Errata for 2017 Exam 7 Products
Errata for Practice Problems
RF Brosius - 7 and RF Brosius - 8: For these two problems, there is a mistake in the best linear approximation formula, L(x). Var(Y) should be changed to Var(X) in both of these problems. You can download the fixed problems here:
RF Clark - 2: The parameters in the question are missing. They disappeared in the final draft. Below are the Loglogistic parameters:
RF Mack (1994) - 2: Z_3 should be 0 in the solution. This changes the total Z to 4 for the problem.
RF Mack (1994) - 5: The labeling of the accident years is incorrect in the problem. The accident years should be 2011 through 2015 (not 2012 through 2016). This doesn't impact the solution.
RF Mack (1994) - 7:
The x-axis labeling of the graph in part b is incorrect and should be labeled "Loss at 12 Months." The graph itself is correct.
RF Brehm - 22 (2/15/17): The risk and return labeling should be switched. I think this change better reflects how the Brehm paper shows the efficient frontier in section 2.5. You can download an updated version of the problem here:
RF Sahasrabuddhe - 3 (3/20/17): The formula in part b has incorrect subscripts on the Basic Limit CDF. The Basic Limit CDF should be CDF_n,k.
RF Goldfarb - 10 (3/30/17):
Since there is net borrowing, we can't use the simplified growth formula. Instead, the growth rate should be calculated as the % change in capital in order to reflect net borrowing. You can download an updated version of the problem here:
RF Brosius - 5: Part a should read: "... estimated loss reserves..." instead of unpaid losses.
RF Shapland - 9 (4/6/17): The problem is missing the scale parameter symbol.
RF Meyers - 1 (4/6/17): The two graphs in the solution didn't show up in the final draft. You can download the corrected version of the problem here:
RF Brehm - 18 (4/18/17): There is an error in Net RI Cost formula in the solution. Commission should be subtracted. This doesn't change the solutions because there are no commissions in the problem. The formula should read:
Net Cost = Ceded Prem - Expected Recoveries - Reinsurance Commission
ERRATA FOR Exam 7 Cookbook
Brehm - Efficient Frontier (2/15/17): The risk and return labeling should be switched. I think this change better reflects how the Brehm paper shows the efficient frontier in section 2.5. You can download an updated version of the recipe here:
Verrall - Estimated Reserve from Fully Stochastic BF: The question asks for the expected ultimate loss for accident year 2015, but the boxed solution shows the unpaid loss. The final solution should include the paid loss-to-date for an ultimate loss estimate of 718.7 ( = 430 + 288.7).
Sahasrabuddhe - Calculate Layer LDFs from Basic Limit LDFs: Simplified Model (3/11/17): The formula is step 5 is incorrect. The Basic Limit LEV in the numerator should be have the subscript AY, inf instead of n, inf. The numerator in the formula should be the same as the formula in step 3. This is the correct formula that's in the Sahasrabuddhe errata.
Sahasrabuddhe - Calculate Layer LDFs from Basic Limit LDFs (3/20/17): The two formulas on page 80 have incorrect subscripts on the Basic Limit CDF. The Basic Limit CDF should be F_n,k. See formulas 3.9 and 3.10 on pg. 7 of the Sahasrabuddhe paper.
Verrall - Bayesian Model for the BF Method (3/22/17): The last sentence on page 112, running into 113, should read: "Then, by increasing Beta_AY (and increasing alpha_AY so that M_AY stays constant) the variance of the prior distribution is decreased."
The goal here is to manipulate the Beta parameter to adjust the variance of the prior distribution while keeping E[x] the same.
Goldfarb - FCFE Model (3/22/17): The simplified growth formula on page 158 (g = [NI-FCFE]/Beg. Capital) is only appropriate in the simplified case where there's no Net Borrowing or other impacts on FCFE. Other changes to capital should be reflected in the growth formula. A more robust formula for growth is:
Venter Factors - Goodness of Fit (4/20/17): The AIC/BIC formulas in the discussion from Venter Factors are approximations to the AIC/BIC. Shapland also has some formulas for AIC/BIC on pg. 35 and in the footnote points out that different authors have different AIC/BIC formulas. Remember that the absolute value isn't that important. What matters with AIC/BIC is the comparison between models to see which model is a better fit.
Teng and Perkins (Feldblum) - Premium Asset-PDLD Method Enhancement (4/28/17): A few people have asked about whether the Tax Multiplier should be taken into account when we adjust CPDLD_1 to remove the basic premium portion of the retro premium. Below are my thoughts on this from the two papers:
Cross-checking the enhancement against the retro formula, the tax multiplier should be incorporated in order to be completely consistent. I think this is a case where there are differences in the two papers:
In the Teng & Perkins: All of the separate pieces are given explicitly for a problem (tax multiplier, basic premium factor, ...).
In the Feldblum paper: A regression is used to estimate the Average Basic Premium Factor for a book of business.
Feldblum isn't explicit, but I think his use of the average basic premium factor (the "A" intercept in his graphs) incorporates the tax impact on the basic premium. That's where the version of the CPDLD* formula in the Cookbook is from (Feldblum pg. 297).
This is how I might approach an exam question:
IF the problem gives a tax multiplier, then I'd multiply in the TM:
Step 1: CPDLD(1)* = CPDLD(1) - [Basic Prem Factor * TM / ELR]
Step 3: Basic Prem = Standard Prem * Basic Prem Factor * TM
Where Basic Prem Factor = Basic Prem / Standard Prem
IF there's no tax multiplier and it gives an "Average Basic Premium Factor":
I wouldn't make one up. I'd just solve it like the way in the cookbook and maybe write down an assumption like "I assume the average basic premium factor includes the impact of a tax multiplier".