6 (8/30/24) – On Flashcard 19 (page 39 of the standard PDF), the first sentence should say “with non-risk-loaded ILFs.”

Bahnemann Ch. 6 (8/19/24) – Per the text’s errata, the (1+u) factors were removed from the derivatives on Flashcard 13 (page 26 of the standard PDF). In addition, the (1-F_X(a)) factor was removed from the denominator of the risk load on Flashcard 19 (page 38 of the standard PDF).

NCCI Circular – Retro Rating Plan (8/10/24) – The updated study kit was made available by the CAS in the last few weeks. Material changes were made to the NCCI Circular – Retro Rating Plan. The informational exhibits and plan updates were removed, and a bit more detail was added regarding the retrospective development premium. We updated the NCCI Circular flashcards to align with the updated study kit.

High-Level Summary

Bahnemann Ch. 5 (10/25/24) – The Pareto variance formula should show alpha*beta^2 in the numerator. This is shown correctly in the study guide and formula summary.

NCCI Circular (8/10/24) – Updated for the 2024 study kit to include the Retro Development Premium.

Past CAS Problems

CAS 2017 Q15 (9/23/24) –  The solution incorrectly described a SIR policy for 150k-600k as 600 xs 150 SIR, but it should be 450 xs 150 SIR.

CAS 2019 Q11 (9/17/24) –  Part c was updated to correct the calculation of the efficiency test statistic using manual and standard loss ratios rather than the mod.

CAS 2013 Q19 (9/12/24) –  In part a of the solution, it should say XS ratio instead of Loss Elimination Ratio.

Practice Exams

Exam 1 – Q #23 (9/26/24) –  The Med-Only calculations were incorrect. They should be split $1,200 and $0 for the 11/4/22 claim and $2,100 and $4,200 for the 2/14/21 claim. This is updated.

Exam 1 – Q #18 (9/30/24) –  The excess ratio for $100,000 should have been explicitly given in the problem. Also, the problem should ask for the “modified expected loss” for clarity since the schedule rating is used as well. Q #15 and Q #18 used to be part of a much larger problem together and we split them into different problems this year, but missed the excess ratio used in Q #18.

Exam 2 – Q #21 (10/3/24) –  In the latest table from the study kit, E[N] = 74 corresponds with Expected Claim Count Group ECG 37 (not 74). We updated the problem to include the Limited Table M values for ECG 37 to solve the problem correctly.

Study Guide & Review Videos

There are no fixes to announce for Spring 2025.

Cookbook

There are no fixes to announce for Spring 2025.

Practice Problems

RF Bernegger – 2  (11/25/24) – The data in the table didn’t exactly sum to a 100% probability. We fixed this.

High-Level Summaries

Clark (12/20/24) – On page 3 of the Clark summary, the ELF formula has a ‘U’ in the numerator instead of an ‘L’. It has been fixed.

Flashcards

Clark (12/16/24) – On page 48 of the standard PDF, there was an “U” in the subscript of the ELF that should not have been there. It has been removed.