CAS Exam 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.

Spring 2016 #26b/CFR Ch. 19 (4/25/23) – The solution to this problems calculates the reinsurance RBC charge for contract #1 as 43,000(0.10) = 4,300. This is based on the 10% reinsurance RBC charge that was in effect prior to the 2018. In 2018, the new formula was implemented which calculates the reinsurance RBC charge in Schedule F. We have modified the problem so that you are given the total reinsurance RBC charge for contract #1 as $4,300. This impacts the CFR Ch. 19 past problem workbook and the Spring 2016 past exam. We have reposted both of these.

NAIC IRIS (4/30/23) – On page 665, under IRIS Ratio 9, the formula for Liquid Assets should say “+ Investment Income due and accrued,” not “+ Interest due and accrued.” On page 684, in the solution to MP#6a, the “+ Interest due and accrued” should be replaced “+ Investment due and accrued.” The solution is correct otherwise. The IRIS 9 Ratio on Liquid Assets has the same issue and should be corrected to “+ Investment Income due and accrued.”

Study Guide, Cookbook, Flashcards, & 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.

Taylor & McGuire (3/27/23) – In the solution to RF 4 in the Practice Problem Bank, there is a typo in the discussion at the bottom. For p = 3, the distribution should say “Inverse Gaussian,” not “Inverse Gamma.”

Marshall (3/27/23) – In the solution to RF 2 in the Practice Problem Bank, the recommended WC scale is still showing the original scale from the problem. It should be “24%, 16%, 10%, and 6%” to reflect non-linearity.

Shapland (3/31/23) – In the solution to 2017 #12 part b. (item 3), I think it makes more sense to treat the data as if the entire first column is 6 months old (including the most recent AY). In part b., we are treating each data issue independently. When adjusting for the partial first development period issue, it really only makes sense if the entire first column is 6 months old. So, to remain aligned with the Examiners’ Report, the answer should say “Calculate residuals and sample triangle as normal. However, we must divide the latest accident year sample reserves by two to account for the fact that it is a partial year.”

Venter Factors (4/6/23) – On page 345 of the guide, we discuss different ways to reduce the number of parameters in the BF model. Some of the suggested methods are redundant. To clear things up, we can remove the bullet around “assuming several AYs in a row have the same loss level, or at least a  linear progression of AY parameters.” I think it’s more clear to stick with the final bullet in this paragraph that mentions groupings years with similar loss levels (and using a common “h” parameter for each group) OR fitting a trend line through the BF loss parameters. This also impacts EP #4. For this question, assume it is only asking you to “provide two methods for reducing the number of parameters needed to fit a BF model.” Then, in the solution, remove the first bullet.

Venter Factors (4/10/23) – On page 344 of the guide, the explanation of the “2n-2” parameters for the BF model should be revised to the following:

• We need a parameter for each accident period (h(0) – h(4))
• We need a parameter for each development period (f(0) – f(4))
• We can subtract one parameter because the f(d)’s sum to 1, so we only need three of them to calculate the remaining f(d)
• We can subtract the f(0) parameter since we are given the first column in the Venter paper
• This results in 2(4) – 2 parameters

2018 and 2019 CBT Exams, Goldfarb, Teng/Perkins (4/16/23) – I have reposted the CBT versions of the 2018 and 2019 exams after fixing a few minor typos. Most of them are not material so I am only listing the ones that are significant here: -2018 #17 & Teng/Perkins CAS Problems – The solution shows a “part c” that should not be there. Instead, the solution to part c is actually the second half of the solution to part b. I also reposted the Teng/Perkins Past CAS Problems workbook -2018 #16 – This is a Patrik problem and should have been excluded from the exam since it is no longer on the syllabus -2018 #19 – In the solution to part b., the labels are flipped. Cell K27 should say “Under a 2-year scenario” and cell K32 should say “Under a 10-year scenario.” I also reposted the Goldfarb Past CAS Problems workbook

Brehm Ch. 2 (4/30/23) – On page 980, under “Define risk metrics,” the wording implies that there is a difference between “risk metrics” and “risk measures.” That is not the case. The authors use the terms interchangeably throughout the Brehm text. Risk measure (or risk metrics) include items such as standard deviation, VaR, TVaR, EPD, etc.

Practice Exams

RF Practice Exam 1 (4/11/23) – In the solution to #20b, for the final sentence, it should say “the mean under the Wang Transform is known to approximate market prices for cat bonds.”

RF Practice Exam 1 (4/17/23) – In the solution to #6c, the final sentence should be removed. For the ODP Mack Model, it is NOT generally true that the dispersion parameter is constant. I have reposted the exam with this corrected.

RF Practice Exam 1 (4/21/23) – In the solution to #5, the formula for T_3 should be pointing to the s_i3 and r_i3 cells, not the s_i3 and r_i2 cells. Note that T_3 is still -1 after this correction.

RF Practice Exam 1 (4/27/23) – The labels for Triangle B should be “12 mo., 24 mo., 36 mo., 48 mo., and 54 mo.*”

Practice Problem Bank

Grossi – 1 (7/8/23) – Part c should also say that the AAL would increase with the higher hurricane loss. The files have been updated.

Grossi – 9 (7/8/23) – Similar to the example in Grossi (Table 5.1), all values in the table should be “per $1,000” of property value. The files have been updated.

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…”

Butsic Study Guide pg. 183 (4/17/23) – The ruin probability when losses are risky should be PHI(-c / k) instead of PHI(c/k).

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.

BKM 11 – 1 (4/10/23) –  A minor typo in cell in M13. As we have added back in the risk-free rate, the cell should read E(r_X) not E(R_X). The files have been updated.

BKM 15 – 3 part a (4/10/23) – The text in cell P5 is referencing the wrong priced bond. The formula which gives the 2 year spot rate is correct and references the bond price of the 2 year bond.

However, in cell P5 it notes: ‘966.82 = 40/(1.055) + 1040/(1 + y2)^2.

It should be: ‘967.90 = 40/(1.055) + 1040/(1+y2)^2.

The files have been updated.

Kreps – 3 (4/10/23) – Investments don’t always act as a hedge. The discussion should state: “In Kreps’ examples, reinsurance acts as a hedge and has a negative risk load. Hedges are variables that are ‘below their mean when the riskiness leverage on the total is large’ (pg. 37).”

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.

CAS 2019 Q3 (4/10/23) – Cell M13 should refer to the active portfolio. The files have been updated.

CAS 2019 Q12 (4/10/23) – The second bullet should say “Risk capital is calculated using 99.6% CTE and allocated using 99.6% co-CTE”. The “co-” was previously missing. The files have been updated.

CAS 2019 Q7a (4/21/23) – The calculation of the bond price in part a isn’t correct. Each of the cash flows should be discounted using the appropriate spot rate for the timing. See the CAS PDF solution to the problem.

Cookbook

Robbin UW – CY Investment Offset Method [Excel version] (4/10/23) – While the solution is correct, the cells D66 and D87 were referencing to the premium tax rate of 6%, rather than the initial profit provision of 6%. The file has been updated to remove the reference to premium tax.

Extra CBT Problems (online course)

Extra Excel Problems Q3 (4/19/23) – We will probably rewrite this problem for next year. Since it is a RAROC question, investment income should only be earned on (premium – expense), not allocated capital. See pg. 41 in Goldfarb for more context on this.