| Instructor: | Ryan J. Hubscher |
| Email: | rhubsch2! at !uiuc dot eduDeleteTheExtraCharactersAndExclamationMarksFromMyEmailAddress |
| Office Hours: | Time: Wednesday 1-2:50 PM or by appointment Location: The basement of Coble Hall |
Required Text: Broverman, Samuel A. Mathematics of Investment and Credit (2004, 3rd Edition).
We will cover most of the first 5 chapters of the Boverman text and limited sections from chapters 6-8, comprising a thorough exploration of the mathematical theory of interest. Some of the specific topics and concepts covered will include: interest and discount rates, simple versus compound interest, nominal versus effective rates, present value, annuities and perpetuities of many types, yield rates, amortization schedules and sinking funds, the pricing of financial instruments such as stocks and bonds, duration and convexity, and short sales. Other topics may be covered, depending upon time constraints. Emphasis will be placed on the ability to solve problems dealing with these concepts. We will also discuss the broader financial and actuarial contexts and implications of this material.
This course will help you prepare for the interest theory material on the Exam 2/FM national actuarial examination, co-sponsored by the Casualty Actuarial Society and the Society of Actuaries. In addition to this course, you should also study derivative markets on your own or in a different class and take Math 370 Section Z to prepare for Exam 2/FM.
| January 15 (Tuesday) | First day of class: Introduction and Motivation |
| February 26 | Exam # 1 (approximately textbook Chs. 1-2) |
| April 3 | Exam # 2 (approx. Chs. 3-4) |
| April 29 (Tuesday) | Last day of class |
| May 2 (Friday 8:00-11:00 AM) | Comprehensive Final Exam (mostly from chapters 5-8) |
In most non-exam weeks, there will be a homework assignment and one or more short in-class assignments. In addition, practicing actuaries may be invited to give guest presentations to the class during the semester.
| Homework assignments | 20 % |
| In-class/other assignments | 5 % |
| Exams | 75 % (25% each) |
Final letter grades will be assigned as follows:
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Exams may not be made up or taken at different times, except in extremis. In general, the grade weight for a missed exam (provided there is a valid excuse) will accrue equally to any remaining exams. A missed in-class or homework assignment may not be made up. However, in calculating your course score and grade, your worst homework assignment score will be dropped. Thus, if you miss one homework assignment, it will count as your drop. Similarly, your lowest two in-class assignment scores will be dropped in determining your overall grade. Class attendance is expected; serious attendance problems may result in a grade lower than that indicated by the weighting system above.
Please note that the final exam schedule is prescribed by the university; in general, instructors are not permitted to change the final exam timing of their courses.
| Date | Topic | Summary | Reading | Assignments | Other |
|---|---|---|---|---|---|
| Jan 15 | Introduction | Syllabus, Interest rate history, CAS vs SOA | HW1 Due Jan 24 | Day 1 Presentation Interest rate history (3-month T-bills) Bean Actuary SOA website CAS website |
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| Jan 17 | Interest Basics | Accumulation and amount functions. Simple and compound interest. | 1.1 | ||
| Jan 22 | Interest Basics | Present value. Equations of value. | 1.2 | ||
| Jan 24 | Interest Basics | Nominal rates of interest. Effective and nominal rates of discount. | 1.3-1.4 | HW2 Due Jan 31 | HW1 Solution |
| Jan 29 | Interest Basics | Rates of discount. Force of interest. Inflation | 1.4-1.6 | ||
| Jan 31 | Annuities | Accumulated value of annuities. | 2.1.1 | HW3 Due Feb 7 | HW2 Solution |
| February 5 | Annuities | PV of annuities. Annuitie-immediate vs annuity-due. | 2.1.2-2.1.3 | ||
| February 7 | Annuities | Differing interest and payment period. | 2.2.1 | HW4 Due Feb 14 ICA1 Solution |
HW3 Solution |
| February 12 | Annuities | Continuous annuities. Unknown time. Unknown interest. | 2.2.2-2.2.4 | ||
| February 14 | Annuities | Varying annuities. Annuities in Excell. | 2.3 | HW4 Solution | |
| February 19 | Review | Chapter 1. | ICA2 Solution | ||
| February 21 | Annuities | Varying annuities. | 2.3 | ||
| February 26 | Exam 1 | Sections 1.1-2.3 | Exam 1a Solution Exam 1b Solution |
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| February 28 | Annuities | Varying annuities. | 2.3 | HW5 Due Mar 6 | Examples 1 |
| March 4 | Loans | Amortization Schedules | 3.1-3.2 | Examples 2 (Excel) | |
| March 6 | Loans | Amortization | 3.1-3.2 | HW6 Due Mar 13 | HW5 Solution HW5 Solution (Excel) |
| March 11 | Loans | Sinking Funds | 3.3 | Examples 3 (Excel) Examples 4 (Sinking Fund Schedule) |
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| March 13 | Yield Rates | Net present value. Internal rate of return. | 5.1, 2.4.1 | HW6 Solution HW6 Solution (Excel) |
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| March 18 | Spring Break. No Class. | HW7 Due Apr 1 | |||
| March 20 | Spring Break. No Class. | ||||
| March 25 | Yield Rates | Dollar-weighted rate of return. Reinvestment rates. | 5.2, 2.4.1 | ||
| March 27 | Yield Rates | Book value vs market value. Time-weighted rate of return. | 5.2, 2.4.4 | HW8 Due Apr 10 ICA3 Solution | Examples 5 (TWRR) |
| April 1 | Bonds | Price of a bond on a coupon date and between coupon dates. Premium/Discount. Accrued coupon. | 4.1 | ICA4 Solution | Examples 6 (Bond pricing) HW7 Solution |
| April 3 | Exam 2 | HW 5-7, ICA 3-4 | Exam 2a Solution Exam 2b Solution |
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| April 8 | Bonds | Bond/Premium Amortization. | 4.2 | ||
| April 10 | Guest Speakers: Tamara Johnson, Scott Christenson, Tim Ellison. | HW9 Due Apr 22 | HW8 Solution | ||
| April 15 | Bonds | Callable bonds. | 4.3.1 | Examples 7 (Callable bonds) | |
| April 17 | More Yield Rates | Investment Year and Portfolio Year methods. Yield curve. Spot rates. Foward rates. | 5.3.1, 6.1, 6.3 | Examples 8 | |
| April 22 | Financial Mathematics | Macaulay Duration. Modified Duration. | 7.1 | HW10 Due Apr 29 | HW9 Solution |
| April 24 | Financial Mathematics | Exact asset liability matching. Immunization. | 7.2 | ||
| April 29 | Financial Mathematics | Last Day of Class. Immunization. | 7.2 | ICA5 Solution | HW10 Solution |
| May 1 | Reading Day. No Class. | ||||
| May 2 (Friday) |
Exam 3 | Bring one double sided 8.5x11 note sheet. Questions will be on HW8, HW9, HW10, ICA5, and some reading from chapter 8. |