CAS Exam Errata

Study Guide & Review Videos

WM Ch. 15 – (8/19/24) – On page 246, in the paragraph below the fourth step, the final line should be $142,500($34.28) = $4,884,900. We must divide the receipts by 1,000 to align with the trended composite exposures calculated in step 4.

Friedland Ch. 17 – (8/14/24) – At the bottom of page 460, Step 6 uses an incorrect value for the total claims basis B. Using the correct value of B = 545,727, the indicated unpaid ULAE for the B-F and Development Style Methods changes to $16,767 and $17,152, respectively. A corrected video will be posted soon.

Practice Exams

Exam 1 Q #16 – (8/19/24) – The 48-ultimate factor given in the problem is supposed to be 60-ult.

Exam 2 Q #8 – (10/21/24) – The overall relativity change should be calculated by divided the overall exposure-weighted indicated relativity by the overall exposure-weighted current relativity – 1. This results in a relativity change of -5.5% and a proposed base rate of $1,120.

Study Guide & Review Videos

CFR Ch. 7 – (3/8/24) – In the solution to part c. on page 275, the UEPR should only include the first two columns from the U&IE. Hence, UEPR = 2,000 + 500 = 2,500. This changes the final answer to part c. to $8,450,000. Although Odomirok sums all four columns when showing the UEPR on the U&IE, the last columns get subtracted out at the very bottom of the U&IE, which means the final UEPR that makes it way to the balance sheet is just the sum of the first two columns. I will be re-doing this section of the Ch. 7 video to make that more clear. See 2014 #14 for another good example of calculating UEPR from the U&IE.

CFR Ch. 19 – (3/14/24) -On page 562, the description of the RBC charge for an investment affiliate should simply say “the RBC charge for an investment in an investment affiliate is 0.225 times the carrying value of the common and preferred stock, adjusted for the owernship in the investment affiliate.” In our opinion, there is an error in this section of Odomirok. In 2016, the NAIC moved from the “look through” approach (described in the second paragraph of this section in Odomirok) to the “22.5% of the carrying value of common and preferred stocks.”

NAIC Preamble – (3/18/24) – On page 795, the bullet around precision should say “The degree of precision matters. If a judgment item can be precisely estimated, the materiality threshold should be lower.” On page 798, the solution to 3b should say “MORE precision leads to a lower materiality threshold.”

Porter 6 – (3/25/24) – On pages 95, part a. should ask for the “minimum requirement for this insurer.” On page 96, the solution should say “the minimum requirement is the sum…”

Flashcards

NAIC Preamble – (3/18/24) – On card 3 (page 6 of standard PDF, page 2 of printable PDF), the last sentence should say “…significantly different outcomes in regulatory requirements.” On card 4 (page 8 of standard PDF, page 4 of printable PDF), it should say “Lower materiality thresholds should be used when there is more precision in estimating errors.”

Practice Exams

PE 1 Q5 – (4/26/24) – In the problem prompt, the Scenario B industry losses should be $4B, not $4M.

PE 1 Q20 – (4/26/24) – The problem prompt for part b. should refer to 2022, not 2021.

Study Guide & Review Videos

Friedland (12/7/23) – There is a typo on page 142. The title of the third table should be “Abs. Diff. — Reptd. Age-to-Age Factors.”

Taylor & McGuire (1/21/24) – On the Over-Dispersed Poisson slide of the video, the factorial after “(y/phi)” was missing in the first few lines. The video has been corrected and reposted.

Venter Factors (1/25/24) – The conclusion shown in the Venter Factors Stability Tests workbook (located under “Extras for Download -> Paper Exhibits & Other Examples” in the Online Course)  for Stability Test #2 is not valid. Since the age-to-age factors do not appear to rotate around some fixed level, we should give more weight to the most recent age-to-age factors when making a final selection. The workbook has been corrected and reposted.

Venter Factors (1/25/24) – In MP #1 part c., the language used in the problem prompt is misleading. The word “improving” should be replaced with “dealing with.” The point is that using a weighted average of age-to-age factors does not mean the instability improves. It’s just a way of handling it.

Verrall (2/16/24) – On page 739, the first disadvantage of the ODP model should just say, “It requires the column sums of incremental values to be positive to ensure a positive variance.”

Venter Factors (2/26/24) – On page 343, in the second to last bullet, it should say “left with four f(d) parameters and h = 1.”

Mack 1994 (3/29/24) – In the Excel version of the Mack 1994 OPs, the solution to EP #1  has a typo under Option 3. It should say “This formula ensures that alpha_I-3/alpha_I-2 = alpha_I-2/alpha_I-1.”

Teng & Perkins (4/1/24) – On page 611, the retro premium ratios in the Expected & Actual graphs were chosen poorly. The Expected graph should have a point of (55%, 82.5%) and the Actual graph should have a point of (50%, 70%). These changes will produce the shown slopes of 1.5 and 1.4.

Taylor & McGuire (4/11/24) – In the Excel solution to MP #3e, there is a small typo. It should say “gamma” distribution, not ODP distribution.

Hurlimann (4/11/24) – This is a clarification on the reserve iteration formula on page 27 of the guide. The quantity R_i^(0) is equal to R_i^coll. This has to be true in order for U^(m+1) = q_i * U^(m) to work.

Taylor & McGuire (4/19/24) – Clarification on page 701. The formula mu = [(1-p)*theta]^(1/(1-p)) holds for p NOT EQUAL to 1. For p = 1 (Poisson), mu = e^theta.

Cookbook

Shapland – Expected Incremental Losses from GLM (2/29/24) – In the Excel version, the second formula in the discussion section should show:

nu_1,d = c + sum(betas)

Shapland (1/25/24) – In the Excel version of the “Negative Incremental Values” recipe, the solution to part a. is pointing to the incorrect set of incremental losses. The adjusted log-link triangle should be pointing to the incremental losses in cells D8:F10. The workbook has been corrected and reposted.

Past CAS Problems

Venter Factors 2016 #6 – The second 48-60 LDF of 1.027 shown in the triangle should not be there.

Problem Bank

Siewert (2/7/24) – In the first line, it should say that the deductible is 100k (not 500k).

Taylor & McGuire (3/13/24)– In the solution to RF #7a, the condition of “X_k,j” should not be there. It should just say “Y_k,j ~ …”

Marshall (3/16/24)– In the solution to RF #2b, the WC CoV chart should be 24%, 16%, 10%, and 6% so that it is NOT linear.

Taylor & McGuire (3/29/24) – In the Discussion section of RF Taylor-4, the Distribution when p = 3 should say Inverse Gaussian, not Inverse Gamma.

Friedland (4/1/24) – In the text shown in cells M2:T4, it should say “so only Policies B and C attach…” The rest of the solution is correct.

Practice Exams

PE 1 Q6 (4/3/24): It should say 95% confidence interval in cell L5.

PE 2 Q11 (4/9/24): The prompt for part b. should say “For two of the assumptions stated…”

PE 2 Q13 (4/9/24): In the solution to part c., the pro (explicitly recognized excess loss development) was duplicated by error. The other two statements are the cons.

PE 1 Q5a (4/11/24): The option “Observations Y comes from the ODP distribution” should also be checked. This is discussed on pg. 49 in the Clark paper for modeling incremental losses.

Flashcards

Taylor & McGuire (2/2/24) – On card 11 (page 22 of standard PDF, page 8 of printable PDF), the condition of “X_k,j” should not be there.

Shapland (4/7/24) – On card 18 (page 35 of standard PDF, page 12 of printable PDF), the formula should show an “H” above the “r” to represent standardized residuals.

High-Level Summaries

Siewert (3/23/24) – “Deductible Loss Charge” should instead be “Per Occurrence Charge” (chi).

Taylor & McGuire (2/2/24) – On page 50, under the “Cross-Classified Model” Assumptions, the condition of “X_k,j” should not be there.

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.

Practice Exams

PE 1 Q#3 (4/2/24) – There was a referencing error in this problem. The combined ratio in part a should now be 100.7%. We quickly caught this and uploaded a corrected version.

PE 2 Q#18 (4/21/24) – We should use a = 9%, b = 1 and k = 15%. For next sitting, I will reword the part c prompt to: “Calculate the updated duration of total economic value if the target return is set to the risk-free rate of interest plus a risk premium, such that current target return matches management’s selection.”

Study Guide & Review Videos

The first five errata were posted before we uploaded the revised study guide due to the changes in Exam 9 Content Outline. If you downloaded the study guide after December 6, you can ignore the first five errors below since they were corrected in the revised guide.

Clark (11/8/23) – There is a typo on page 8. In the paragraph below the table, the second line should say “1.03^5 = 1.159,” not 1.086.

Clark (11/12/23) – There is a typo on page 34. In the fourth bullet of the Swing Plan example, the minimum premium should be 10%, not 15%.

Clark (11/29/23) – There is a typo on page 29. In the General Liability exposure rating example, it should say that “an actuary is pricing a 7.5M XS 2.5M excess of loss treaty.” We will correct the video as well.

Mildenhall Ch. 4 (12/1/23) – On page 123, an extra row needs to be added at the bottom of the table in the example. When p = 0.9, VaR = 12, TVaR = 25, and CTE = 25. When p > 0.90, VaR = TVaR = CTE = 25.

Clark (12/5/23) – A few items were included in the Clark outline that are not included in the most recent version of the paper. The following items have been revised:

• Page 5 – Discussion under step 5
• Page 8 – Discussion under step 4
• Page 41 – Discussion under pricing cat covers
• Pages 45 – 46 – Discussion around ROE and allocated surplus have been removed

The following errata were posted after we uploaded the revised study guide on December 6.

Clark (12/12/23) – On page 18, the Trended, Developed Treaty Losses should be $1,071,280.

Mildenhall Ch. 4 (12/22/23) – In the crossed pairing example on page 113, we should only be crossing the top 4 values of X_1 and X_2. Thus, the pairs should be (52, 8), (36, 12), (18, 23), and (10, 40). These pairs produce X values of 60, 48, 41, and 50. Then, VaR_0.70(X) = 41. See the forum discussion on this for more details.

Clark (1/16/24) – On page 36, the Poisson probability formula has an error in it. The formula should be lambda^(n) * exp(-lambda) / (n!).

Grossi Ch. 6 (1/17/24) – On page 77, the final amount ceded to the XOL treaty should be 0.50 x MIN(6.8 – 2.0, 4) = 2.0. The final net loss to the insurer is $6.8M – $2.0M = $4.8M.

Mildenhall Ch. 9 (1/17/24) – On page 158, at the top of the page, the “Net X2” value for the second row in the table should be 1. On page 161, under the second step, the alpha shown should be 100, not 50. The calculated VaR shown in step 2 is correct.

Brehm Ch. 5 (1/17/24) – On page 330, under the “Supply and demand” section, the last sentence in the first bullet should say “better performing business,” not better performing firms.

Mildenhall Ch. 10 (1/20/24) – On page 167, the “and h” should be removed from the last bullet. On page 169, under the big Example in the middle of the page, the second bullet should be h(p) = h(0.05) = 1 – g(0.95) = 0.0203. Since this is the bid price, 1_U>0.95 means that the probability of an investment payout of $1 is 0.05. Hence, p = 0.05 for this bullet since h(p) is the value of a bond with a Bernoulli payout have probability p of full payment.

Clark (1/21/24) – On page 18, there is a typo at the end of the fourth step. The words “expected treaty loss ratio” should say “expected treaty loss cost.”

Mildenhall Ch. 4 (1/25/24) – On page 113, the crossed pairing in the second step is incorrect. Since there are 10 values and p = 0.70, we only care about the top 4 values (since the fourth largest loss is VaR_0.70). We should pair the largest X1 value (52) with the fourth largest X2 value (8), the second largest X1 value (36) with the third largest X2 value (12). This produces a VaR_0.70(X) = 41. You can find a more detailed discussion of this example on the course forum. We corrected this example in the video.

Grossi Ch. 6 (1/25/24) – On page 78, the guide implies that we can re-calculate OEP($100M) by subtracting the three earthquake events from the original OEP of 0.557%. However, this is only an approximation. In reality, we would need to do the same OEP math covered in Grossi Ch. 2. You can find a more detailed discussion of how to calculate OEP($100M) after removing the EQ events in the course forum.

Clark (2/1/24) – At the top of page 38, the second term in the variance equation should say “Var(Freq) x [E(Sev.)]^2.”

Grossi Ch. 6 (2/1/24) – On page 77, in the first bullet, the final loss should be $2.8M.

Mildenhall Ch. 4 (2/1/24) – There is an error in the textbook that made its way into the guide. On page 108, the definition of the n-year occurrence PML should say “at most 1/n instead of “at least” 1/n.

Mildenhall Ch. 10 (2/10/24) – Minor typos. On page 207, for j = 7, S should be 0. On page 209, the first step should show 0.313^0.5 = 0.559. On page 213, the denominator of bullet 2 should be 0.441.

Mildenhall Ch. 5 (2/10/24) – Clarification for the definition of comonotonic additive on the top of page 128. If X and Y are comonotonic AND rho(X+Y) = rho(X) + rho(Y), then rho is comonotonic additive (COMON).

Mildenhall Ch. 5 (2/20/24) – On page 130, the fourth bullet under Dual Utility Theory should say “Dual utility theory is linear in outcomes based on distorted probabilities.”

Mildenhall Ch. 9 (3/5/24) – On page 160, the first bullet in the takeaway section should say “if two units are the same size, the riskier unit will have a HIGHER gross premium and LOWER gross loss ratio.”

The following errata impact the new version of the guide uploaded on 3/12/24. All prior errata were fixed in the 3/12/24 version.

Mildenhall Ch. 4 (3/15/24) – On page 118, the definition shown for CTE is for the Lower CTE. The definition of the upper CTE is E(X|X >= q^+(p)). The example shown further down in the page is calculating the upper CTE. We have reposted the video to make this clear.

Mildenhall Ch. 4 (3/18/24) – On page 118, the Lower CTE calculation should say (4+8+12+25)/4 = 12.25. The Upper CTE calculation should say (8+12+25)/3=15.

Clark (3/27/24) – On page 33, under the formula for the exposure factor for drop-down coverage, it should say that “the first two terms in the numerator are capped at UL + PL and the last two terms in the numerator are capped at PL.”

Flashcards

Mildenhall Ch. 4 (1/17/24) – On card 16 (page 32 of standard PDF, page 12 of printable PDF), the general relationship is incorrect. It should say “Var <= CTE <= WCE <= TVaR.” The flashcard PDFs and Anki deck have been reposted with the corrected card.

Mildenhall Ch. 10 (1/20/24) – On card 15 (page 30 of standard PDF, page 24 of printable PDF), the “and h” should be removed from the fourth bullet. The flashcard PDFs and Anki deck have been reposted with the corrected card.

Clark (2/1/24) – On card 35 (page 70 of standard PDF, page 10 of printable PDF), the second term in the variance equation should say “Var(Freq) x [E(Sev.)]^2.”

Bernegger (2/2/24) – On card 7 (page 14 of standard PDF, page 6 of printable PDF), the first term in the second equation should be G((AP + Limit)/MPL), not G(AP + Limit)/MPL.

Mildenhall Ch. 10 (2/5/24) – On card 15 (page 30 of standard PDF, page 10 of printable PDF), the final bullet point is incomplete. It should say “discount uncertain assets. Thus, h(p) <= p and g(s) >= s.”

Mildenhall Ch. 5 (2/10/24) – On card 10 (page 20 of standard PDF, page 8 of printable PDF), the definition of comonotonic additive needs to be clarified. It should say “If X and Y are comonotonic AND rho(X+Y) = rho(X) + rho(Y), then rho is comonotonic additive.”

Mildenhall Ch. 5 (2/20/24) – On card 16 (page 32 of standard PDF, page 12 of printable PDF), the second bullet should not have the word “not.” On card 18 (page 34 of standard PDF, page 12 of printable PDF), the fourth bullet should say “Dual utility theory is linear in outcomes based on distorted probabilities.”

Mildenhall Ch. 4 (3/15/24) – On card 15 (page 30 of standard PDF, page 10 of printable PDF), we added the upper CTE definition.

Clark (3/27/24) – On card 28 (page 56 of standard PDF, page 20 of printable PDF), it should say  that “the first two terms in the numerator are capped at UL + PL and the last two terms in the numerator are capped at PL.”

Mildenhall Ch. 4 (4/16/24) – On card 4 (page 8 of standard PDF, page 104of printable PDF), the Occurrence PML definition should say less than or equal to “1 – p = 1/n.”

Problem Pack

Bernegger 2 (4/21/23) – We need to adjust this problem for next sitting. E[X] should refer to the expected severity, similar to how it’s shown in the RF Bernegger – 3 problem.

Sahasrabuddhe 4 (3/25/24) – In part b, the numerator in the formula should show (LEV[ X | Theta_AY,ult ] / LEV[ B | Theta_AY,ult ] ). This was a correction in the Sahasrabuddhe paper errata (equation 3.10) and I didn’t update this formula in the problem.

The actual solution is correct though.

Bernegger 2 (1/26/24) – Minor errors. For conditions 3 and 4, it should state that g > 1 for this MBBEFD curve. Also, the quantity “1+(g-1)*x” in the denominator should not be squared in the G'(x) formula.

Mildenhall Part II – 3 (1/2/24) – The Cookbook formula for WACC had an error in it. This problem is updated to fix the error in the reinsurance cost formula.

Mildenhall Part I – 1 (1/17/24) – The original Mildenhall Part 1 problem bank had an error in the CV calculations for #1. The problem bank has since been reposted with the errors corrected.

Mildenhall Part I – 8 (2/1/24) – The solution, while correctly using the probability of 0.25, incorrectly notes 0.1 as the probability used in part a. Problem pack has been updated.

Mildenhall Part I – 12 (2/1/24) – Some grammar mistakes caught and updated. Solution did not change, but question and solution now read better.

Mildenhall Part III – 19b (2/1/24) – Because the calculations in the table are based on unlimited losses, the headers should not read X(a), etc. The headers have been updated and the file posted.

Mildenhall Part I – 11 (2/1/24) – The 0.75-VaR for X should be 90, not 75, and for X’ 140, not 125. The remainder of the solution is consistent.

Mildenhall Part I – 12 (2/1/24) – The TVaR for X + Y should be the sumproduct of the probabilities and loss amounts for the four losses above the threshold, not the simple average. The file has been updated and reposted.

Mildenhall Part I – 4 (2/1/24) – Definition of crossed pairing has been updated and the resulting solution has changed. The file has been reposted.

Mildenhall Part I – 8 (2/19/24) – Part a. should be asking for the assets (as shown in the solution), not the capital. The file has been reposted.

Cookbook

Bernegger – Exposure Curve (3/30/24) – This is a NEW recipe that I just posted in the Bernegger section of the course.

Mildenhall Part 3 – Unit Funding Analysis (4/15/24) – For the first asset layer (0 to 16,000), the cost of capital should be iota = 1 – .731 / .731 = 0.368. This is the limit as s -> 1. I added a section in the discussion about what happens to the cost of capital for s = 1 with different distortion functions. This is discussed on pg. 286 (bottom) in the textbook. The Excel version is posted and updated. We will update the PDF version for next sitting.

Mildenhall Part 3 – Allocated CCoC – Implied Target Loss Ratios (3/22/24) – I modified steps 2 and 3 a little bit to put the right formulas so that it’s easier to follow. Nothing changed with the solution, but the original version made it seem like WACC = risk discount rate (delta), which isn’t correct. Instead, WACC = Cost of capital (iota).

Download the updated Excel version to see the clean version.

Clark – Recursive Aggregate Generalized (2/27/24)- The formula for b and Pr(n) should show alphas instead of ‘a’ in the formula.

Portfolio Constant Cost of Capital Pricing (2/22/24)- The final formula should show:

Cost of capital=Target return on capital × Amount of capital

Insurer Insolvency and Liquidation (2/22/24) – In step 1, it should say “Liabilities > Assets, so the insurer is bankrupt.”

Allocated CCoC – Implied Target Loss Ratios (2/19/24) – Minor typo. In the PDF, the calculation shown in step 1 should show “= 9,350 x 37%”

Bernoulli Layers & Distortions / Spectral Risk Measures (2/17/24) – For the Wang Transform Excel formulation, the sign was wrong and should read “+ lambda”:

g(s) = NORM.S.DIST( NORM.S.INV( s ) + 𝜆 , TRUE )

One-Period DCF Model (2/17/24) – The prompt should state “net premium (excluding expenses)” not excluding taxes.

Weighted Average Cost of Capital (WACC) (1/18/24) – The Cookbook formula for WACC had an error in it. The numerator for the reinsurance cost should be: Ceded Premium x (1 + risk-free rate) – E[Recoveries]

This is because the loss of investment income from paying the ceded premium at t = 0 is an added cost.

Mildenhall Part III – Euler Gradient (2/1/24) – The problem listed the incorrect coefficients. It should now read 𝜌(𝑃,𝑅,𝑎)=√((0.36𝑃)^2+(0.34𝑅)^2+(0.08𝑎)^2 ) to match the solution.

Mildenhall Part II – Classical PCPs (2/1/24) – In the discussion section, the second formula for semivariance should note E(X – E[X])^2 as the formula for variance.

Past CAS Problems

CAS 2011 #9 (Exam 8 Bernegger) – The numerator of the G(x) function should be ln(a+b^x) – ln(1+a).

CAS 2014 #24 (Exam 8 Grossi) – The solution incorrectly used the payback pure premium from part a to calculate the reinstatement premium. It should use the actual premium given in part b ($1.2M).

High-Level Summaries

Midenhall Part II – Ch. 8 (2/19/24) – On page 30, it incorrectly states that IFRS loss reserves are undiscounted. Should say IFRS loss reserves are discounted including a risk adjustment.

Mildenhall Part I – Ch. 5 (2/20/24) – On page 25, the second row of the table under Utility Theory should not have the word “not.” The fourth row of the table under Dual Utility Theory should say “Linear in outcomes based on distorted probabilities.”

Formula Summary

Portfolio Constant Cost of Capital Pricing (2/22/24)- The final formula should show:

Cost of capital=Target return on capital × Amount of capital