**Who Wants to Be a Fellow?**

*By Steven D. Armstrong, FCAS, and Shantelle A. Johnson of the of the Student Liaison Committee*

It's 8:00 p.m. and the popular television show *Who Wants to Be a Millionaire?* is preempted by a new kind of game show called *Who Wants to Be a Fellow?* I'm amazed that ABC would give an hour of prime-time TV to promote the CAS. Nevertheless, Regis has gone through the fastest-finger round and has brought to the hot seat a gentleman named Alec Smart for what appears to be a grueling test of an actuary's wits and stamina.

The rules are a bit different. A question will be asked pertaining to each of the nine CAS exams. The questions will be asked in order of the exams. There will be one final question, the tenth question, which can be on any topic relevant to the Casualty Actuarial Society (exam-related or nonexam-related). If this tenth question is answered correctly, the new Fellow will also win $1 million! Lifelines still exist and the audience is surprisingly made up of candidates, Associates, and Fellows. The 50-50 option is always a popular choice in eliminating the two most obviously wrong answers, and the most popular, Phone a Fellow, can help Alec in a time of need.

It's time to begin the show. To play along at home, I hit the mute button at the appropriate time so that I would not hear the answer. "So, let's begin *Who Wants to Be a Fellow?*!" roars Regis.

*Regis:* For the first exam, Mathematical Foundations of Actuarial Science, please answer the following question:

Assume 10% of a company's life insurance policyholders are smokers. The rest are nonsmokers. For each nonsmoker, the probability of dying during the year is 1%. For each smoker, the probability of dying during the year is 5%. Given that a policyholder has died, what is the probability that the policyholder was a smoker?

a) 5%; b) 20%; c) 36%; d) 56%

*Regis:* Congratulations, you now have credit for Exam 1. Now for our second question, coming from the syllabus on Interest Theory, Economics, and Finance, please answer the following:

Sean and Anna-Marie each make deposits of $100 at the end of each year for 40 years. Starting at the end of the 41^{st} year, Anna-Marie makes annual withdrawals of X for 15 years and Sean makes annual withdrawals of Y for 15 years. Both funds have a balance of $0 after the last withdrawal. Anna-Marie's fund earns an annual effective interest rate of 8%. Sean's fund earns an annual effective interest rate of 10%. What is Y-X?

a) $2,792; b) $2,824; c) $2,859;

d) $2,893

Alec got the question right and is now moving onto the third exam.

*Regis:* So far so good. You have all your lifelines intact and are now going for Exam 3, Actuarial Models. And I am not talking about Cindy Crawford determining case reserves, if you know what I mean. The question is:

The annual number of accidents for an individual driver has a Poisson distribution with mean l. The Poisson means, l, of a heterogeneous population of drivers have a gamma distribution with mean 0.1 and variance 0.01. What is the probability that the driver selected at random from the population will have two or more accidents in one year?

a) 1/121; b) 1/110; c) 1/100; d) 1/90

After polling the audience, Alec gets this question right, too. It looks like the question for Exam 4 is about to begin.

*Regis:* For Exam 4, Actuarial Modeling, answer the following question:

What is the minimum number of expected claims for full credibility if the coefficient of variation of the distribution at hand is 2.0 and we are looking for full credibility to be defined as +/- 10% of the true value with 95% probability?

a) 1,153; b) 1,537; c) 1,921;

d) 2,305

That was a tough question, but luckily Regis offered that the point corresponding to 95% probability on the Normal Table equaled 1.96, making this question a bit more palatable. After the commercial break, Regis is ready to offer Alec the fifth question.

*Regis:* So, Alec, you have made it through four exams so far. Let's take a look at the fifth question from the material on Introduction to Property and Casualty Insurance and Ratemaking.

Given that the loss and loss adjustment expense pure premium is $100 and that the fixed expense per exposure is $15 with a variable expense factor equaling 19% and a profit and contingency factor totaling 5%, what would be the appropriate rate for this risk?

a) $142; b) $143; c) $147; d) $151

*Regis:* He's got it right! This guy could go all the way to Fellowship! Let's see what the sixth question brings from the topics of Reserving, Insurance Accounting Principals, and Reinsurance.

Given the three link ratios of 1^{st}-2^{nd }development period =^{ }1.50, 2^{nd}-3^{rd} = 1.15, and 3^{rd}-Ult = 1.00, the expected loss IBNR factor for the 1^{st}-2^{nd} development period is:

a) 0.40; b) 0.42; c) 0.44; d) 0.46

*Regis:* You're right! Just one away from Associateship! With two lifelines intact, let's see what Alec can do! For Exam 7, from the U.S. material on Annual Statement, Taxation, and Regulation, please answer the following:

According to G.E. Rejda and using the intermediate assumptions (best estimate), what is the year that combined OASDI trust funds' assets will be exhausted?

a) 2022; b) 2025; c) 2032; d) 2034

Using the 50-50 narrowed the scope for Alec and he guessed correctly, making his Associateship. After this commercial break, let's see if Alec can make it to Fellowship by answering two more questions and the final bonus question.

*Regis:* Alec, you have now made it to Associateship. Only two more correct answers and you will be a Fellow. After that, the final bonus question could win you $1 million. Are you ready? From Exam 8, Investments and Financial Analysis, answer the following question:

The Macaulay Duration for an 8.0% semiannual coupon bond with yield to maturity of 8.0% and a term 2 years until maturity with a Par Value and Price of $100 is:

a) 1.85; b) 1.87; c) 1.89; d) 1.91

*Regis:* After a lot of number punching on your calculator, you got the correct answer! You are in a good position to achieve Fellowship with one lifeline left and only one question left to answer! So let's go for it! Good luck! >From Exam 9, Advance Ratemaking, Rate of Return, and Individual Risk Rating Plans, answer the following question:

The Experience Modification, M, for a risk with actual losses equal to $100,000 and expected losses totaling $120,000 with credibility only being 50% is:

a) 0.92; b) 0.93; c) 0.94; d) 0.95

After phoning a friend who passed Part 9 during the last sitting, Alec answers the question.

*Regis:* That's incredible, Alec! You have achieved Fellowship live here on ABC—a first in television history! You must feel great right about now. Let's see if we can add $1 million to add to your celebration! The tenth and final question is:

In which year's online version of the CAS *Proceedings* were the Casualty Actuarial Society Examinations last printed within the publication itself?

a) 1959; b) 1960; c) 1970; d) 1980

*Alec is obviously stumped. Can you help him win $1 million? Log on to the CAS Web Site and enter through the Student Discussion Forum to locate the thread entitled Student Liaison Committee—*Who Wants to Be a* *Fellow?* There you can find the answers to the first nine questions and you will be able to post your answer to the final question. *

*Good luck and have fun!*