Practice Exams

[TwoStep]

##### Update #####
I passed!!! I'm sorry to future exam 7 takers, but I wont be updating these exams to fix any outstanding errors or make adjustments for new material. Feel free to pm me with your email if you want the raw Word files (I cant post them because of their size). Hopefully someone will start a thread with the with updates reflecting fixing errors, new material, or more original questions (its more difficult than you think to maintain these things, so maybe a few people could do it).




I've created four practice exams of varying difficulty. I did this because my study routine includes taking several simulated timed exams. I'm not trying to step on any toes for those participating in Bobby's practice problem project (for which I participated in!).

Exam Blue: Designed to match the 2011 exam in difficulty
Exam Green: Designed to act like the CAS exam 5 from 2011 (average difficulty questions, but too long to finish in four hours).
Exam Yellow: Designed to be the hardest exam one would encounter in five sittings.
Exam Red: This is a test to destruction; hardest exam we would see in ten sittings.

I was only able to go through these once since I wrote them, and there is a good chance that there are still some mistakes, or you may disagree with an answer, or suggest another acceptable answer. If there are errors or changes you want to make, post them here and I will update the exams every Tuesday and Friday, rather than once an issue comes up.

I hope this helps; I did my best to make these as realistic as possible, and to incorporate Bloom's taxonomy as best as possible.

There are some extra problems that don't fit in these exams, so I will either post them later, or add some more to build a fifth exam.

PM me if you want me to email you either the exams in Word (so you can edit them) or the master file of seed questions (separated by syllabus section).

## Updates ##
See release log for changes.

Wall of Fame (some from my A5-A7 questions which impacted these exams):

Bobby
Shouxiaozi
strand
dmbaldwi
G. Stolyarov II
cutenephew

2012-03-22: Fixes made, only impacted Blue, Green, and Yellow.

2012-03-27: Fixes made, only impacted Blue and Red

2012-04-10: Made some fixes, added Exam Orange

2012-04-23: Fixed exam Green and Yellow

2012-04-29: Fixed changes to Oranage and Green

2012-05-03: Fixed 12,13,16 and 25 in Exam Red


Good Luck,

I'm sorry, but I wont have time to post any updates like I promised. See all the AO comments if you think there is an error, and check them before grading any practice exams.

A few comments:

-- Exam Orange is contains too many 'Appendix', 'Foot Note', and 'Hybrid Topic' questions to be realistic in an exam setting. It also has 1.5 times the points of the prior sitting, which again makes it un-realistic.

-- Green is probably too long, since it was almost 25% longer than 2011, and given they lengthen exam 9, I would guess that they are being more time conscious this sitting.

-- Blue might be too easy

-- That leaves red and yellow as the true contenders for a realistic exam


My bets on questions that will covered:
-- There will most likely be a calculation based question from the EVT paper
-- Verall will most likely be covered in a theory question, with possibly some calculations
-- Mack 2000 will be covered in some way
-- There is a moderate chance that we will see a venter financial question
-- They will either ask a question from the McNeil paper, or a question from Mango and Venter about UW cycle management

[Bobby]

Nice! Thanks. It will probably be a while before I'm at a point where I want to take these, but I'll be sure to comment once I get a crack at 'em.

[Shouxiaozi]

Thanks! This is great!

[Ceej]

High five, TwoStep.

And pish posh to the stepping on anyone's toes - any additional practice is a gift.

[TwoStep]

Please post any issues by noon today (Thursday) to make them into Friday's fix.

## Edit ##
Fixes posted early

[G. Stolyarov II]

Greetings, TwoStep.

I am currently working through Exam Blue. Thank you for compiling these, as they will be immensely helpful to me and to many others.

I do have one question, though. In the given conditions for problem 6, the parameter error is given as negative for the later parameters. I may be missing something – but how is it possible to have negative error, and what would the real-world interpretation of such negative error be? My understanding is that parameter error is, in essence, the parameter standard deviation. It is the square root of the parameter variance, and so cannot be negative.

In the England and Verrall paper, for instance, all of the tables with error columns list positive values for errors.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[G. Stolyarov II]

One further brief correction on problem 6 in Exam Blue: In the solution to part b, one of the steps for the calculation for the process variance is the term ((Lambda_3)^2)*Var(Nu_3). I think that, in this term, the factor (D_2,2)^2 was omitted – even though it is taken into account in subsequent steps and is correctly incorporated into the numerical result for the process variance.

Thus, this is a quibble not with the answer, but with one of the intermediate steps, which should be the expression
((D_2,2)^2)*((Lambda_3)^2)*Var(Nu_3).

Overall, this is an excellent practice problem for the England and Verrall paper, and I can certainly see a question of this nature realistically appearing on the exam.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Greetings, TwoStep.

I am currently working through Exam Blue. Thank you for compiling these, as they will be immensely helpful to me and to many others.

I do have one question, though. In the given conditions for problem 6, the parameter error is given as negative for the later parameters. I may be missing something – but how is it possible to have negative error, and what would the real-world interpretation of such negative error be? My understanding is that parameter error is, in essence, the parameter standard deviation. It is the square root of the parameter variance, and so cannot be negative.

In the England and Verrall paper, for instance, all of the tables with error columns list positive values for errors.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

This was a mistake on my part. This comes my EV problems (in another thread), and I was able to use SAS to model actual development for all models but this one, which was made up. They should be the same value, but positive.

[TwoStep]

One further brief correction on problem 6 in Exam Blue: In the solution to part b, one of the steps for the calculation for the process variance is the term ((Lambda_3)^2)*Var(Nu_3). I think that, in this term, the factor (D_2,2)^2 was omitted – even though it is taken into account in subsequent steps and is correctly incorporated into the numerical result for the process variance.

Thus, this is a quibble not with the answer, but with one of the intermediate steps, which should be the expression
((D_2,2)^2)*((Lambda_3)^2)*Var(Nu_3).

Overall, this is an excellent practice problem for the England and Verrall paper, and I can certainly see a question of this nature realistically appearing on the exam.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE


This whole problem is getting a fix, so the correct answer will out on Tuesday.

[G. Stolyarov II]

Greetings, TwoStep.

While working through Question #2 on Exam Green, I have a further observation. In calculating the upper and lower bounds of the confidence interval, one must add to or subtract from E(Z) the term 1.96*StandardDeviation(Z), rather than 1.96*Var(Z).

In this case, StandardDeviation(Z) = SQRT(1.375) = 1.17260394, and so (by my calculation), the lower bound of the confidence interval is 1.201696278, and the upper bound is 5.798303722.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Greetings, TwoStep.

While working through Question #2 on Exam Green, I have a further observation. In calculating the upper and lower bounds of the confidence interval, one must add to or subtract from E(Z) the term 1.96*StandardDeviation(Z), rather than 1.96*Var(Z).

In this case, StandardDeviation(Z) = SQRT(1.375) = 1.17260394, and so (by my calculation), the lower bound of the confidence interval is 1.201696278, and the upper bound is 5.798303722.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

I'll put that fix in on Tuesday. Note to everyone that there are errors on Green 1,4,5,6 that I will also be fixing on Tuesday. #5 a and b will be slightly re-written.

[G. Stolyarov II]

Greetings, TwoStep.

Thank you for posting a revised version of Problem 6 in Exam Blue.

I noticed two further small items deserving revision.

1) In the answer key, the problem is currently labeled as “3.” instead of “6.” I recommend changing this to "6."

2) The expression for the mean should be corrected from exp(.25 + 0.895)* 3,957 to (exp(.25 + 0.895)-1)* 3,957. This is consistent with all subsequent calculations as well as the formula from England and Verrall.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[G. Stolyarov II]

Greetings, TwoStep.

Here are a few observations on items in Problem 18 from Exam Blue:

(1) In each model answer, every instance of “Pr(X > 1,250 and Y>1,225)” should be replaced with “Pr(X > 1,150 and Y>1,225)” – since the conditions of the problem use 1150 as the threshold level for X.

(2) In the model answer for part b, the word “below” should be changed to “above”.

(3) The solution key for part d is currently mislabeled as “c.”

(4) Also, as a conceptual matter, it would seem that to calculate whether the company falls into the next RBC threshold, it would be necessary to find out whether either of the loss levels for the two lines is exceeded, rather than whether both are exceeded. As an extreme example, if auto losses were 1149 (just under the line-specific RBC threshold) but homeowners’ losses were 50000 (far over the line-specific RBC threshold), this would certainly produce more concern than if both lines’ losses were slightly over the threshold. Also, extrapolating this to a multi-line insurer that writes 10 or 15 lines, it would seem quite difficult to fall into the next RBC threshold if every line’s losses had to exceed a certain amount.

If you agree with this reasoning, then some of the calculations would need to be revised as well. I would be interested in your thoughts.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Greetings, TwoStep.

Here are a few observations on items in Problem 18 from Exam Blue:

(1) In each model answer, every instance of “Pr(X > 1,250 and Y>1,225)” should be replaced with “Pr(X > 1,150 and Y>1,225)” – since the conditions of the problem use 1150 as the threshold level for X.

(2) In the model answer for part b, the word “below” should be changed to “above”.

(3) The solution key for part d is currently mislabeled as “c.”

(4) Also, as a conceptual matter, it would seem that to calculate whether the company falls into the next RBC threshold, it would be necessary to find out whether either of the loss levels for the two lines is exceeded, rather than whether both are exceeded. As an extreme example, if auto losses were 1149 (just under the line-specific RBC threshold) but homeowners’ losses were 50000 (far over the line-specific RBC threshold), this would certainly produce more concern than if both lines’ losses were slightly over the threshold. Also, extrapolating this to a multi-line insurer that writes 10 or 15 lines, it would seem quite difficult to fall into the next RBC threshold if every line’s losses had to exceed a certain amount.

If you agree with this reasoning, then some of the calculations would need to be revised as well. I would be interested in your thoughts.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

I agree with everything but (4). If we were really setting capital levels, you are correct, but this is an exam question. I'll just add a line that forces the candidate to assume both losses over those two points will cause a drop in RBC.

I had a hard time with copula excercises because out of all the papers that discuss them, not one of them actually shows you a numerical example of how to apply them, but yet its perfectly possible that the CAS will test this.

:furious:

[G. Stolyarov II]

Greetings, TwoStep.

Thank you for your reply on Problem 18. Here are two more minor observations for Problems 21 and 23 in Exam Blue:

- Problem 21: In the calculation of the discount rate in part a, the model answer uses 8% for the market rate in place of the correct 10.5%. The displayed answer of 12% is correct, however.

- Problem 23: In the problem instructions, the phrase “form a risk to spread the risk” should be changed to “form a risk pool to spread the risk”. I think the word “pool” was inadvertently omitted.

I found Exam Blue to be quite valuable now that I have gone through it in entirety. I plan to similarly work through the other three exams and will post any observations here.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Greetings, TwoStep.

Thank you for your reply on Problem 18. Here are two more minor observations for Problems 21 and 23 in Exam Blue:

- Problem 21: In the calculation of the discount rate in part a, the model answer uses 8% for the market rate in place of the correct 10.5%. The displayed answer of 12% is correct, however.

- Problem 23: In the problem instructions, the phrase “form a risk to spread the risk” should be changed to “form a risk pool to spread the risk”. I think the word “pool” was inadvertently omitted.

I found Exam Blue to be quite valuable now that I have gone through it in entirety. I plan to similarly work through the other three exams and will post any observations here.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

Thank you for doing QA on them. I've gone through and taken Blue, Green, and Yellow under real exam conditions. A few observations:
-- Blue and Green had a lot of errors
-- Yellow had only a few errors
-- Yellow seemed to be the best distribution of questions

I'll do Red this Friday. I will post my corrections to the exams tonight some time. I think they have some corrections.

[G. Stolyarov II]

Greetings, TwoStep.

I am now beginning to work through Exam Yellow. On Problem 1c, your answer is correct, but the “Formula” column contains Excel formulas that reference cells that were specific to the spreadsheet you used. I think the intent is just to substitute the “Claims @ 15 Months” and “Claims @ 27 Months” numbers from each row into the fields with the Excel references.

Sincerely,
G. Stoylarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Actually, thats not an Excel reference, I was just trying to show how to come up with the probabilities, without having to write it out for each.

Greetings, TwoStep.

I am now beginning to work through Exam Yellow. On Problem 1c, your answer is correct, but the “Formula” column contains Excel formulas that reference cells that were specific to the spreadsheet you used. I think the intent is just to substitute the “Claims @ 15 Months” and “Claims @ 27 Months” numbers from each row into the fields with the Excel references.

Sincerely,
G. Stoylarov II, CPCU, ARe, ARC, AIS, AIE

[Smartbill]

On Exam Green, problem 4, I believe you want to switch the 1.2 and 25 Weibull parameters around
Thanks for the practice exams!

[Smartbill]

Exam Green, problem 14, part b, solution, risk free rate = 3.5-.9=2.4
should be 2.6% (unless I'm going crazy haha)

this would effect the rest of part b also as part d

[TwoStep]

Sorry everyone, but my new work laptop wont let me upload stuff here. I'll have to do it when I get home tonight, but I have the fixes everyone mentioned done.

[TwoStep]

I'm really sorry for the lack of updates, but I've been working on a new exam. I will update everything by Tuesday. The new exam will cover some new topics not touched on by prior exams:
-- Mean and variance of discounted reserves
-- England and Verall's recursive variance calculation
-- Partial accident year and policy year reserve estimation
-- Verall's accident year factors
-- Mack's test for correlation (different from Venter)

Also note that the new exam will be VERY IAA heavy and recycles some questions from prior exams (about 70% new and 30% recycled).

[G. Stolyarov II]

Greetings, TwoStep, and thank you for posting the revised exams.

I am continuing to work through Exam Yellow and found two issues:

(1) In Problem 5, the given conditions have ω and θ switched. In order for the answer key to be correct (and for the problem to be interesting with respect to the paid percentages being different from 100% each time), it should be the case that ω = 1.20 and θ = 9.50, rather than the other way around.

(2) In Problem 9a, I calculate the chain-ladder pure IBNR to be 16242.82. The answer key only subtracts the total paid losses to date from the ultimate paid losses. However, since we are looking for pure IBNR, we should exclude also all case reserves and ACR (as these are components of losses reported to date). Thus, instead of subtracting 13900 from the ultimate amount, we should subtract 23700.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[Bobby]

Here's a stupid question:

What paper is Blue - Question #1 from?

ETA:

I guess it's from Brosius? But the equation I see in that paper is:

L(X) = Z\dfrac{x}{d} + (1-Z)E(Y)

where \dfrac{x}{d} is the Chain Ladder estimate.

But in the problem you use \dfrac{x-x_0}{d}

And you use an equation for the link ratio that I have not seen before. Where did you get that?

[Bobby]

I believe the wrong alpha parameter is being using in the solution to Blue Quesiton #3.

\alpha_2 corresponds to the 12-24 LDF.
\alpha_3 corresponds to the 24-36 LDF.

We are given D(2,2), which is the cumulative loss in the second accident year and the second development year. We are trying to estimate C(2,3), which is the incremental loss for the second accident year in the third development year.

So we need to apply the 24-36 LDF to D(2,2) to estimate C(2,3) (i.e. use \alpha_3 instead of \alpha_2)

[TwoStep]

I believe the wrong alpha parameter is being using in the solution to Blue Quesiton #3.

\alpha_2 corresponds to the 12-24 LDF.
\alpha_3 corresponds to the 24-36 LDF.

We are given D(2,2), which is the cumulative loss in the second accident year and the second development year. We are trying to estimate C(2,3), which is the incremental loss for the second accident year in the third development year.

So we need to apply the 24-36 LDF to D(2,2) to estimate C(2,3) (i.e. use \alpha_3 instead of \alpha_2)

I made this same mistake originally. See my thread on my practice problems for A5-A7.

Look at page 26 of EV: (Lambda(j)-1) = exp(c + alpha(j-1))

Hear j = 3, so we pick alpha(2). Remember that alpha(1) = 0, so lambda(1)-1 = exp(c).

This question is wrong for a different reason though: the estimation variance is off, it should be using (Lambda(j)-1) ^ 2, and not (Lambda(j)) ^ 2.

[G. Stolyarov II]

Greetings, TwoStep.

Here are some further observations regarding Exam Yellow.

(i) In Problem 14a, the answer key’s references to “M” (millions) should be changed to “K” (thousands) in order to be consistent with the problem’s given conditions.

(ii) In Problem 18a, two of the commercial loss ratios (for 2009 and 2011) are the same (88.7%), and therefore the question arises as to whether 3 swaps really need to be done, or whether 2 swaps would suffice if each of the 88.7% loss ratios could be considered to have either rank 2 or rank 3. I would recommend revising the problem to make the two loss ratios different and to therefore leave no ambiguity about the number of swaps needed.

(iii) In the answer key to Problem 25, regarding Assumption 3, “bets practices” should be revised to “best practices”.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[Bobby]

I made this same mistake originally. See my thread on my practice problems for A5-A7.

Look at page 26 of EV: (Lambda(j)-1) = exp(c + alpha(j-1))

Hear j = 3, so we pick alpha(2). Remember that alpha(1) = 0, so lambda(1)-1 = exp(c).

Ok thanks.

[Bobby]

Green Q#2:

Your solution ranks the cumulative losses to check for calendar year effects but Mack's calendar year test is performed on development factors, not cumulative losses. (Check the first paragraph on page 163 in 1994 Mack. Also see the solution to the 2011 Exam question #3.)

[Bobby]

Green Q#4:

The values of the Weibull parameters need to be switched.

[G. Stolyarov II]

Greetings, TwoStep.

I have begun looking at Exam Orange and have the following observations on the first two problems:

Problem 1a.
(i) In calculating the completion factor of 2, the answer key has the numerator and denominator flipped.
(ii) The problem’s initial conditions should state that the table displays incremental, rather than cumulative, claims.

Problem 1b. In the answer key, “on period” should be changed to “one period”, and “this would like” should be changed to “this would look like”.

Problem 2.
(i) In the problem’s description, “Wiebull” should be changed to “Weibull”.
(ii) The cumulative distribution function for the Weibull distribution, using the notation in the problem, should be provided. The standard CDF on CAS exams is

F(x) = 1 – exp(-(x/θ)^τ). This problem seems to use λ in place of τ.

(iii) Furthermore, if I assume the above CDF and that λ = τ, I calculate very different values for A: % Paid, where I assume that x = number of months.

My calculations are as follows:
% Paid at 12 months: 38.15%
% Paid at 24 months: 56.68%
% Paid at 36 months: 68.56%

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[G. Stolyarov II]

Greetings, TwoStep.

I have gone through a bit more than the first half of Exam Orange and have the following further observations. I am only commenting here on problems that do not appear in other practice exams.

Problem 3

(i) For part a, the technically correct null hypothesis would be that there is no correlation. (The null hypothesis is always the absence of the characteristic we are trying to test.) By having 0 in the interval, we do not “reject the hypothesis that there is a correlation”. Rather, we “fail to reject the hypothesis that there is no correlation”.

(ii) It seems that the same question is repeated for parts 3c and 3d. Was 3d intended to be a different question?

(iii) An editorial recommendation is to change all instances of "Maack" to "Mack".

Problem 4

It is not clear how the values for IBNR, “IBNR Paid Next”, and “Discount2” are calculated in the answer key. I would recommend including formulas.

Conceptually, it is difficult to determine IBNR from the information given, since we are only given paid claims, and not reported claims. But if we assume that Paid Claims = Reported Claims, then IBNR would be (Paid Claims / % Paid) – Paid Claims.

“IBNR Paid Next” would be (Paid Claims / % Paid)*(% Paid Next) - Paid Claims.

Problem 6

(i) In parts a and b, the answer key gives ultimate excess losses, but the problem instructs candidates to find excess IBNR. To find IBNR, there should be an extra step of subtracting $100,000 from ultimate losses.

(ii) In part b, the answer key’s reference to “Ultimate Limited Losses” should be changed to “Ultimate Excess Losses”.

(iii) In part c, I think the problem should ask the reverse – to state the advantages and disadvantages of the indirect method over the direct method, as this is what the answers in the answer key refer to.

Problem 8

The answer key’s final calculation of the coefficient of variation (105.3271/3240) is correct, but the numerical answer is 0.032508, rather than the displayed value of 0.030797.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[G. Stolyarov II]

Greetings, TwoStep.

Here are some observations regarding Problem 14 in Exam Orange.

(i) For part c, in calculating c, the correct formula is “0.10^2 = 0.04^2 + c”. The answer key arrives at the correct value of c but lists the term “0.04^2 + c” twice on the right-hand side of the equation.

(ii) I recommend that the answer key provide the formula for the variance in terms of b and c:
Var = (1+b)*(λσ^2+ (μ^2)*( λ + cλ^2)) + b(μ^2)(λ^2).

(iii) My calculations differ from yours slightly:

For λ =2500, Var = (1+0.0016)*(2500*2.50^2 + (10^2)*(2500 + 0.0084*2500^2)) + 0.0016*(10^2)*(2500^2) = 6524450.
Standard error = SQRT(6524450) = 2554.300296

For λ = 25000, Var = (1+0.0016)*(25000*2.50^2 + (10^2)*(25000 + 0.0084*25000^2)) + 0.0016*(10^2)*(25000^2) = 628500500. [I think your answer key displays the same answer as for λ = 2500 here.]
Standard error = SQRT(628500500) = 25069.91225

(iv) In the answer key for part e, with respect to the factor-based model, the calculations are correct, but the displayed formula is not. The displayed formula suggests subtracting CAT PML, whereas CAT PML should, in fact, be added.

(v) In the answer key for part f, I think the word you are looking for is “assess”.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

I updated Green and Yellow with your fixes. In some cases, I changed to problem instead of the answer key.

Thanks to everyone who found issues. Sorry for not keeping up to date on the fixes, but this is more challenging that it would seem.

[cutenephew]

Twosteps:

I have some observations and just wanted to comment on them. Just wanted to see if you or other people agree with my findings.

Question #1. I believe the process variance terms are not right. For 2010, there should be incremental MSE calculation for 1 to 3 instead of 2 to 4. For example in 2010 age 2 should be 2010 age 1, and it should be 1/23295.61 instead of 1/36388.94 for the process variance part.

Question #5 b) Relativity=50/80. I think this should be 80/80 since we are comparing the relativity of 1000k limit and unlimited. But 80/80 doesn't make any sense in terms of question in hand.

[TwoStep]

Twosteps:

I have some observations and just wanted to comment on them. Just wanted to see if you or other people agree with my findings.

Question #1. I believe the process variance terms are not right. For 2010, there should be incremental MSE calculation for 1 to 3 instead of 2 to 4. For example in 2010 age 2 should be 2010 age 1, and it should be 1/23295.61 instead of 1/36388.94 for the process variance part.

Question #5 b) Relativity=50/80. I think this should be 80/80 since we are comparing the relativity of 1000k limit and unlimited. But 80/80 doesn't make any sense in terms of question in hand.

So, #5 you are correct on, this was something that I thought I corrected already, but will make the fix again.

I dont know that I agree on number #1. Let me do some more thinking.

[Ogre_8]

Twosteps:


Question #1. I believe the process variance terms are not right. For 2010, there should be incremental MSE calculation for 1 to 3 instead of 2 to 4. For example in 2010 age 2 should be 2010 age 1, and it should be 1/23295.61 instead of 1/36388.94 for the process variance part.



Hi Two-Step,


I agree with nephew. Except I don't know why he insists on skipping over a year of development.


The best way to think of it is that for Mack's model alpha, f work on taking Ck to Ck+1.
Since you are using the f and alpha going from year 1 to 2 then the 1/Ck should correspond to the Losses at C1.

The new variance is proportional to the prior term, not the term being estimated.

Also, I don't see why the development starts from 0 to 1. Losses at time 0 = 0 (usually).

In the solution, "the calculate MSE" formula has unnecessary squares in the C terms.


Also problem 1 should be worth like 5 points IMO. :smile:


Great job on these tests.
:toast:

[cutenephew]

Question 20 b.

I thought mean excess loss is just TVaR-VaR. And EPD is (TVaR-VaR)(1-prob of default) as what you are calculating. Correct me if I am wrong.

Thanks.

[G. Stolyarov II]

Greetings, TwoStep.

Here are two additional observations regarding Exam Orange:

Problem 15
In the answer key for part e, there is a typographical error. The answer is stated as 25.35, whereas the actual calculation results in an answer of 28.35.

Problem 18
In the answer key for part b, a step is missing. The value of y is actually 400/30-ln(1500) = 6.020112946. Then Λ(y) = Λ(6.020112946) = exp(-exp(-6.020112946)) = 0.997573553.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

So, this idea is coming back to bite me, becuase maintaining these exams is more difficult and time consuming than I thought it would be.

I'll go through and post updates this weekend.

If anyone would the word document version to make the corrections for themselves, let me know.

[G. Stolyarov II]

Greetings, TwoStep.

Just one further observation:

Problem 20a in Exam Orange should ask for the lowest required capital level, rather than the lowest surplus, since the calculations that must be performed to answer the problem are calculations for required capital.

I appreciate all the work you have put into these exams and have gotten some excellent practice out of them.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

[TwoStep]

Greetings, TwoStep.

I have begun looking at Exam Orange and have the following observations on the first two problems:

Problem 1a.
(i) In calculating the completion factor of 2, the answer key has the numerator and denominator flipped.
(ii) The problem’s initial conditions should state that the table displays incremental, rather than cumulative, claims.

Problem 1b. In the answer key, “on period” should be changed to “one period”, and “this would like” should be changed to “this would look like”.

Problem 2.
(i) In the problem’s description, “Wiebull” should be changed to “Weibull”.
(ii) The cumulative distribution function for the Weibull distribution, using the notation in the problem, should be provided. The standard CDF on CAS exams is

F(x) = 1 – exp(-(x/θ)^τ). This problem seems to use λ in place of τ.

(iii) Furthermore, if I assume the above CDF and that λ = τ, I calculate very different values for A: % Paid, where I assume that x = number of months.

My calculations are as follows:
% Paid at 12 months: 38.15%
% Paid at 24 months: 56.68%
% Paid at 36 months: 68.56%

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

I agree with Q1, but disagree with 2: you need to use the midpoint (t = 6,18,30). I'll add that in the key.

[TwoStep]

Greetings, TwoStep.

I have gone through a bit more than the first half of Exam Orange and have the following further observations. I am only commenting here on problems that do not appear in other practice exams.

Problem 3

(i) For part a, the technically correct null hypothesis would be that there is no correlation. (The null hypothesis is always the absence of the characteristic we are trying to test.) By having 0 in the interval, we do not “reject the hypothesis that there is a correlation”. Rather, we “fail to reject the hypothesis that there is no correlation”.

(ii) It seems that the same question is repeated for parts 3c and 3d. Was 3d intended to be a different question?

(iii) An editorial recommendation is to change all instances of "Maack" to "Mack".

Problem 4

It is not clear how the values for IBNR, “IBNR Paid Next”, and “Discount2” are calculated in the answer key. I would recommend including formulas.

Conceptually, it is difficult to determine IBNR from the information given, since we are only given paid claims, and not reported claims. But if we assume that Paid Claims = Reported Claims, then IBNR would be (Paid Claims / % Paid) – Paid Claims.

“IBNR Paid Next” would be (Paid Claims / % Paid)*(% Paid Next) - Paid Claims.

Problem 6

(i) In parts a and b, the answer key gives ultimate excess losses, but the problem instructs candidates to find excess IBNR. To find IBNR, there should be an extra step of subtracting $100,000 from ultimate losses.

(ii) In part b, the answer key’s reference to “Ultimate Limited Losses” should be changed to “Ultimate Excess Losses”.

(iii) In part c, I think the problem should ask the reverse – to state the advantages and disadvantages of the indirect method over the direct method, as this is what the answers in the answer key refer to.

Problem 8

The answer key’s final calculation of the coefficient of variation (105.3271/3240) is correct, but the numerical answer is 0.032508, rather than the displayed value of 0.030797.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

Agreed, all fixed.

[TwoStep]

Greetings, TwoStep.

Here are some observations regarding Problem 14 in Exam Orange.

(i) For part c, in calculating c, the correct formula is “0.10^2 = 0.04^2 + c”. The answer key arrives at the correct value of c but lists the term “0.04^2 + c” twice on the right-hand side of the equation.

(ii) I recommend that the answer key provide the formula for the variance in terms of b and c:
Var = (1+b)*(λσ^2+ (μ^2)*( λ + cλ^2)) + b(μ^2)(λ^2).

(iii) My calculations differ from yours slightly:

For λ =2500, Var = (1+0.0016)*(2500*2.50^2 + (10^2)*(2500 + 0.0084*2500^2)) + 0.0016*(10^2)*(2500^2) = 6524450.
Standard error = SQRT(6524450) = 2554.300296

For λ = 25000, Var = (1+0.0016)*(25000*2.50^2 + (10^2)*(25000 + 0.0084*25000^2)) + 0.0016*(10^2)*(25000^2) = 628500500. [I think your answer key displays the same answer as for λ = 2500 here.]
Standard error = SQRT(628500500) = 25069.91225

(iv) In the answer key for part e, with respect to the factor-based model, the calculations are correct, but the displayed formula is not. The displayed formula suggests subtracting CAT PML, whereas CAT PML should, in fact, be added.

(v) In the answer key for part f, I think the word you are looking for is “assess”.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

I disagree with your first observation, but agree with others. I would be lying if I said the typo you bring up was the worst I've ever made in a professional setting :lol:.

[TwoStep]

Greetings, TwoStep.

Here are two additional observations regarding Exam Orange:

Problem 15
In the answer key for part e, there is a typographical error. The answer is stated as 25.35, whereas the actual calculation results in an answer of 28.35.

Problem 18
In the answer key for part b, a step is missing. The value of y is actually 400/30-ln(1500) = 6.020112946. Then Λ(y) = Λ(6.020112946) = exp(-exp(-6.020112946)) = 0.997573553.

Let me know if you agree.

Sincerely,
G. Stolyarov II, CPCU, ARe, ARC, AIS, AIE

Agreed, fixed.

[TwoStep]

Twosteps:

I have some observations and just wanted to comment on them. Just wanted to see if you or other people agree with my findings.

Question #1. I believe the process variance terms are not right. For 2010, there should be incremental MSE calculation for 1 to 3 instead of 2 to 4. For example in 2010 age 2 should be 2010 age 1, and it should be 1/23295.61 instead of 1/36388.94 for the process variance part.

Question #5 b) Relativity=50/80. I think this should be 80/80 since we are comparing the relativity of 1000k limit and unlimited. But 80/80 doesn't make any sense in terms of question in hand.

Alright, I'm sold on your #1.

[TwoStep]

I made fixes to Orange and Green based on AO feedback.

I will only be making one more update on Friday May 4th. After that, I still encourage people to post any issues, but keep in mind they wont be updated before the exam.

[Bobby]

Exam Yellow #5:

On Clark pg. 67-68, he does not truncate the development pattern when calculating the expected loss ratio. He only truncates to get reserves. In the solution, it is truncating when calculating the loss ratio.

For example, for AY 2008, the used up premium for calculating the ELR should be 85.61% * 2715 instead of 85.61%/91.10%*2715. This will change the ELR and consequently the reserves.

[Bobby]

Exam Yellow #12:

In part A the solution assumes the plowback ratio is equal to one (since you are growing the book value with all of the ROE).

Then in part B the solution derives the growth rate as ROE - k, but goldfarb defines the growth rate as plowback * ROE (book value growth does not rely on the required market return.) So the growth rate here would be 8.75% according to part a (since plowback=1).

[Bobby]

Exam Yellow #15b:

The question asks for the difference between Type A and Type B risk and the solution answers the question in the context of credit risk. But Type A and Type B risk is mentioned multiple times in IAA and is defined in both the market risk section and credit risk question. So the question should be more specific about in whether it is asking about market or credit type A/B risk. Below are the definitions of each.

Page 132: Type A Market Risk: Liabilities have durations comparable to readily available assets. Therefore it is possible to select assets whose cash flows provide close match to liability cash flows. In this situation, market risk focuses on the volatility of the market value of actual assets held and the market value of the replicating portfolio assets.
Page 132: Type B Market Risk: Long-duration liabilities require consideration of long term rates of reinvestment since replicating portfolio of assets with sufficient duration not offered in market. Market risk for these liabilities entails considerable uncertainty about reinvestment and long term options and/or guarantees in insurance contracts.
Page 146: Type A Credit Risk: Liabilities have short duration where assets can be purchased to replicate cash flows. Credit risk focuses on actual assets held.
Page 146: Type B Credit Risk: Liabilities have long-term duration and assets cannot be purchased to replicate cash flows. Credit risk must be assessed not only for current assets but credit risk involved with future reinvested assets.

[Bobby]

Solution to Exam Yellow #17a:

Does an arc in a Chi-Plot signify dependence? If you saw that in a paper, could you point me where that is? I thought that it was points not randomly being around zero that signified dependence. From Felbdlum's paper on page 11:

If most points in a Chi-plot stay close to the line Chi = 0, then the variables Y and Z in the scatterplot are independent. For example, the left panel in Figure 5 shows independent random draws from two uniform random variables Y and Z. The right panel shows the corresponding Chi-plot. Notice how all the points in the Chi-plot are concentrated around the line Chi = 0.

In Figure 6 we have the Chi-plots associated with the normal, Frank, and t-copulas. The scatterplots all have a Kendall  statistic of 80%. Notice how each panel shows a `signature' pattern.

[Bobby]

Solution to Exam Yellow #18:

You have 2011 as 88.7% in problem, but in solution to find Kendall's Tau you have it as 88.6%. This changes the number of swaps required and consequently Tau (should be four swaps I believe).

BTW, nice problem here on #18. If the CAS wrote a problem like this, I'd be very impressed.

[Bobby]

Exam Yellow #20:

Not sure what is right here... but in Venter Non-Tail, he defines the Wang transform by adding lambda. In the solution you subtract lambda. However, in Venter Strategic, he defines the Wang transform with parameter b (similar to lambda) that he subtracts.

Doing some googling on the Wang Transform, I don't see a consensus whether you're supposed to add or subtract lambda. Not sure what they'll do on the test.

[Bobby]

Solution to Exam Orange #2:

Clark calculates that the parameter \sigma^2 based on incremental losses (see pg. 49 of Clark). The solution calculates it based on cumulative losses.

[Bobby]

Solution to Exam Orange #3a:

On page 158 of Mack, Mack has the expected value of T equal to zero. In the solution it says it is -0.2 ?

Also, just an FYI... for Mack's correlation test he recommends using a shorter confidence interval (such as 50% as opposed to 99%) because the test is an approximate nature and we want to detect correlations already in a substantial part of the run-off triangle.

[Bobby]

Solution to Exam Orange #3a:

Formula for T_k is incorrect. Denominator should subtract I and add k.

And the test is being done incorrectly... you are checking to see if actual T is within confidence interval, not if zero is. Since E[T]=0, zero will always be in the confidence interval. (see page 161 of Mack for when he does the test.)

[Bobby]

Solution to Exam Orange #5:

Shouldn't the G(x) be multiplied by the exposures rather than (1-G(x)) ?

For example, for part a:

Percent paid claims for the accident year before exposure adjustment = 0.298.
After adjustment, (1/2) * 0.298 = 0.1489 paid.
Then we have unpaid claims = Ult * Pct Unpaid = 35 * (1-.1489) = 29.79 M.

Part b has a similar problem. In the solution, part b has a much smaller reserve than part a, even though part b is policy year and it should have a bigger reserve than part a because less exposure has been earned (part a = accident year).

[Bobby]

Exam Orange #7:

Part a has the solution right after the question.

[TwoStep]

Solution to Exam Orange #5:

Shouldn't the G(x) be multiplied by the exposures rather than (1-G(x)) ?

For example, for part a:

Percent paid claims for the accident year before exposure adjustment = 0.298.
After adjustment, (1/2) * 0.298 = 0.1489 paid.
Then we have unpaid claims = Ult * Pct Unpaid = 35 * (1-.1489) = 29.79 M.

Part b has a similar problem. In the solution, part b has a much smaller reserve than part a, even though part b is policy year and it should have a bigger reserve than part a because less exposure has been earned (part a = accident year).

You would have a lower reserve for Policy year claims since you've earned less of the exposures. The reserves only exist for earned exposures (Clark makes a point of this in Appendix B).

The appendix shows, for a 9 mo example, 9/12 * G as the % paid, but since you are only looking at 9/12 of a year, unpaid would be 9/12 - 9/12 * G, or (1-G) * 9/12.

[TwoStep]

Solution to Exam Yellow #18:

You have 2011 as 88.7% in problem, but in solution to find Kendall's Tau you have it as 88.6%. This changes the number of swaps required and consequently Tau (should be four swaps I believe).

BTW, nice problem here on #18. If the CAS wrote a problem like this, I'd be very impressed.

Thanks!!
The error is small enough to ignore.

[TwoStep]

Solution to Exam Orange #3a:

Formula for T_k is incorrect. Denominator should subtract I and add k.

And the test is being done incorrectly... you are checking to see if actual T is within confidence interval, not if zero is. Since E[T]=0, zero will always be in the confidence interval. (see page 161 of Mack for when he does the test.)

Agreed.

[TwoStep]

Good Luck,

I'm sorry, but I wont have time to post any updates like I promised. See all the AO comments if you think there is an error, and check them before grading any practice exams.

A few comments:

-- Exam Orange is contains too many 'Appendix', 'Foot Note', and 'Hybrid Topic' questions to be realistic in an exam setting. It also has 1.5 times the points of the prior sitting, which again makes it un-realistic.

-- Green is probably too long, since it was almost 25% longer than 2011, and given they lengthen exam 9, I would guess that they are being more time conscious this sitting.

-- Blue might be too easy

-- That leaves red and yellow as the true contenders for a realistic exam


My bets on questions that will covered:
-- There will most likely be a calculation based question from the EVT paper
-- Verall will most likely be covered in a theory question, with possibly some calculations
-- Mack 2000 will be covered in some way
-- There is a moderate chance that we will see a venter financial question
-- They will either ask a question from the McNeil paper, or a question from Mango and Venter about UW cycle management

[Kongo]

Anyone going to go through these and detail the ones not on the syllabus anymore. Same with past exam questions? Anyone? Dedicated?

[Dedicated111]

I have them printed out, but I haven't gotten to them yet. I'm going to CF's seminar next week, and I'm going to start on these after that.

[Dedicated111]

Not sure where the best place to post this is, but I will start here. If you think I should create a separate thread let me know:

UPDATE FOR 2013 SYLLABUS:
I went through Exam Yellow this weekend: This is what I found (I hope I caught them all)...

1. Question 1's total points do not add up. Should be 3.50
2. I really think question 1c is unrealistic. Not sure if this was from another paper not on the syllabus anymore and I know these exams are supposed to range in difficulty. But I still think there is no chance this would be asked.
3. For Question 5a) I would recommend doing this problem EXACTLY how the paper does it. In the answer, TwoStep truncates the % paid before finding ELR, but in the paper, they find the ELR prior to truncation. Again, I recommend doing exactly how the paper does it, don't ask questions, just do it. LOL Any objections?
4. Question 7 - not on syllabus
5. Question 11, half of part (b) - not on syllabus (The England and Verrall paper reference)
6. Question 15 - not on syllabus
7. Question 16 - not on syllabus
8. Question 19 - I think part (c) isn't on the syllabus anymore. Can anyone confirm?

Adjusted total points: (Originally 76)
1. Adjustment for incorrect point total Q1: 76+0.75=76.75
2. Delete Q1 (c): 76.75-1.5=75.25
3. Delete Q7: 75.25-2.75=72.5
4. Delete half of 11(c): 72.5-0.50=72
5. Delete Q15: 72-1.50= 70.5
6. Delete Q16: 70.5-2.25= 68.25
7. Delete Q19 part (c): 68.25-0.75=67.5

NEW PASS MARK (~72.5%) = 49

[Kongo]

Exam Yellow #12:

In part A the solution assumes the plowback ratio is equal to one (since you are growing the book value with all of the ROE).

Then in part B the solution derives the growth rate as ROE - k, but goldfarb defines the growth rate as plowback * ROE (book value growth does not rely on the required market return.) So the growth rate here would be 8.75% according to part a (since plowback=1).

Dedicated, did you get confused by the Goldfarb problem. I am having bobby's issue.

[Dedicated111]

Dedicated, did you get confused by the Goldfarb problem. I am having bobby's issue.

Yes I did, then I studied the answer for awhile and this is how I tried to reconcile the logic in my head, I could be completely wrong, but here it goes:

ROE (return on equity) = 8.75%
Required Market Return = 6.75%

...

150*.0875 = 13.125 (this goes in my pocket)
But the market requires 6.75% to be returned to them, 150*.0675 = 10.125 (but I haven't earned the 13.125 yet, the market only knows I have invested my beginning book value of $150, so I'm sneaky ;) and I hide my 13.125 from them until the next year)

150+13.125-10.125 = 153

153/150 - 1 = 2% and since the ROE and k are to remain constant, we can call this 2% = g

Took me forever to wrap my head around this, so I sure hope I'm correct because there's probably no way I can change the way I think about it now LOL

[ActuarialSound]

Although I am not positive (I am about 99.9% positive), I have reason to believe the solution given is incorrect.

Yes, the growth rate=ROE*p; therefore, g=8.75%.

The 2% does come into play here as it is the % of Beginning BV to calculate AE...but it is NOT a growth rate.

The growth rate =8.75%, the year-over-year beginning capital =8.75%, the year-over-year abnormal earnings =8.75%. These all equal the growth rate since the plowback ratio is 1.

Finally, as we may or may not recall from Exam FM, when g>k in an infinite series, such as this one, the geometric progression diverges and the present value of the perpetuity does not exist. Therefore, there is no solution.

I would love to be proven wrong by someone and have this problem make sense but this is the best solution I have come up with yet.

[Dedicated111]

Sure, that's what I concluded at first...but then I thought about it and thought about it... no one told us the plowback ratio was 1, sure in a problem like this, you could state that as your assumption and proceed. However, I thought about TwoStep's logic and to see if I could make sense of it...he seems like a smart fellow...and what I posted is what I came up with.

So with that, you will have to disprove my logic. I meerly thought about how and where the cash flows were going....very manual, brutal thought process, but I think it makes sense. Like I said, I could be wrong...but you didn't disprove what I said...

[ActuarialSound]

Dedicated, I would like to begin by stating that I have an incredible amount of respect for the amount of effort you have put forth both in learning this material and in helping others (myself included) to learn this material and to be better prepared for this exam. Point being, I mean no disrespect by the following response.

If you accept TwoStep's solution to part (a), then you obviously agree that the plowback ratio is 1 seeing as the year ending capital is the next year's beginning capital. None of it goes away; therefore, none of it is paid out as a a dividend, buyback, etc. It most definitely proves that the plowback ratio =1. [You can calculate it yourself if you would like using the solution to part (a) by taking the Change in Capital/Net Income and finding it is equal to 1]. Further, nothing is stated in the problem suggesting there is a dividend; therefore, we assume there is no dividend. If you did not make this assumption, what made you make the the assumption that a dividend was paid and how did you determine how much of a dividend was paid?

Point of all of the above is that it is clear from the solution of part (a) that the plowback ratio is indeed 1 which disproves the solution for part (b) by use of every formula.

Last, I did disprove the 2% growth in the previous post by stating that it was equal to the abnormal earnings, NOT some variable that we will call g (or "growth"). All of these ratios have relationships, that must hold true. You can suggest that the growth rate is 2% for part (b) but then you must change your answer to part (a) and assume a plowback ratio of ~23%. However, you cannot make these assumptions and proceed to calculate (a) and (b) as they are in their current state.

[Joshua0317]

In an AE model, doesn't the plowback have to be equal to 1? If the plowback were not equal to 1, then we would be paying out dividends and the shareholder required return would be less. It was stated in the paper that if we instead invest at the required rate, the investors are indifferent. So instead of tracking the dividend requirements and calculating a dividend rate and plowback ratio we simplify by using the shareholder required return. The difference between this return and the return we earn is the AE.

If we assume there is a p<>1 then we have some explaining to do with dividend payouts and shareholder return requirements.

As far as part B, we are assuming actual return of 8.75% and we are discounting at the actual rate required. So we are concerned with BV(0)+PV(AE):

PV(AE)=BV(0)*(.0875-.0675)/(1.0675)+1.0875*BV(0)*(.0875-.0675)/(1.0675)^2+...

Does that make sense

[Dedicated111]

Dedicated, I would like to begin by stating that I have an incredible amount of respect for the amount of effort you have put forth both in learning this material and in helping others (myself included) to learn this material and to be better prepared for this exam. Point being, I mean no disrespect by the following response.

If you accept TwoStep's solution to part (a), then you obviously agree that the plowback ratio is 1 seeing as the year ending capital is the next year's beginning capital. None of it goes away; therefore, none of it is paid out as a a dividend, buyback, etc. It most definitely proves that the plowback ratio =1. [You can calculate it yourself if you would like using the solution to part (a) by taking the Change in Capital/Net Income and finding it is equal to 1]. Further, nothing is stated in the problem suggesting there is a dividend; therefore, we assume there is no dividend. If you did not make this assumption, what made you make the the assumption that a dividend was paid and how did you determine how much of a dividend was paid?

Point of all of the above is that it is clear from the solution of part (a) that the plowback ratio is indeed 1 which disproves the solution for part (b) by use of every formula.

Last, I did disprove the 2% growth in the previous post by stating that it was equal to the abnormal earnings, NOT some variable that we will call g (or "growth"). All of these ratios have relationships, that must hold true. You can suggest that the growth rate is 2% for part (b) but then you must change your answer to part (a) and assume a plowback ratio of ~23%. However, you cannot make these assumptions and proceed to calculate (a) and (b) as they are in their current state.


I completely agree...that's what I concluded at first...then I thought maybe part (a) and part (b) were mutually exclusive, so then you can/assume whatever you want with (b) essentially. So I was trying to make sense of it all (assuming (b) was correct). Hey I don't care, the exam question will be written in a much better fashion so that there is no ambiguity (well..maybe not completely no ambiguity...but ya know what I mean). I'm not spending anymore brain power on the question...it's not worth it. I think we all understand how AE works, just reminds us to continually state our assumptions before proceeding with a problem.

and we're cool ActuarialSound...no hard feelings ;)

[ActuarialSound]

Dedicated, I do appreciate the discussion we had about this and I like that you're staying true to your quote (well a modification of your quote...that we should move past it to drill down on other areas). It helps to be able to talk/write about some of these topics to make the ideas more solid in my head.

Is anyone focusing on certain parts of IAA and Brooks more than others? Or anyone having any premonitions about which topics will be touched on. Some topics were tested the past two years (Brooks - capital models), I feel like its time for them to pick on a new topic...any ideas?

[Dedicated111]

Okay, can someone point me to the paper where I can find the variance formula used in Exam Yellow - Question 13(a)?

[Joshua0317]

This is a wicked question...

Its in the IAA appendix page 112. It is in the discussion of the underlying Loss model for a factor based formula. Its a generalization of a mixed process where the count and size are not independent so Var(T)=Var(E(T|Z))+E(Var(T|Z)) doesn't entirely work. (Or at least I think it has similar derivation...).

[Dedicated111]

UPDATE FOR 2013 SYLLABUS: EXAM ORANGE

Some of these are very unrealistic, and I didn't want to waste too much time on them when I could use my time more efficiently...but there are a few comments and this is how I'd adjust this exam....

1. Question 3a - answer is incorrect. See Mack paper to see how the test is supposed to be completed. (TwoStep knows of this issue but did not have time to fix the exam)
2. Question 4 - extremely unrealistic. I wouldn't even attempt. Do review discounting of reserves formula though. (Clark)
3. Question 5 - I think they will definitely give you the equation for a Weibull. Look this up when doing the problem (don't be ashamed lol)
4. Question 7b - too difficult, change to only calculating Var(C2,3)
5. Question 8 - change to Parameter Variance = 8583. And keep the rest of the problem the same. (i.e. you don't have to calculate the parameter variance, instead they will give it to you in the problem)
6. Question 14c - delete. extremely unrealistic.
7. Question 14h - delete. I don't even remember reading anything about prudential requirements. I think the way this part of the question is written is unrealistic. just delete.
8. Question 18 - not on syllabus

Adjusted total points: (Originally 95.75)
1. Delete Q4: 95.75 - 4.00 = 91.75
2. Change 7(b): 91.75 - 0.75 = 91.00
3. Change 8: 91.00 - 1.00 = 90.00
4. Delete 14(c) and 14(h) = 90.00 - 3.50 = 86.50
5. Delete Q18: 86.50 - 2.00 = 84.50

NEW PASS MARK (~68% (because of difficulty)) = 57.50

[shmiluy]

Did you also do the first 2 practice exams and have a list of problems that no longer come from the current syllabus? I did not do any yet, so just wondering if you did. Thanks a LOT!

[kaskomm]

Question on the BLUE exam... what paper(s) do(es) #14 and #15 come from? Are these now off the exam or did I just miss something there?

Thanks!

[dan_4000]

I completely agree...that's what I concluded at first...then I thought maybe part (a) and part (b) were mutually exclusive, so then you can/assume whatever you want with (b) essentially. So I was trying to make sense of it all (assuming (b) was correct). Hey I don't care, the exam question will be written in a much better fashion so that there is no ambiguity (well..maybe not completely no ambiguity...but ya know what I mean). I'm not spending anymore brain power on the question...it's not worth it. I think we all understand how AE works, just reminds us to continually state our assumptions before proceeding with a problem.

and we're cool ActuarialSound...no hard feelings ;)

I don't want to beat a dead horse here, but I just got to this problem (taking the yellow exam right now), and I thought I'd weigh in and see if anyone has any strong feelings about my interpretation of this.

If you review the Goldfarb material on page 30 at the bottom, he says that "in this model growth in abnormal earnings reflects both the growth rate in the book value of the firm as well as the amount by which the ROE exceeds the required return."

So no real help there. He doesn't give any specifics about what he means.

On the next page, he shows calculations. His calculations show an ROE of approximately 15.5% (toward 2007-2009) and a required return of 8.95%. The book value growth rate is (confusingly) around 4%.

So what do we have:
Amount by which ROE > k = 15.5 - 8.95 = 6.55%
Given book value growth rate = 4%

And for the coup de grace, in table 26 he assumes that abnormal earnings continue in perpetuity without growth - they're $8,010 forever after 2009.

For his part, Goldfarb seems to indicate that the 4% is the abnormal earnings growth rate.

In problem 12, no plowback ratio is given. In Goldfarb's examples, you can't determine the plowback ratio from the ROE or required return. These things just tell you, given a beginning book value, what your net income or your required return is. If you were a shareholder, you wouldn't care particularly whether you got all the income back in the form of dividends or if they reinvested in the company (increasing the value of your shares) because the two are equivalent for you. ROE and k are not related to dividend rate in this way.

In this case, Twostep seems to have taken the text from page 30 and said that the growth rate is the amount by which the ROE exceeds k, giving a growth rate of 2%. But Goldfarb doesn't seem to actually use this method in practice, preferring to look at growth in book value (see just below Table 25 on page 31).

If I were answering this question on a test, I would probably just state "assume plowback ratio = 100%" or "assume plowback ratio = k" (implying that all abnormal earnings are paid out as dividends) or something like that. But given the limited information from Twostep's problem, you're best off assuming a growth rate and going for it.

I think Twostep is wrong for assuming a 2% growth rate, but it's still defensible in a sense. Goldfarb never mentions what he actually means when he says that on page 30, so I'm not sure it EXACTLY means that g = ROE - k. I would prefer to explicitly state a plowback ratio assumption and go from there.

[Dedicated111]

Did you also do the first 2 practice exams and have a list of problems that no longer come from the current syllabus? I did not do any yet, so just wondering if you did. Thanks a LOT!

I've only done yellow and orange so far. Will get to the others soon

[Dedicated111]

Dan - that's exactly what we should all do. State our assumptions when the question is vague. I agree that it's not 100% clear

[Dedicated111]

Question on the BLUE exam... what paper(s) do(es) #14 and #15 come from? Are these now off the exam or did I just miss something there?

Thanks!

These are off. I think it's the Venter Financial paper, if I'm remembering correctly (I found it the other day)

[Dedicated111]

UPDATE FOR 2013 SYLLABUS: EXAM BLUE

I agree that this is a pretty realistic exam. I definitely recommend taking. There are a couple changes worth noting...

1. Question 1 - Is it correct that the question is asking for the "reserves"? Because shouldn't the answer subtract 75 from L(x)? Or am I thinking about it incorrectly?
2. Question 6 - I don't think we are going to need to calculate parameter variance. I really think they will give it to us. Instead of the problem giving you Var(n), change to Parameter Variance = 510503
3. Question 7 - same as Q6, change to Parameter Variance = 180242
4. Question 14 - not on syllabus.
5. Question 15 - not on syllabus.
6. Question 19 - for part a, b, and c, change wording to Evaluate [the appropriateness] of the method...
7. Question 21 - delete part (b), this is in question 22

Adjusted total points: (Originally 70)
1. Delete Q14: 70 - 2.25 = 67.75
2. Delete Q15: 67.75 - 1.75 = 66
3. Delete Q20 (b): 76 - 0.50 = 65.50

NEW PASS MARK (~72.5%) = 47.50

[shug0972]

Thank you Dedicated. Very useful information.
Have you done exam green yet?

[Dedicated111]

shug - I will probably do exam green this weekend, it says that it's expected question difficulty, but too long. I might try to suggest some questions to throw out to make it more of an "expected" exam.

[Kongo]

shug - I will probably do exam green this weekend, it says that it's expected question difficulty, but too long. I might try to suggest some questions to throw out to make it more of an "expected" exam.

Be careful about throwing out too many questinos. I agree with you that there won't be all these crazy questions, but the trend on the fellowship exams I ahve taken is around 5 points an exam are on "obscure, they won't possibly ask that questions". While I agree Two STeps exams are littered with them, you are going to feel like an a** when one of those questions appears on the exam (either this year or a few years down the road).

[Dedicated111]

Kongo - I agree. I already have that in mind. I haven't even looked at the exam to see what type of questions there are. I might not suggest throwing any of them out (and they are suggestions, so take it or leave it...your choice)

[dballs33]

For exam yellow Q8b, is the answer supposed to use the incremental for 2-3 instead of using cumulative 2-4?

[Dedicated111]

dball - I'm not 100% sure I understand what you are asking. The formula in part 8b is correct, HOWEVER, i did forget to mention that the notation for Z is wrong. It should be Zij, therefore, Z_2010,3 (not Z_2011,2)

(remember the notation for this paper - Verrall: C = incremental, D = cumulative)

[dballs33]

dball - I'm not 100% sure I understand what you are asking. The formula in part 8b is correct, HOWEVER, i did forget to mention that the notation for Z is wrong. It should be Zij, therefore, Z_2010,3 (not Z_2011,2)

(remember the notation for this paper - Verrall: C = incremental, D = cumulative)

nevermind. I was using lambda = 1.15 instead of calculating the ldf as 95%/80%

[ActuarialSound]

Not sure where the best place to post this is, but I will start here. If you think I should create a separate thread let me know:

UPDATE FOR 2013 SYLLABUS:
I went through Exam Yellow this weekend: This is what I found (I hope I caught them all)...

1. Question 1's total points do not add up. Should be 3.50
2. I really think question 1c is unrealistic. Not sure if this was from another paper not on the syllabus anymore and I know these exams are supposed to range in difficulty. But I still think there is no chance this would be asked.
3. For Question 5a) I would recommend doing this problem EXACTLY how the paper does it. In the answer, TwoStep truncates the % paid before finding ELR, but in the paper, they find the ELR prior to truncation. Again, I recommend doing exactly how the paper does it, don't ask questions, just do it. LOL Any objections?
4. Question 7 - not on syllabus
5. Question 11, half of part (b) - not on syllabus (The England and Verrall paper reference)
6. Question 15 - not on syllabus
7. Question 16 - not on syllabus
8. Question 19 - I think part (c) isn't on the syllabus anymore. Can anyone confirm?

Adjusted total points: (Originally 76)
1. Adjustment for incorrect point total Q1: 76+0.75=76.75
2. Delete Q1 (c): 76.75-1.5=75.25
3. Delete Q7: 75.25-2.75=72.5
4. Delete half of 11(c): 72.5-0.50=72
5. Delete Q15: 72-1.50= 70.5
6. Delete Q16: 70.5-2.25= 68.25
7. Delete Q19 part (c): 68.25-0.75=67.5

NEW PASS MARK (~72.5%) = 49

Q8 - Solving for Z, Beta=12.5 not 12.25 as is calculated. The impact is immaterial.
Q18 - Calculating Spearman's Rho. Rho=.7143, not .7714. The Sum Square Diffs = 10, not 8. The ranking order of the Commercial LR's should be 6,5,1,3,4,2.

[Elsaball]

Has anyone here tried red? I'm finding it easier than the other ones...

[shug0972]

Dedicated, can you comment on the difficulty of exam BLUE compare with CAS past exams (2011, 2012)?

I wish to pick an easier exam to start with and gradually move on to the more difficult ones

[Dedicated111]

elsaball - I'm hoping to do Red tomorrow.

shug - i haven't taken 2011 yet, I'm saving that for the beginning of next week. but I would say Blue is comparable to 2012, maybe slightly easier?! It's all relative though right? Some questions might be harder for you than for me and vice versa. I think blue is a good place to start.

[TwoStep]

Where were you guys last year? It seems like everyone is always taking the exam I'm not taking in a given season.

[PeasnCarrots]

I took red yesterday, and I didn't find it as hard as some of the other ones.

[Elsaball]

On Blue 21a, why does the solution subtract the liquidity premium from the risk-free rate for CAPM? I thought you were only supposed to do that for higher-yield proxies of rf, such as T-Bonds.

[ActuarialSound]

In the problem, it mentions the fact that the liquidity premium is 1.2%, suggesting that this premium is loaded in the "risk-free rate" given. Therefore, you subtract it. Normally a liquidity premium is built in if one is using a longer term rate (ie. 20-yrs). To my knowledge, it has nothing to do with the magnitude of the rate being given. I hope this helps!

[Elsaball]

In the problem, it mentions the fact that the liquidity premium is 1.2%, suggesting that this premium is loaded in the "risk-free rate" given. Therefore, you subtract it. Normally a liquidity premium is built in if one is using a longer term rate (ie. 20-yrs). To my knowledge, it has nothing to do with the magnitude of the rate being given. I hope this helps!

How does it make sense that the risk free rate is loaded with a liquidity premium??? Then it's not risk free!

[Joshua0317]

It is risk free in the sense that the rate is guaranteed. The liquidity premium is due to the unavailaility for a GIVEN time of your investment. A 20 year rate on a CD mean your money will be locked away for 20 years. You know when it is going to be returned for certain, you know the rate you will be getting for certain. There is no risk for the rate.

BUT if you are going to use the rate to determine a shorter term discount factor, you want to remove the premium that they must give in exchange for holding your money. Basically they are paying extra so that you actually invest in the longer term.

Hope that helps.

[John Doe]

Red, Q. 13 a): at first glance, I was sure this was another off-syllabus question based on the old Venter Financial paper or some other paper that was removed this year.

I must admit, I was a bit shocked when I realized it was from IAA pages 150 and 151. All I can say is that I sincerely hope the CAS doesn't go overboard on testing obscure formulas for which no example was proided in the original paper.

[Joshua0317]

But what would be the fun in that. Our ability to answer should derive via Bloomish learning. Who needs examples when we have the best reasoning capabilities the world has ever know?

[Dedicated111]

UPDATE FOR 2013 SYLLABUS: EXAM RED

This is definitely more difficult, but I HIGHLY recommend taking. Few things to point out...let me know if I missed anything...

1. Q6: delete, not on syllabus
2. Q7: delete, not on syllabus
3. Q8 (a): the solution is wrong. Z = credibility factor * lag. In this case, it would relate to % reported.
4. Q12 (a): the terminal value should be divided by 1.08^5 (not ^4)
5. Q14: not on syllabus
6. Q18: I don't think this is on the syllabus but cannot find the paper that it is in for confirmation. The ARCH process?! pfftt...get outta here.

Adjusted total points: (Originally 88.50)
1. Delete Q6: 88.50 - 3.25 = 85.25
2. Delete Q7: 85.25 - 4.00 = 81.25
3. Delete Q14: 81.25 - 2.75 = 78.50
4. Delete Q18: 78.50 - 4 = 74.50

NEW PASS MARK (~70% (based on difficulty)) = 52.25

[John Doe]

A few of my own comments on Exam Red:

Q3: Generalized Pareto? I was convinced we needed to solve for the missing alpha parameter some way or another. It should have really said loglogistic instead.
Q5: f(3) = 0.5%, not 0.4%. The IBNR however is calculated correctly.
Q6: I would argue that part a) is also off-syllabus. None of the papers show how to fit a lognormal model to incremental claims. Unless, of course, the CAS expects us to derive how to do so on the fly, as per a higher level "Blooms" question...
Q8: Just to add to Dedicated's comment, IBNR should be calculated by accident year and then aggregated. My final answer was 6,553.58.
Q9: Total actual emergence was incorrectly calculated as 8,270 as given in the problem. It is actually 8,070. Also, % error should be shown as a %age of actual reserves, not expected reserves.
Q11: In part b), the 30 month premium is subtracted from the 39 month premium, which is incorrect. The 27 month premium should be subtracted. The final answer, however, is correct.
Q12: The growth rate is really reinvestment rate * ROE. It is not appropriate to divide the FCFE at one period by the previous period FCFE.
Q21: Part a) asks for which method produces the lowest surplus, which in reality is the no reinsurance option, as it produces the highest reserves (since the sum of reserves + surplus is fixed, higher reserves means lower surplus). The question should really ask which method requires the least capital/produces the lowest capital charge.
Q23: In ths solution to part a), a distress probability of 4.25% is used, when in fact we were given 4.76%. This doesn't change the conclusion, though.

[TwoStep]

UPDATE FOR 2013 SYLLABUS: EXAM RED

This is definitely more difficult, but I HIGHLY recommend taking. Few things to point out...let me know if I missed anything...

1. Q6: delete (b) and (c), not on syllabus
2. Q7: delete, not on syllabus
3. Q8 (a): the solution is wrong. Z = credibility factor * lag. In this case, it would relate to % reported.
4. Q12 (a): the terminal value should be divided by 1.08^5 (not ^4)
5. Q14: not on syllabus
6. Q18: I don't think this is on the syllabus but cannot find the paper that it is in for confirmation. The ARCH process?! pfftt...get outta here.

Adjusted total points: (Originally 88.50)
1. Delete Q6 (b) & (c): 88.50 - 2.00 = 86.50
2. Delete Q7: 86.50 - 4.00 = 82.50
3. Delete Q14: 82.50 - 2.75 = 79.75
4. Delete Q18: 79.75 - 4 = 75.75

NEW PASS MARK (~70% (based on difficulty)) = 53.25

18 was based on Embrechts, and I think they dropped that paper.

[TwoStep]

When I wrote these, I tried to focus on one paper per a question. There were a few where I did not do that, but for the most part it was just one paper.

I have notes that map every question to the paper for my exams 8 and 9 (sorry, I was just a noob when I did 7).

[John Doe]

Kudos to you for setting those up. On the whole, I must say that you did an amazing job.

Besides, I find that the few minor vagaries/errors are similar to what we can actually expect on an actual CAS exam, which just makes the experience even more realistic.

[briere48]

Regarding the Exam Red, anyone else finding that Question 20 does not really agree with some of the definitions presented in the Non-Risk Measures paper? I would ask the exam creator where he derived the formulae in parts C and D? Particularly for Part D, I cannot find anywhere in the papers where the allocation procedure is described as in the solution on the practice exam.

Similarly for 20 Part C, idea of using what he describes as "allocation percentage" (at least as he defines it) does not agree with what is really presented in Venter.

I keep referring to CF practice problem 2 in the Non Risk Measures section, which IMO, provides a much clearer problem that agrees with the definitions shown in Venter.

[Dedicated111]

Red Q20, I believe comes more so from Venter Strategic Management paper. This is a good question because it makes you think about how to apply the formulas. I don't see how it doesn't agree though. I could be wrong. I definitely see some bloomsy-mathy-type questions coming from this capital allocation type stuff, so be ready to think outside the box.

[TwoStep]

Red Q20, I believe comes more so from Venter Strategic Management paper. This is a good question because it makes you think about how to apply the formulas. I don't see how it doesn't agree though. I could be wrong. I definitely see some bloomsy-mathy-type questions coming from this capital allocation type stuff, so be ready to think outside the box.

I'm going to use my 700th post to thank you for that.

[Dedicated111]

:party: Nice! Winner winner chicken dinner!

[briere48]

Red Q20, I believe comes more so from Venter Strategic Management paper. This is a good question because it makes you think about how to apply the formulas. I don't see how it doesn't agree though. I could be wrong. I definitely see some bloomsy-mathy-type questions coming from this capital allocation type stuff, so be ready to think outside the box.

Specifically in Part D, the method used is a proportional allocation. Now, because this is based on a transformed mean, VaR in this case, the proportional allocation method does provide a marginal decomposition. The question, however asked for a marginal allocation, and I question whether the provided solution provides this.

(Also, just a side note as I re-read Part E, but unless the marginal allocation procedure is based on an incremental marginal allocation procedure, it may NOT sum to the entire risk of the company. Clearly in this case, the method used does add up as it was a proportional method.)

And just a last point, and correct me if I am wrong, but it appears to me at least, that many of the methods used implicitly assume the capital for the entire firm is based on a risk measure, as opposed to a more arbitrary amount (i.e. the 20 million in his problem). So to apply the methods in the context of this problem certainly does go beyond what is shown, and I agree makes it a very bloom-esque problem.

[asile]

On orange #2 the Clark process variance parameter, in the solution, is calculated with cumulative losses. I think it needs to be done with incremental. This increases the process variance. Thoughts?

[Calvin]

Yes, I'm with you asile. I used incrementals, which is how Clark does it. I calculated sigma squared to be 312.8

[actuarialista]

UPDATE FOR 2013 SYLLABUS: EXAM BLUE

I agree that this is a pretty realistic exam. I definitely recommend taking. There are a couple changes worth noting...

1. Question 1 - Is it correct that the question is asking for the "reserves"? Because shouldn't the answer subtract 75 from L(x)? Or am I thinking about it incorrectly?

.......



I agree with what Dedicated says above about #1.

On #6, the solution doesn't quite make sense to me. Maybe it is just a notation change from the old papers to our papers, but I thought that exp(c+alpha_2) would give us the expected value of C_{2,3}, however, in the solution it actually turns out that exp(c+alpha_2} is what Verrall would denote by (lambda_3 - 1), in other words it is only the development factor by which we need to multiply D_{2,2} to get C_{2,3}. Does anyone see what I'm talking about?

[shug0972]

Not sure where the best place to post this is, but I will start here. If you think I should create a separate thread let me know:

UPDATE FOR 2013 SYLLABUS:
I went through Exam Yellow this weekend: This is what I found (I hope I caught them all)...

1. Question 1's total points do not add up. Should be 3.50
2. I really think question 1c is unrealistic. Not sure if this was from another paper not on the syllabus anymore and I know these exams are supposed to range in difficulty. But I still think there is no chance this would be asked.
3. For Question 5a) I would recommend doing this problem EXACTLY how the paper does it. In the answer, TwoStep truncates the % paid before finding ELR, but in the paper, they find the ELR prior to truncation. Again, I recommend doing exactly how the paper does it, don't ask questions, just do it. LOL Any objections?
4. Question 7 - not on syllabus
5. Question 11, half of part (b) - not on syllabus (The England and Verrall paper reference)
6. Question 15 - not on syllabus
7. Question 16 - not on syllabus
8. Question 19 - I think part (c) isn't on the syllabus anymore. Can anyone confirm?

Adjusted total points: (Originally 76)
1. Adjustment for incorrect point total Q1: 76+0.75=76.75
2. Delete Q1 (c): 76.75-1.5=75.25
3. Delete Q7: 75.25-2.75=72.5
4. Delete half of 11(c): 72.5-0.50=72
5. Delete Q15: 72-1.50= 70.5
6. Delete Q16: 70.5-2.25= 68.25
7. Delete Q19 part (c): 68.25-0.75=67.5

NEW PASS MARK (~72.5%) = 49

A bit late... but here are my thoughts:

1c: The Bayesian method was discussed in Brosius. In fact I think this is a possible question - not highly likely, but definitely very possible. Given X = 2, Y got to be either 2 or 3. So you only need to solve one Bayesian probability equation (discussed in Brosius page 5) to get the answer:

P(Y=2 given X=2) = [ P(X=2 given Y=2)*P(Y=2)] / [ P(X=2 given Y=2)*P(Y=2) + P(X=2 given Y=3)*P(Y=3) ]
= [(0.6^2)*(1/3)] / [(0.6^2)*(1/3) + (3*0.6^2*0.4)*(1/3)] = 0.12 / [0.12 + 0.144] = 0.4545
Hence P(Y=3 given X=2) = 1 - 0.4545 = 0.5455

It follows estimated ultimate claim = 0.4545*2 + 0.5455* 3 = 2.545

3b: I dont quite understand what the question and solution mean. Could someone explain this?

"Q: What caution does Venter give when applying this methodology to cumulative development factors?
A: Venter notes that when testing the slope of the model, that the null hypothesis should be that it is different from 1.00, and 0.00 as is the case with predicting incremental claim values."

16: This is still on syllabus, it's from IAA - see page 136

19c: Again still on, t-Copula is discussed in some detail in IAA - see page 176.

20c/d: i think p represents the survival function not CDF, so p should equal to 0.01, not 0.99?

21: My answer is no option can satisfy state requirement because I thought the VaR table represents the distribution of underwriting results. Check the presentation from Venter & Underwood page 12 - the author calculated "VaR" from the distribution of underwriting results (already net of reinsurance premium / recovery /expenses), not from a table of distribution of losses.
Since question did not specify its VaR table has a different meaning from the paper, I will stick with the interpretation from the paper. Any thoughts?

[John Doe]

For Exam Orange, questions 1 and 23, there is no indication as to whether the triangles shown are cumulative or incremental. And in both cases, the solution assumes the reverse of what is normally standard for those types of triangles in those situations. Also for Q19, there is no mention as to whether the TVaR values apply to losses or to underwriting profit. Again, the papers tend to go with U/W profit.

In all cases, if you go with the standard, you definitely deserve full points. If it's unclear, however, just state your assumptions.

[Calvin]

Q 13 from exam Yellow: Can someone please tell me what paper this topic is in? I vaguely remember seeing it, but don't remember where. Also, do you think the formula for this question is worth memorizing? Not sure if I'll get to it, it seems to obscure.

[Elsaball]

Iaa