Errata

Study Guide & Review Videos

CFR Ch. 7 (3/18/23) – On page 295, in the solution to MP #1c, there is a note for the calculation of UEPR that states that we should only include columns 1 and 2. That is incorrect. All four columns should be included. The correct UEPR figure is $2,425. As a result, the final surplus figure changes to $8,525. I have corrected and reposted the CFR Ch. 7 Excel workbook as well.

Study Guide & Review Videos

Mack 1994 (1/7/23) – On page 278 of the Spring 2023 Guide, a clarification is needed. In the first three bullets, the words “the rank of” should be added before the words “age-to-age factor.” In other words, when performing this test, the ranks of the age-to-age factors should be compared to the median rank when determining S, L, or *. You can also compare the raw age-to-age factors to the median age-to-age factor. This will be fixed in the review video as well.

Taylor & McGuire (1/29/23) – On page 702 of the Spring 2023 Guide, the CC loss ratio is using the incorrect formula shown in the original source paper. In the numerator and the denominator of the calculation, the premium for each accident period should be multiplied against the weight and loss ratio. For example, the first term in the numerator should be 20000(1)(18125/20000) and the first term in the denominator should be 20(1). The final answer remains unchanged.

Friedland (2/1/23) – On page 151 of the Spring 2023 guide, the policy limit for Insured #1 and Insured #2 should be changed to 3.0M and 4.0M, respectively. Otherwise, we would need to apply the policy limit to the gross loss. By changing the policy limits to 3.0M and 4.0M, the final answer for part b. remains the same. I will re-post the problem video with this fix for MP #1.

Friedland (2/14/23) – On page 169 of the Spring 2023 guide, EP 17b should not be there. The same question appears in EP 16. You can ignore EP 17b.

Friedland (2/19/23) – On page 142 of the Spring 2023 guide, a few of the cells in the aggregated USD loss triangles are incorrect. In the first aggregated triangle, AY 2015 at 48 months and 60 months should both be 843.13. In the second aggregated triangle, AY 2014 at 60 months and 72 months should be 812.83 and 806.90, respectively. AY 2015 at 60 months should be 843.13. The development patterns in the second triangle will change slightly since the 60-72 age-to-age factor is now 0.993 instead of 1.000.

Venter Factors (2/20/23) – On Flashcard #15 (Testing Implication 3: Test of Linearity), the second sentence on the back that states “residuals should random around zero” should be removed. Since Venter plots raw residuals rather than weighted residuals, we are only concerned about strings of positive and negative residuals in a row. The flashcards have been corrected and a new Anki package has been uploaded.

Clark (3/6/23) – In the Clark Cookbook Recipe “Variance of Reserves (LDF Method),” we state that the parameter process should be greater than the process variance. However, in the problem shown for the recipe, the given parameter variance is less than the process variance. To address this, assume that the parameter standard deviation is 180,000 instead of 120,000. Then, the standard deviation of the total reserve changes to $241,300. Revised versions of the CBT workbooks for the Clark Cookbook recipes have been posted.

Shapland (3/12/23) – In the Shapland Cookbook Recipe “Heteroscedasticity Fix: Standard Deviation,” the given standard deviations for each development period and hetero group should include the zero cells ((6,1) & (1,6)) per Shapland’s excel workbook that comes with the paper (the current version of the recipe excluded the zeroes). This does not change the mechanics of the recipe but does change the numbers slightly. I have uploaded a revised version of the Shapland Cookbook Excel workbook.

Venter Factors (3/25/23) – In the solution to part a. of 2011 #4, we should also comment on the significance of the constants. Since the factors are more than twice their standard deviations AND the constants are less than twice their standard deviations, the chain-ladder model is the better model.

Cookbook

Clark – Final Price [PDF Version] (8/12/22) – There is a typo. The loss cost should be 9.2%, not 9%. The Excel version is correct.

Clark – Property Per Risk – Experience Rating (8/9/22) – The loss experience should have an “as of” date to select the appropriate LDFs. Since none is given, the effective date (1/1/2019) is assumed to be the as-of date.

Fisher Retro – Deductible-Retro Cash Flow [Excel Version] (8/9/22) – Step 7 should read: “7) Calculate the Expected Insurer Cash Flows for the Deductible Plan. The insurer receives the deductible premium and deductible loss reimbursements and pays all losses and expenses.” We updated the Excel version on the course site.

Bahnemann – Risk Load [Excel Version] (8/9/22) – In the discussion, the risk load for the variance method should be k*E[X^2;l] without the square root. We fixed the Excel workbook on the course site for this.

Fisher Retro – Lee Diagrams and Expected Retro Premium (8/9/22) – In the discussion, it should show: ψ(r) → inf as  r → inf and the second derivatives of phi(r) and psi(r) should be positive f(r). We fixed the PDFs and Excel workbooks on the course site for this.

Mahler – Lagged Correlations [PDF Version] (8/5/22) – There’s a typo in the PDF, the first pair should refer to Y = Loss Ratio_t-1

Robertson – Weighted k-Means Cluster Analysis [Excel version]  (8/4/22) – The L^1 formula in the discussion is incorrect and shouldn’t have the square root. I updated the Excel version on the course site to correct this.

Mahler – Finding Optimal Z: Limited Fluctuation [PDF version]  (7/21/22) – The large error threshold given in the problem should be 10%, not 8%. The Excel version is correct and the rest of the solution is correct. I updated the PDF files on the course site to correct this.

Problem Pack

Couret & Venter – 4 (8/9/22) – There was a mistake in the part b calculation of m_i1 * (W_ij  –W_i)^2. We fixed this in the posted Excel file.

Bahnemann – 4 (8/5/22) – There was a mistake in part c. The calculation was incorrect. I fixed part c and added some additional derivation so that you can more easily follow the calculations in part b and c. Download the updated version from the course site.

Study Guide & Review Videos

BKM 7 (1/7/23) – There is a typo on page 19. Under the step that begins with “Lastly, let’s determine…,” the numerator of the weight calculation for D should say “sigma^2_E – Cov(r_D, r_E).” The numbers used are correct. This will be fixed in the review video as well.

BKM 15 (1/30/23) – A clarification is needed on page 103. Under the “Example” at the bottom of the page, Strategy 1 needs to be revised to say “Purchase a two-year zero coupon bond with a face value of $1,000 for $890.” By specifiying the purchase price, we are implying a guaranteed 6% YTM. Without the purchase price, we cannot state that a 6% YTM is guaranteed.

BKM 8 (3/2/23) – (Page 36) E(rA) = α + rf (1 − Adjusted Beta) + Adjusted Beta*(RM).

The last term should be Adjusted Beta * E(r_M), the expected market return, not R_M, the market risk premium.

BKM 11 (3/15/23) – (Page 67) Under Anomaly 1: The Small-Firm Effect, the first sentence should say “smaller firms (i.e. lower market capitalization) produce higher AVERAGE return than larger firms.” A revised video of BKM 11 has also been posted that clarifies the semi-strong form tests.

Robbin UW (3/16/23) – (Page 280) Minor typo in the second bullet under the fourth step. It should say “To calculate the PV(Loss amounts), we discount each loss figure by…”

Practice Problem Bank

BKM 16 – 3 (1/18/23) – The formula in the cell { =F32/(D32*(1+D8/2)^2) } should not be divided by 2, as the coupons are paid annually. The formula should be{ =F32/(D32*(1+D8)^2) }. The files have been updated.

Robbin IRR – 4 & 8 (1/23/23) – Practice Problem, Robbin IRR-4: cell P9 is incorrectly bolded and italicized, leading the student to believe it includes the fourth policy. It does not (and should not, as GAAP expenses are incurred as premium is earned from the fourth policy.

Similarly, cell P19 from Robbin IRR-8 was incorrectly bolded and italicized. The files have been updated to reflect these corrections.

Bodoff – 3 (2/6/23) – The problem and solution do not match. The problem should state that line A has 12.482M in premium net expenses, and line B should have 13.881M (prior version had 30M and 48M, respectively). The problem file has been updated to correct this issue.

BKM 8 – 4 (3/6/23) –  R^2 was incorrectly input as 0.3123. The corrected number is 0.3022. The problem is still solvable without referencing R^2, but the number has been updated and discussion added to explain how to use R^2 in this type of question. The file is updated to correct this issue.

Bodoff – 4 (3/9/23) –  The integral derivation in the solution should have a negative sign in front of it. The solutions are correct.

Past CAS Questions

CAS 2014 Q7 (3/6/23) – The problem incorrectly had bond 4 with 4.0 years to maturity instead of 3.0. An errata has been posted and the files have been updated.

CAS 2018 Q16, part c (3/9/23) – The solution is correct and uses the appropriate formula. However, the equation typed in cell 47 has the allocated capital and E[L] flipped. The files have been updated.