Study Manual For Exam FM/Exam 2 Financial Mathematics & Financial Economics

To the student: Please read this Introduction. It contains important information. This manual is a study guide for the Society of Actuaries' Exam FM and the Casualty Actuarial Society's Exam 2. Each topic is illustrated by examples and is followed by questions, with solutions, from past SOA and CAS exams dating from the early 1980s. The manual consists of 19 sections, followed by five original full-length practice exams. • Part I, Sections I to 9: Financial Mathematics These sections cover the required readings in the four reading options: Braverman, Ruckman & Francis, Daniel & Vaaler, and Kellison. • Part II, Sections 10 to I 9: Financial Economics These sections cover the required readings in McDonald's Derivatives Markets. • Part III: Five Original Practice Exams (35 questions each, 3 hours long) Following each section or subsection, there is a summary of the key concepts and formulas. Goals of this Manual • To explain the concepts of financial mathematics and financial economics in a way that appeals to your intuition and common sense. • To point out shortcuts and tricks that can get you to the answer more quickly. • To warn you about common traps that students fall into and help you to avoid them. • To provide you with hundreds of problems, with solutions, from past exams. • To also provide you with original practice exams made up by the authors. To highlight the concepts, tricks, shortcuts, and traps, you will see special symbols such as the following throughout the manual: CD Concept Alert! @shortcut Alert! @Trick Alert! ~'Trap Alert! Problems There is an old cliche in the real estate industry: What are the three most important factors in evaluating property? Answer: Location! Location! Location! If we had to say what the three most important factors are in studying for (and passing) this exam, they would be Problems! Problems! Problems! You must do a great variety of problems, preferably under time pressure, and especially as you get closer to the date of the examination. Most of the problems in this manual are taken from past SOA and CAS examinations. We want to thank the two actuarial societies for their kind permission to publish these questions. Copyright© 2009 ASM. I Oth edition 1 2 Introduction There are a number of points about past exam questions that you should be aware of: • These questions, which date from the early 1980's, were created by different exam committees, under different syllabi, for exams of different length, etc. Thus, they can vary greatly in style, difficulty and emphasis of topics. Under the current syllabus, you can expect changes in style, difficulty and emphasis to continue, as the exams evolve and committee members change. This is just one of those things that students have to live with. • This manual does not contain the questions and solutions included in the Study Notes for Exam FM/2 published by the SOA/CAS. Currently, the Study Notes include the actual May 2005 and November 2005 exams and 45 sample questions (there were 52 questions but numbers 38-44 were eliminated), many of which are from past exams. There are also 30 sample questions on the topic of derivatives, which was added to the syllabus in 2007. The Study Notes have solutions for all of these problems. You should definitely get these additional practice problems. You can download them for free from the SOA or CAS web site. We have not included them in this manual because we didn't want to waste space by duplicating material that is freely available from another source. • The recent history of the exam format is as follows: Year 2005-2006 2007 2008 (CBT) Covers Derivatives? No. of Questions no 25 yes 30 yes 35a Exam Length 2 hours 2.5 hours 3 hours a. Several questions (perhaps five) are pilot questions that will not be graded, but you will have no way of knowing which ones they are. • The order of the past exam questions that follow each topic in this manual is from the most recent to the oldest. • There is a code following each question in this manual from a past exam that tells you where the question came from. For example, the code [SOA 5/88 #2] means that this was question 2 on the May 1988 SOA exam. Some codes say "SAMPLE." These questions are from sample exams that the SOA/CAS have published from time to time. • Some of the questions have answer choices in ranges, such as "(A) Less than 11.3% (B) At least 11.3% but less than 11.5%," etc. These questions almost always come from CAS exams, which have used this style for many years. Virtually all questions on the SOA/CAS Exam FM/2 since 2000 have had specific answer choices, rather than ranges. • Many of the CAS past exams gave a different point value to each question (I, 2, or 3). We have omitted the questions with a point value of I, since we consider them to be too easy for the purpose of preparing for the exam. To make it easier to locate them, the sections of the manual with past exam questions and solutions have running heads that are shaded like this: Past Exam Questions on Sections I b to If and Solutions to Past Exam Questions on Section 1 b to l f Copyright© 2009 ASM. lOth edition Original Practice Exams ' . Introduction In addition to the questions from past exams, the manual contains five original full-length practice exams, with solutions. Most students think that the first three practice exams are somewhat more difficult, on average, than the problems from actual past exams. This is just fine, because it's a good idea to practice on problems that are a little harder than the real thing. So don't be discouraged if you don't do too well on the firs! three practice exams. Practice exams 4 and 5 are more on par with actual past exams. Calculators Begin using your calculator immediately. Become thoroughly familiar with its operation. It should become like a trusted friend to you after awhile. Our advice is to get a financial calculator for the exam, such as the BA-35©, BA II Plus©, or BA II Plus Professional©. These calculators have special keys that are very useful for solving problem in financial mathematics. Which one should you use? Any of them will serve you well for the exam. However, Texas Instruments discontinued manufacturing the BA-35 in 2005. In our opinion, you don't need the Professional model, unless you are willing to spend extra money for some additional features that aren't essential for the exam. For these reasons, we have based the Calculator Notes in this manual on the BA II Plus. You will find these notes at appropriate points in the manual, identified by this icon: Please note that some students follow a different strategy with respect to calculators. They prefer to use one of the TI 30X series as their primary calculator because of the two-line display and superior algebraic capabilities. These students feel that they can even calculate certain interest functions, such as aiil, more quickly on the TI 30X, even though the BA series has special keys for this function. They use the BA series as a backup calculator, mainly to calculate an unknown interest rate when the amounts of payments and their present value are given. You can do a search on the Actuarial Discussion Forum to get other students' opinions on which calculators to use, and then make your own decision. Studying for the Exam Everyone is different. Some people like to study in the morning, some late at night. Some people can only study for an hour or two before their brain begins to fry; others can study for long stretches. Some people can cram very effectively, but others need to cover the material over a period of several months. Almost everyone finds ways to procrastinate from time-to-time. You know your own study habits best, so build on your strengths and be aware of your weaknesses. We recommend that you set up a study schedule right now. Determine how many hours you will realistically be able to put in between now and the exam. Many students u;5e this rule-of-thumb: devote I 00 hours of study time for each hour of exam time. For a 3-hour exam like FM/2, this would mean 300 hours. Of course, people vary considerably in how quickly they learn new material, so use this rule-of-thumb only as a rough guide. The following is a very rough guide for the percentage of time that you should devote to each section of this manual. This breakdown is based in part on the distribution of questions in past exams.