Syllabus for Financial Math Math 319 — Fall 2016
Instructor: Margaret
Menzin
menzin@simmons.edu
Office
Hours: I am here MWF from 9:00-10:00 (sometimes from 7:15-8:00) and
Mon 12:30 - 2:00 and 4:00-6:00 (and after lab)
Office: tel: x2704
physical office: S209
Home tel: 781-862-5107 (not after
Wed 11:00 - 12:00 and sometimes 1:30-3:00
Fri 11:00 -2:00 and sometimes after 3:00.
Please
give me a heads up if you plan to come during lunch.
Note: There is no class or lab on
These
meetings will be made up at a time to be determined by us.
Accommodations for Special Needs: Reasonable accommodations Title IX and the Simmons College Gender—Based Misconduct Policy
Title IX Federal law states that all students have the right to gain an education
free of gender—based discrimination. Some examples of gender—based discrimination, as defined by this law include
sexual harassment or exploitation, sexual assault, domestic/dating violence, and stalking.
In compliance with Title IX, Simmons College has a "Gender—Based Misconduct Policy" which defines these forms of misconduct,
outlines College protocol and procedures for investigating and addressing incidences of gender—based discrimination,
highlights interim safety measures, and identifies on and off-campus resouces. The policy and a list of resources is located
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Additionally, the Gender-Based Misconduct Policy has a Consensual Relationships clause that prohibits intimate, romantic or sexual
relationships between students, faculty, staff, contract employees of the College, teacher's assistants, and supervisors at internship/field placement sites.
Text books: There are 3 books we will use and ALL of them are
available at very good prices used. (Basically they are the n-1 edition). I am giving you some places to find these books, but I am
sure you know others. The URL shows a picture of the cover - helpful to be sure
you get the right edition. The first book is Anderson & Sweeney
"Quantitative Methods for Business" and any edition from the 7th on
is just fine. You can find the 7th edition via http://isbn.nu/9780538876018
(please note the ISBN number is 978 etc) You can find the 8th edition via http://isbn.nu/9780324044997 (we won't use the CD) You can find the 9th edition via http://isbn.nu/9780324320114
PLEASE do NOT order a book which is shipped from outside the U.S. --- delivery
times are unreliable. The second book we will use is Bodie & Merton
"Finance" FIRST edition You
can find it via http://isbn.nu/9780133108972 The last book we will use is Hull "Options Futures
and Other Derivatives " _ EIGHTH edition You can
find it via http://isbn.nu/9780132164948 The first and
second books are pennies plus shipping, the third is under $30 plus shipping
--- so I have worked hard to make sure that the course stays within your
budgets. (Seems very appropriate for this course). Software: We will
make extensive use of Excel and of proprietary financial industry software
which is available to you either free or in the Math Collaboratory (S211.) General Philosophy of This Course This course is of interest to students who
wish to use mathematics to make decisions in the financial world. In it we will
be learning contemporary quantitative approaches to financial mathematics and
using contemporary computer-based tools. The course also gets you started on
the road to taking the CFA-Level 1 exam and the second and third Society of
Actuaries exams. In addition to learning about
contemporary theory and tools in financial mathematics, we will also discuss
making decisions about other kinds of problems, especially personal financial
decisions (how to choose an investment when you want to save for a down payment
on your first house). Where appropriate we will also talk about other kinds of
(non-financial) decision making. The emphasis of this course is on
analyzing the problem, deciding on a particular mathematical approach,
formulating the problem, using a computer to solve the problem, and
interpreting and analyzing the solution, including asking about "what
if" scenarios, and the sensitivity of our decision to our input data.
Throughout the course we will discuss the limitations of a particular method.
For example, how accurate are our estimates of the probability of the economy
expanding at least 10% next year? Are the assumptions of the Capital Asset
Pricing Model met? What does behavioral finance have to say about a situation? On the other hand, many problems in real
life have lots of variables and they should be solved on a computer. It is a
waste of your time to solve medium or large problems by hand. That is what the
computer is there for. Using a computer also enables us to handle much larger
data sets. So, you will solve a few small problems by hand and then move to the
computer. (There is a package with Hull
and we can work wonders with Excel.) The
major part of your effort will be directed towards the things the computer can
not do for you - formulating the problem, interpreting the solution, etc. Accommodations for Special Needs: Reasonable accommodations Course Outline 1. Introduction, Probability and Bayes Theorem - ASW Chapters 1, 2, and 3.1
and 3.2 We will also be reading some articles
(especially by Kahneman and Tversky), which will provide an introduction to
Behavioral Economics and to Risk Management. Chapter 1 is an introduction to the course,
and you should read it on your own. In reading Chapter 1 please pay particular
attention to section 1.2 on decision making (which we will discuss on day one
of class) and to the material in Appendix 1.2 on formatting data. The material in section 1.4 is illustrative of
a kind of decision-making you have undoubtedly encountered elsewhere. In Chapter 2 we will review and extend certain
topics from Math 118/Math 238 Statistics - namely the concepts of an event
space, probability as a frequency, and subjective probability and marginal distributions.
We will also delve further into probability
theory, examining the addition and multiplication laws of probability, and the
notions of independent events and conditional probability. Two events are
independent when knowing whether or not one event occurs (e.g. it is Monday )
does not effect the probability of another event occurring ( e.g. more than 10%
of our employees are absent). When we speak of conditional probability we ask
about the probability of one event, given information about another event
occurring; for example, what is the probability of more than 10% of the
employees being absent, given that we know it is Monday. These ideas are very
useful in thinking about how things are or are not related. For example, if we
suspect that employee absenteeism is higher on Mondays and Fridays, we might
ask if the absenteeism rate is independent of the day of the week. Conditional probability also allows us to
"turn things inside out" in a way which is particularly important for
decisions which are made only once, and sharpens your analytic skills. For
example, suppose that the Olympic Committee knows that 3% of all athletes who
are steroid-free will test positive ("false positives") and that 5%
of all athletes who do use steroids test negative ("false
negatives"), and that 1.5% of all athletes use steroids. Now let us
suppose that we have an athlete who tests positive. What is the probability
that this athlete uses steroids? Notice how we have turned things inside
out----we know the probability of a positive result, given information about
whether or not the athlete uses steroids; we then ask the probability of the
athlete using steroids given information about the test result. The theorem that allows us to make this
calculation is called Bayes Theorem and it is particularly useful for decisions
which are made once. (What do we do about this particular athlete? Do we buy a
particular stock?). We will look at many applications of Bayes Theorem. The calculations here are relatively simple;
they may be done by hand or on a spread sheet. We will also talk about problems with
estimating probabilities, our first insight into behavioral economics. The
discussion of risk, including ideas on how to measure it and on risk tolerance,
in Units 1 and 2 of the course is fundamental to financial mathematics and
portfolio management. We will read two
of Kahneman and Tversky's classic papers on this subject. Test. 2. Decision Analysis and Utility Theory ASW Chapters 4 and 5 Problems will be assigned. Outside reading includes sections from Peter
Bernstein's classic book Against the Gods and from Dembro and Freeman's Seeing
Tomorrow, both of which are about risk, and from a popular book about how
even smart people make dumb mistakes when it comes to money. In this part of the course we will examine how
to choose among several alternatives when you have some events that you can't
predict completely. For example what size office should you rent for your
consulting practice (the alternatives might be small office, medium office or
large office) when you don't know how much business the practice will generate?
Should you buy technology stocks now when you don't know how that industry will
do next year? We will look at several different ways to
approach this problem - the optimistic criterion, the pessimistic criterion,
the expected value approach, and the Minimax Regret criterion. In looking at
these approaches we will spend a fair amount of time examining the notions of
risk, risk tolerance and risk aversion and asking in what situations is one
more or less risk tolerant. We will also read from Bernstein Against the
Gods and Dembro and Freeman Seeing Tomorrow, two important books on
the matter of risk, and read about how rational/irrational individuals are in
making financial decisions, and examine a number of case studies. We will also ask about when it pays to get
more information before making a decision (e.g. doing some market research
before launching a product or taking an option to buy a piece of real estate so
that we can see more about how an area is developing before committing to the
land) and how much that information is worth to us. We will use both Excel. When we turn (briefly) to Utility Theory we
ask about how to evaluate alternatives when our aims are harder to quantify
(e.g. quality of life or feeling financially secure). We carry this further in
Chapter 18 (Unit 4) when we ask about problems where we have multiple goals,
and how to weight them. For example, suppose you want to buy a new car and have
multiple goals related to minimizing cost, and maximizing safety and maximizing
convenience. How do you weigh the relative importance of those goals and how do
you use that to make a decision? Many important decisions, both personal and
financial (portfolio management) ones, have multiple goals. We will examine
case studies and look at software which can be used for this. Much of this
process is art, rather than science. The purpose of the theory is to help you
think more clearly about your values and goals. 3. Time Value of Money, CAP-M and Financial Options: Readngs from Hull Ch.1-
10, from Bodie and Merton, and Handouts; selected chapters from Kellison NOTE:If you have not had the Investments
course yet, you should browse thru Ch. 1-2 of Bodie & Merton (on Reserve in
the Library); we will not discuss Ch. 5 in this course, but you will find the
material interesting for your own financial life. Problems will be assigned. We will first learn how to evaluate two
investments which give different streams of income over many years (the time
value of money). This is important in, for example, determining the price of
bonds. It is also important for comparing two packages of investments whose
outcomes are spread out over time. The time value of money is a simple but
enormously useful idea which crops up in many contexts. (For example, should we
invest in a computer system which costs $1 million now and saves $350 thousand
in labor for each of the next 3 years?). Many of you have learned about this in
the Money and Banking or Investments course. We will work though some rather
complicated examples. Next we turn our attention to the Capital
Asset Pricing Model (CAP-M) and the various forms of the Efficient Market
Hyptothesis, and the measures associated with Modern Portfolio Theory (MPT). We will also examine the most popular measures
of risk for financial instruments (standard deviation, and Sharpe, Sortino and
Treynor ratios and VaR or Value at Risk.) Group research project on whether or not past
risk-adjusted performance of mutual funds over a complete market cycle may be
used to predict risk-adjusted performance for the next market cycle. 4. Options, Black-Scholes Models and Simulations: Readings from Bodie-Merton, and from Hull Ch. 11-18 . Handouts An option is the right to
buy or sell a stock or other asset at some time in the future. We will
introduce the basic idea that if two packages of financial investments have the
same results then they should have the same price (Law of One Price or
Principle of No Arbitrage). This allows us to price options and other financial
derivatives. Problems will be assigned Simulations are, of course, particularly
useful when we are dealing with random processes - such as, according to some
theorists, the prices of stocks. Indeed, the Black-Scholes model for options
pricing assumes a random component to price movements. Another very important
tool is the idea of a replicating portfolio.We will look first at binomial tree
models and then at the derivation of the Black-Scholes formula and its
applications. As time allows we will examine exotic options. Again, this is an
introduction to a fascinating field. Group Project (in lieu of final exam)
will be provided for students with documented physical, sensory, systemic,
cognitive, learning, and psychiatric disabilities. If you have a disability and
anticipate that you will need a reasonable accommodation in this class, it is
important that you contact the Academic Support Center Director at 617-521-2471
early in the semester. Students with disabilities receiving accommodations are
also encouraged to contact their instructors within the first 2 sessions of the
semester to discuss their individual needs for accommodations.
I
have worked hard to keep the cost of books for this course low.
Because some of this material is hard, and because I find it is always better
to read material at different levels, I am asking you to buy several books.
So here is the list:
OPTIONAL BOOKS FOR THOSE PREPARING FOR THE ACTUARIAL EXAMS BUT NOT NEEDED FOR
THIS COURSE:
4. Derivative Markets -2nd edition - by McDonald
Intermediate in difficulty between Bodie/Merton and Hull, and a well known
book. The Society of Actuaries requires it for 2 of their exams (where it
is the only text they suggest.)
I am able to find it used for $120 at Amazon, but you may be able to find it
for less.
http://www.amazon.com/gp/offer-listing/032128030X/ref=dp_olp_used?ie=UTF8&condition=used
There is a 3rd edition, but the SOA is still going with the 2nd.
5. Theory of Interest-2nd edition by Kellison
(Again, there is a newer edition, but the 2nd is fine). You can find this
used for under $5 at
http://isbn.nu/9780256091502
or
http://www.amazon.com/gp/product/B004K37PJC/ref=oh_details_o05_s00_i00
Very simple problems may be solved by hand or with a calculator. The
advantages of doing this are two-fold: first it is often faster to solve a
simple problem by hand; second, hand-solution of simple problems reinforces
your understanding of the general process.
will be provided for students with documented physical, sensory, systemic,
cognitive, learning, and psychiatric disabilities. If you have a disability and
anticipate that you will need a reasonable accommodation in this class, it is
important that you contact the Academic Support Center Director at 617-521-2471
early in the semester. Students with disabilities receiving accommodations are
also encouraged to contact their instructors within the first 2 sessions of the
semester to discuss their individual needs for accommodations.
Problems will be assigned