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After a decade of relatively slow change, effective 1 January 2000 the professional actuarial exams will undergo a complete restructuring. In particular, the new structure replaces with one exam the two exams most commonly taken yearly by thousands of undergraduates wanting to test the actuarial waters.

This article outlines the changes of greatest interest to teachers and students of undergraduate mathematics and provides links to much more detailed information. The opinions and advice stated are those of the author, Jim Daniel; they do not necessarily reflect the view of the Mathematical Association of America, the Casualty Actuarial Society, or the Society of Actuaries.

This article is constructed as one long document. You can scroll through it, reading one screen at a time, or jump immediately to one of the following Sections:

- History
- Current basic exams
- The coming changes
- The new basic Joint Exam 1
- The new sort-of-basic Joint Exam 2
- Jobs and the new exams
- Transition to the new exams
- Advising interested students
- Contacts and resources
- The author

Actuarial exams in the United States have been administered for over a century by what is now the Society of Actuaries (SoA) and for over 80 years by what is now the Casualty Actuarial Society (CAS). The exams have changed quite a bit over the years---there are many actuaries working today whose first actuarial exam was over English grammar, for example. For many years both organizations had ten exams, with all required.

In the late 1980's, the SoA instituted its Flexible Examination System in force today that features a huge battery of exams worth various amounts of credit; some of the exams are required, some are elective---in fact, the system is structured much like the degree requirements of many colleges and universities. The CAS maintained its system of ten exams, although some were subdivided.

Most people working as actuaries in the U.S. are either an Associate or Fellow of one or more of the SoA or CAS. One now becomes an Associate essentially by completing roughly two-thirds of either the CAS exam system or the SoA exam system; to become a Fellow one must complete either's full system.

The two exams most commonly taken by undergraduates are jointly administered by the CAS and the SoA. The exam called 100 by the SoA and Part 1 by the CAS covers calculus and linear algebra, although it is usually about 90% calculus. I'll refer to this as Exam 100/1. The calculus tested is that of the standard three-semester undergraduate sequence (not the business-calculus sequence many schools offer), while the linear algebra is that of the standard one-semester sophomore course. At present Exam 100/1 is a three-hour, 45-question, multiple-choice test.

The exam called Part 2 by the CAS and 110 by the SoA covers probability and statistics. I'll refer to this as Exam 110/2. The material tested is usually covered in the fairly standard two-semester undergraduate sequence of calculus-based mathematical probability and statistics, much as described by the MAA's Committee on the Undergraduate Program in Mathematics. At present Exam 110/2 is a three-hour, 45-question, multiple-choice test.

Starting 1 January 2000, both the SoA and CAS exam systems change significantly:

- The new SoA system
will contain eight exams, all required, plus a professional
development project. The eighth exam covers advanced specialized
actuarial practice, and the examinee chooses one from a small set of
practice areas---otherwise, there are no electives in the system.
- The new CAS
system will contain nine exams, all required. There are no
electives in the system.

New SoA Exams 1, 2, 3, and 4 will be identical to new CAS Exams 1, 2, 3, and 4 and will be jointly administered. I refer to these as Joint Exams 1, 2, 3, and 4. According to present plans, each of these four will be administered twice yearly, once in spring and once in fall; there will no longer be February exams as there are now for 100/1 and 110/2.

Joint Exam 1 is a basic exam, much as are the current Exams 100/1 and 110/2---its content is taught in standard undergraduate mathematics classes. Exams 3 and above for both the SoA and the CAS are uniquely actuarial in that they cover content not normally offered at most colleges and universities other than possibly those that offer special actuarial programs (a list in pdf format of such programs can be downloaded). Joint Exam 2 is viewed by the CAS and SoA as "basic", although in fact it covers topics not universally taught in U.S. colleges and universities.

The new Joint Exam 1 will cover calculus (at the level of the
current Exam 100/1 but *without the
linear algebra*) and probability (at the level of the
current Exam 110/2 but
*without the statistics*), with as many as possible of the questions
placed in a *risk management* setting. The exam is currently planned
to last three hours, with approximately 40 multiple-choice questions.

Standard textbooks for the standard calculus and probability classes are suggested as covering the mathematical content of the exam, just as for the current basic Exams 100/1 and 110/2. A "study note of at most 50 pages" will be made available to introduce some risk terminology and to provide illustrative problems and solutions.

As part of the report on Joint Exam 1, a sample exam was released. Many actuarial educators think that passing the new Joint Exam 1 will be more difficult than passing either the current Exam 100/1 or the current Exam 110/2, and possibly more difficult than passing both those exams. One new difficulty in passing Joint Exam 1 is that it requires some ability to select a model to apply in a problem---this is an important skill, but not one that has been tested previously.

For example, the current Exam 110/1 might well contain the following problem:

A geometric random variable N has expected value 11.5; compute the probability that N equals 5.Problem #7 on the sample exam for Joint Exam 1 reads instead as follows:

As part of the underwriting process for insurance, each prospective policyholder is tested for high blood pressure. Let X represent the number of persons tested until the first person with high blood pressure is found (counting that person with high blood pressure). The expected value of X is 12.5. Calculate the probability that the sixth person tested is the first one with high blood pressure.Mathematically, these two problems are identical, but the added challenge of picking the appropriate probability distribution will stretch many students. Solving problems from old exams (once there exist Joint Exam 1 old exams) that are available from commercial study manuals will probably be even more important than now.

The new Joint Exam 2 will consist of about 40% economics, about 30% finance, and about 30% mathematical interest theory. Since many colleges and universities do not teach classes on all this material, although some do so, I've called it "sort-of-basic". The exam itself is currently planned as a four-hour exam having a mixture of multiple-choice and true/false questions; the approximate number of questions had not been announced as of late January 1999. As part of the report on Joint Exam 2, however, many sample questions were released.

The economics has been described by the SoA and CAS as at an intermediate level. Economics advisers at The University of Texas at Austin informed me that most of the recommended material would be covered in UT-Austin's three-semester sequence consisting of introductory microeconomics, introductory macroeconomics, and intermediate microeconomics. Many colleges and universities teach classes that cover most of this material.

The finance has been described by the CAS and SoA as the fundamentals of business (or corporate) finance. Finance advisers at UT-Austin informed me that most of the recommended material would be covered in UT-Austin's introductory finance-majors course on business finance (which has accounting as a prerequisite). Many colleges and universities with business schools or business departments teach classes that cover this material.

The mathematical interest theory includes a mathematical treatment of interest rates and present value, annuities, yield rates, amortization, and applications. While few schools other than those with special actuarial programs teach classes that cover this material, there exist readable textbooks and study manuals that students could read on their own or with faculty guidance in an individual instruction or reading course.

Actuaries often quip that passing exams doesn't matter unless you want to get a job. That's not going to change. Except possibly in times when demand for entry-level actuaries has been extremely high, for many years the typical person getting hired has passed two or more actuarial exams. In recent years that has usually meant current Exams 100/1 and 110/2. Most actuarial educators and actuarial employers with whom I've spoken expect the typical person hired under the new system to have passed one or more actuarial exam---probably exactly Joint Exam 1. As always, people that have passed more exams will be in greater demand---as will those with better communication skills, better computing skills, greater business background, greater leadership potential, and so on.

Transition rules for converting credit for exams passed in the current
system into credit for the new exams have been announced by both the SoA and CAS. Transition credit
for Joint Exam 1 can be obtained
by passing *either* current Exam 100/1 *or* current Exam
110/2 by the last time the current exams
are given in November 1999. The most likely manner for undergraduates to
obtain transition credit for Joint Exam 2 is by having passed SoA Exam 140
on mathematical interest theory together with either Exam 100/1 or Exam
110/2. Note that transition credit for both Joint Exam 1 and Joint Exam 2
can be obtained by passing three current exams: 100/1, 110/2, and SoA Exam
140. For all the transition rules, follow the two links at the start of
this section.

What should current or future students do if they are interested in taking actuarial exams? How can faculty help such students?

**Before January 2000.**

Students that will have finished the basic regular calculus sequence (not a
business-calculus sequence) in time to prepare for the current Exam 100/1 by the last time it is given in
November 1999 should make every effort to pass Exam 100/1 and thereby
receive transition credit for
the more difficult new Joint Exam
1. They will no doubt find practice exams
crucial for their preparation---along with mature advice about how to
prepare for a timed multiple-choice exam on calculus (about 90%) and linear
algebra (about 10%). Students with the academic background to pass other
exams that generate transition credit should look carefully at the transition rules in order to
maximize credit.

**Starting in January 2000**.

Students interested in an entry-level actuarial job need to take as much
relevant coursework in mathematics, economics, and business as is available
to them and need to pass new Joint
Exam 1 on calculus and probability; basic microcomputer skills
(skillfully using word-processing and spreadsheet programs, for instance)
and basic programming skills are highly valued as well.

Appropriate standard mathematics classes include the basic calculus sequence (again, not business-calculus), calculus-based probability, and a mathematical statistics class having calculus-based probability as a prerequisite; matrix algebra will prove helpful in later actuarial learning. In theory, these classes would cover most of the mathematical facts needed in later actuarial study; in practice, the mathematical maturity developed by taking other advanced undergraduate mathematics classes will prove extremely useful.

If available, classes in economics and business will provide not only
material that may be tested in new Joint Exam 2 but also background for a career that is, after
all, a *business* career with a strong mathematical base.

Faculty can help most simply by providing advice and guidance (like the preceding) as well as resources from which students can obtain more information. More active help might consist of offering an organized class or individual-instruction class that would help students that have completed calculus and probability prepare for new Joint Exam 1; still more active would be to provide an organized class or individual-instruction class in the mathematical interest theory covered on new Joint Exam 2.

I recommend that faculty members that have students preparing for Joint Exam 1 become familiar with that exam so that they can provide informed advice about how to prepare and so that they can solve the Exam questions that students will invariably bring to them.

There are lots of resources, both formal and informal, for information about actuarial careers, actuarial exams, and actuarial education. Here are a few:

**Career information**. Phone the SoA (847/706-3500) and the CAS (703/276-3100) to receive free general information on actuarial careers, exams, and the like. Faculty can have their departments put on regular distribution lists to receive such materials. Individual actuaries---especially alums of your school---working near your school are usually delighted to come talk about their careers.**Actuarial exam systems**. Phone or look at the Websites of the CAS (703/276-3100) or the SoA (847/706-3500) to get detailed catalogs of the exam system of each organization. The two organizations jointly publish*The Future Actuary*three times yearly for people taking actuarial exams; phone the SoA to subscribe if you are not taking exams.**Practice actuarial exams**. For some time the SoA and CAS have distributed free a booklet containing a couple of practice exams (with answers) for the current Exams 100/1 and 110/2; this will probably continue for Joint Exam 1. Call the SoA (847/706-3500) or CAS (703/276-3100) for copies. The Actuarial Bookstore is one source of commercial study manuals (and actuarial textbooks) published by various publishers that typically contain several old exams with solutions.**Actuarial education and research**.- Information on both education and research is available in the
*Expanding Horizons*newsletter of the SoA's special interest Section on Education and Research; the newsletter is free to Section members and available to others for a modest fee. The Section also sponsors and organizes the annual Actuarial Research Conference in August, where many actuarial educators get together. - The Actuarial Faculty Forum (AFF) is an informal organization
of faculty interested in actuarial education; free membership
is open to faculty by contacting the Actuarial Education and
Research Fund at the SoA (847/706-3500). The AFF usually
sponsors an MAA session on actuarial education at the combined
mathematics meetings each January, and it publishes its free
newsletter
*Conversations*.

- Information on both education and research is available in the

Dr. James W. Daniel, A.S.A.: Although I've taught a wide range of mathematics at UT-Austin for nearly 30 years and once was very active in research, since 1989 I've focused on actuarial education---I hold the Paul V. Montgomery Centennial Memorial Professorship of Actuarial Mathematics and serve as Director of Actuarial Studies in the Mathematics Department at The University of Texas at Austin. In 1990 at the ripe old age of 50 I started taking the SoA exams, becoming an Associate of the Society of Actuaries---an A.S.A.---in 1991.

MAA Online is edited by Fernando Q. GouvÃªa (fqgouvea@colby.edu). Last modified: Thu Apr 22 13:04:27 -0500 1999