 

November 26, 2018
(1) Assignment No. 10 is now posted and will be due on Monday, December 3.
Please remember to bring your handout from last class with you to class this
evening.


November 9, 2018
(1) Assignment No. 9 is now posted and will be due on Monday, November 26.
Please note that you will need market information as of the close of trading
on Tuesday, November 13.
Please note that you will need to do this after the market closes on
Tuesday, but before it opens for trading Wednesday morning as the price
information is not stored historically.
(2)
In our next class, following our review of the second midterm exam, we will continue with our discussion of options. We will
discuss boundary conditions and delve into various pricing models including
the binomial and BlackScholes models. As time permits, we will discuss (a)
historical and implied volatility estimation, and (b) how to make
adjustments to pricing models to accommodate dividends, both discrete and
continuously paid dividends. Please remember to bring your option handout
from the Monday, November 5 class to our next class.


October 24, 2018
(1) Assignment No. 8 is now posted and will be due on Monday,
November 5. Please note that you will need market information as of
the close of trading on Tuesday, October 30.
(2) In our next class on Monday Oct.
29 we will review assignment 7 and then have a concluding discussion of
swaps. With the
remaining time, we will then move into optionsour second derivatives
building block. Initially, we will look at option payoff diagrams and
associated strategies, look at how to read price quotations and option
chains, and discuss other institutional arrangements.
(3) Please familiar yourself
with the optionseducation.org website (formerly 888options.com) and how to
read an option quote and option chain. To practice, go to the website, look
for "Quotes", then enter a stock symbol and click "Go." Then click and look
around to see the variety of information presented.
(4) The second
midterm exam will be on Monday, November 5 and will cover material up to
and including the October 29 class.
(5)
Finally, next week I will send the class a copy of the Option! software for
pricing options using different models.


October 10, 2018
(1) Assignment No. 7 is now posted and will be due on Monday, October 29.
Please note that you will need market information as of the close of trading
on Tuesday, October 16.
(2) During our next class we will spend the entire time discussing swaps.
We will discuss various institutional dimensions of the market as well as
how to both price and value a swap. The initial focus will be on interest
rate swaps. As time permits, we will also get into bootstrapping techniques
for constructing the zero discount curve. Discussion of currency and
commodity swaps will be covered later depending on progress.
(3) I have emailed you a teaching note on "The Pricing and Valuation of
Swaps" that you should read carefully before coming to class. (This can
also be found on the course website under Syllabus/Readings and also in
Chapter 28 of Financial Derivatives: Pricing and Risk Management, Kolb and
Overdahl, editors, Wiley, 2010). I also emailed you a copy of the *SWAP*
software that you can also find posted under Syllabus/Readings on course
website. Please be sure that you have your *SWAP* software fully
operational and that you have turned on the appropriate "system
requirements" including the required addins and enabled macros.


October 2, 2018
(1) On Monday Oct.
8, we will discuss currency futures and forwards
including their valuation, institutional arrangements, and some
applications. I will also email the class a preread on the topic.
(2) We will also review the first midterm exam.
(3) Homework 6 is now posted and is due on Monday, October 15.


September 25, 2018
(1) In our next class we will continue our discussion of stock index and
single stock futures. We will focus on how market professionals use these
products in both active and passive strategies. We will also discuss
institutional issues such as performance bonds and circuit breakers. Please remember to bring with you the handout from our last class "SIF
Pricing and Arbitrage".
(2)
Follow the above discussion, we will use the remaining time for exam 1.
(3) MiniLecture 7
***Please carefully study the following illustration to convince yourself
that the arguments hold.
Assume that you are in a world with the following current market conditions:
S (a stock or stock index) = $100; L (Libor) = 6%; d (div yield) = 2%; and
you have a 1 year (360day) investment horizon.
Thus, based on this information, we know that the oneyear futures price
should be:
F = S*[1 + (Ld)*(Tt)/360]
F = 100*[1 + (.06.02)*360/360] = 104
Now, consider the following two investment strategies, which I argue are
equivalent or that you would be indifferent between choosing:
1. Invest $100 in the stock, or
2. Invest $100 in a money market account and go long one futures based on
that stock (at 104).
Scenario A:
Suppose that after 1 year the stock is now at $120. Your ending wealth from
each of the two strategies are:
1. Wealth = 120 + .02*100 = 122 (stock value plus dividends received)
2. Wealth = 100*(1+.06) + (120104) = 106 + 16 = 122 (money market
investment plus gain on the futures)
Therefore, both strategies produce the same terminal wealth.
Scenario B:
Suppose that after 1 year the stock is now at $80. Your ending wealth from
each of the two strategies are:
1. Wealth = 80 + .02*100 = 82 (stock value plus dividends received)
2. Wealth = 100*(1+.06) + (80104) = 106 24 = 82 (money market investment
plus loss on futures)
Again, both strategies produce the identical ending wealth.


September 18, 2018
(1) Assignment No. 5 is now posted and will be due on Monday, October 1.
Please note that you will need market information as of the close of trading
on Monday, September 24.
(2)
In our next class, we will conclude for now our discussion of interest rate
futures and risk management, which we will resume at a later date when we
will discuss interest rate swaps. During the remaining time in class, we
will begin our discussion of stock index and single stock futures, with our
initial focus being on institutional details, valuation, and hedging. Please
be sure to read in advance the assignment reading in Chapters 7 and 8 of
your text if you have one.
(3) Our first midterm exam will be on Monday, October 1.
(4) MiniLecture 6
Reading Corporate Bond quotations Corporate bond quotations are typically quoted in points and one hundreds of
par (whereas government securities such as Treasury bonds and notes are
quoted in points and thirtyseconds of par). To illustrate, suppose you saw
a corporate bond quoted at say 108.93. This simply means its price is
108.93% of par. Thus, if you are working with a par or face amount of
$1,000, then the price would be $1,089.30. alternatively, the quote may be
reported with a $ sign in front; e.g., $108.93. This price would be
interpreted the same and would mean $108.93 per $100 of par or $1089.30 per
$1000 of par. Similarly, a quote of 97.500 would translate into a price of
$975.00 per $1000 of par.
Also, in contrast to equities, the secondary market for most corporate bonds
is not very liquid (and feature relatively large bidask spreads). This
problem has been further exacerbated by DoddFrank that has diminished the
role of banks as liquidity providers in this market.
Sometimes when computing the yield to maturity on a bond, you may or may not
get the same reported yield that you see on the Finramarkets quote site. If
not, this could be for a variety of reasons including the fact that the bond
may be callable. Some reporting agencies provide what is known as the yield
to worst, which is the lower of yield to maturity and yield to call.
Regardless, you can easily calculate your own yield from the information
provided.


September 11, 2018
(1) Assignment No. 4 is now posted and will be due on Monday, September 24.
Please note that you will need market information as of the close of trading
on Tuesday, Sept. 18 best obtained by going to the indicated site after
Tuesday's close for price quotes for corporate bonds, and then accessing the
onlineWSJ and/or the cmegroup.com website for your Tuesday futures prices.
(2) In our next class, we will study the hedging of interest rate risk. We
will begin by discussing the construction of synthetic fixed rate and
floating rate loans using futures (with some mention of how you similarly
may hedge using swaps, caps, and forward rate agreements). In doing so, we
will examine the merits of stack versus strip hedging strategies. These
examples will then provide a nice leadin to our exploration of more
involved hedging situations in which we will introduce models that involve
duration. To help you prepare for class, please read in advance of class and
pay particular close attention to the examples and material on pages 211217
and 219229 of your text (or equivalent pages if you are using an older
edition of the text).
(3) MiniLecture 4
Understanding Eurodollar futures
Recall that the underlying "asset" of the Eurodollar futures is actually the
rate on a $1 million 3month Eurodollar time deposit, which you can think of
as the 3month or 90day Libor rate. However, rather than quote prices in
terms of a rate or yield, the exchange uses a convention called the IMM
Index. That is, the futures price is quoted in terms of a number that is
equal to 100 minus the 3month Libor rate. Thus, if you observed a
Eurodollar futures quoted at 96.00, then this corresponds to a 3month Libor
rate or yield of 100.00  96.00 = 4.00%. Similarly a quote of 97.12 would
correspond to a rate of 100  97.12 = 2.88%. (For more discussion, see pages
152154 of your text or look in the index for Eurodollar futures.)
(4)
MiniLecture 5
Understanding interest rate futures price quotes and the value of a price
change
Convince yourself that the following price relations indeed hold
a. For the Tbond, 10year Tnote, and 5year Tnote futures contracts
(which each has a notional dollar contract size of $100,000), the dollar
value of a 1/32nd change in the futures price is $31.25. To illustrate,
assume that the reported futures price quote changes from say 104160 to
104170; the contract then has changed in dollar value by $31.25.
b. For the 2year Tnote, the change in value is $62.50 because the notional
size of the contract is $200,000 as compared to $100,000 for the earlier
three contracts.
c. Note that the last digit in a bond or note futures contract stands for a
fraction of a 1/32. For example, you will see a 0, 2, 5, or a 7 (e.g.,
110160, 110162, 110165, and 110167). A 2 stand for .25/32, 5 stands for
.5/32 and a 7 for .75 1/32, and a 0 of course means zero fractions of a
32nd. Also, note that the Tbond futures minimum tick size is 1/32, so the
last digit in its quote is always 0.
d. For the Eurodollar futures (which has a $1mm notional dollar contract
size), a 1 basis point change translates to a change in price of $25. In
other words, if the futures price changes from say 95.00 to either 95.01 or
94.99 (which means a change in yield from 5.00% to either 4.99% or 5.01%),
the change in value of a contract is $25 (positive or negative depending on
whether the position is held long or short, respectively). For this reason,
we refer to the Eurodollar futures as having a DV01 (i.e., the "Dollar Value
of a 1 basis point change") equal to $25. Also, corresponding to this, the
Modified duration of the Eurodollar futures is .25. To see this note that
$25 = MD x 0.0001 x $1mm; thus MD must equal .25. The minimum tick for the
Eurodollar futures depends on the contract maturity: for the nearby contract
it is .25 of a basis point and for all other maturities is .50 basis points.


August 28, 2018
(1) In preparation for our next class, please visit in advance of class the
various websites that we covered (i..e., WSJ and CMEGroup) where futures
price quotes can be found and be familiar with how to read and interpret
prices for the following interest rate futures; specifically, the Eurodollar
futures, and the Tbond, 10year Tnote, 5year Tnote, and 2year Tnote
futures contracts.
(2) In our next class, we will begin by reviewing homework assignment no. 2.
To start our lecture, we will discuss an important role (in
addition to hedging) that futures markets fulfillfacilitating price
discovery. We will explore what is price discovery, how futures prices are
used commercially for pricebasing and improving resource allocation and
decisionmaking, and whether there is a government interest in protecting
markets against manipulation. We will introduce the concepts of
backwardation and contango, and discuss the implications of these terms for
futures prices.
Following this, we will review forward rate estimation, using both bond
yield and money market conventions. We will then review contract specs for
several of the interest rate futures that we will be using throughout the
term (including those for Eurodollars, Tnotes, and Tbonds) and begin
developing an understanding of their cash market linkages. With the
remaining time, we will begin developing models for interest rate hedging.
(3) MiniLectures 1, 2, and 3 Below are a few minilectures to
clarify concepts used in class.
(ML1) Using LIBOR: First, a brief note about performing calculations
with LIBOR interest rates: To determine interest amounts, we will follow
standard market practice. Libor uses an actual/360 day count convention, and
interest is computed using a "simple" or "addon" interest method.
For example, if you were to borrow $1mm today and were to repay the loan in
18 days based on a hypothetical Libor rate of 4%, the amount you would repay
is computed as $1,000,000*(1+L*days/360) or
$1,000,000*(1+.04*18/360)=$1,002,000. (Note that in today's market
environment that shortterm Libor rates are more in the range of 2% to
2.50%.)
Note
that all the LIBOR rates you will see reported in the WSJ, globalrates.com
and elsewhere are already annualized, regardless of the indicated
tenor or maturity (e.g., 1 month, 3 month, 6 month, 1 year). Thus, you just
need to multiply the rate by the relevant day count divided by 360. For
example, for Libor rates for Friday 8/24/2018, the reported the 6month
LIBOR rate to be 2.52300 (see either the WSJ or globalrates.com by
scrolling down and clicking "American dollar LIBOR USD".) This means that
the annualized 6month LIBOR rate is .0252300 or 2.52300% (NOT
252%!!!).
Now, suppose
you want to apply this rate and wish to know how much $1mm will grow to in
180 days. Note that LIBOR is a money market rate, thus there is no
compounding, just simple interest. Therefore to calculate interest we
multiply the rate by the day count divided by 360. In this example, we thus
have:
$1,000,000 x {1 + .0252300 x (180/360)} = $1,012,615.
In the above,
please again note carefully that I used .0252300 and not 2.52300. Do not
make that mistake in your calculations. Also, please verify the
calculation so that you understand the order of the calculations in
parentheses/brackets.
Suppose
instead I want to know what $1mm will grow to in say 194 days. If I am
willing to assume that the term structure is fairly flat around the 180day
maturity and thus the 6month rate is a good approximation to the 194 day
rate, we then get:
$1,000,000 x {1 + .00252300 x (194/360)} = $1,013,596.17.
Finally, if I
was working with say a 100day maturity, I would instead use the 3month
LIBOR rate rather than the 6month rate because of the closer matching
maturity. That is, 100 days is closer to 90 rather than 180 days). The two
sources report the 3month LIBOR rate for the same date at 2.31725%. Thus,
$1mm invested at this rate for 100 days will grow to:
$1,000,000 x {1 + .0231725 x (100/360)} = $1,006,436.81.
In case you have an interest in reading how the ICE (Intercontinental
Exchange) Benchmark Administration determines the daily Libor rates, please
see:
https://www.theice.com/iba/libor.
(ML2) Volume versus Open Interest: For clarification and your future
reference, here is a short summary explanation to help clarify the
difference between Volume and Open Interest as relates to futures trading.
Volume is a measure of the number of contracts traded during some specified
trading interval, e.g., a trading session, a day, a month, and so on.
Open interest is the number of contracts currently open and outstanding.
Volume is related to open interest, but a change in volume can result in an
increase, decrease, or leave unchanged open interest.
Consider the following example:
Assume that there are 3 traders, x, y, and z, who are each interested in
trading the March 2018 natural gas futures, and which just today assume has
been listed for trading for the first time. Thus, volume for the day is
initially zero and open interest is also zero since the contract heretofore
has never traded.
Trader x sells 1 contract to y, the long. Volume is 1 and open interest is
1.
Trader x next sells 1 contract to z, the long party to this second contract.
Volume for the day is 2 and open interest is also 2. Note that x is now
short 2 contracts while both y and z are long 1 contract each.
Trader y sells 1 contract to z. Volume is now 3 and open interest remains at
2. Note that z is now long 2 contracts and that y has exited the market.
Trader x is still short 2 contracts.
Trader z sells 2 contracts to x. Volume for the day is 5 and open interest
is zero as there are now no open contracts.
(ML3) "Production follows Sales": We spoke in class about one
strategic response to ongoing currency risk that many firms follow, which is
to locate operations close to the point of sale. The result of this is to
push more operating costs into the same currency as to which sales are in.
(As an alternative, some firms alter their cost structure by issuing debt
denominated in the same currency.) To illustrate how this reduces cash flow
volatility, consider the following additional simple example.
Assume a U.S. company has annual sales in Mexico in the amount of 100 pesos.
Manufacturing is done in the U.S. where cost of goods sold is $9. The
exchange rate is currently 0.10$/peso, but could fluctuate between .08 and
.12$/peso. Thus, expected $ revenues are $10 and profit (net cash flow) is
$10  $9 or $1. However, if the dollar strengthens to say 0.08$/peso,
$revenues fall to $8 and profit is now a loss of $1. Similarly, if the
dollar weakens to say .120 $/peso, $revenues increase to $12 and profit is
$3. In sum, profits are expected to be $1, but could range between $1 and
+$3.
Now assume the company produces instead in Mexico. Cost of goods sold is
thus 90 pesos (=$9/.1) and profit is 10 pesos (100  90) before conversion
to dollars. $ profits are expected to still be $1 (10*0.10), but could vary
between +$0.80 and +$1.20 (calculated as 10*0.08 and 10*.120). While the
expected profit (net cash flow) remains the same at $1, its volatility due
to exchange rate movements has been reduced.


August 21, 2018
(1) To briefly recap our first lecture, we began by introducing an economic
framework for analyzing whether a firm's engagement in financial risk
management is justifiable from the perspective of its shareholders.
Potential channels that we identified through which risk management can
enhance firm value included "numerator effects" (that is, the potential of
risk management to have effects on future expected net cash flows) due to,
for example, the reduction of expected bankruptcy, financial distress, and
related business disruption costs; the reduction of underinvestment and
adverse selection problems; and the reduction of taxes. Basically, this
means that to the extent that the firm employs more debt, has higher growth
opportunities, and has significant tax loss carryforwards or is in the
convex region of marginal tax rates, then the firm is more likely to
experience greater potential benefits from hedging.
We also discussed "denominator" effects, which refers to the potential of
risk management to have an effect on lowering a firm's cost of capital. I
also referenced the role of executive compensation and ownership structure
on the incentives of managers to engage in risk management.
Following this, we introduced a definition of a derivative, considered a
number of common derivative structures (e.g., swaps, forwards, futures, and
options), and identified their market venue (both OTC and exchangetrade
instruments). In addition, we looked at recent BIS statistics regarding OTC
market size including breakdowns according to product and instrument type,
and by currency and maturity. We also looked at various market statistics
for exchange traded futures.
We then discussed an early and seminal application of hedging, the Salomon
Brothers/Merrill Lynch underwriting of an IBM debt offering and the
accompanying Tbond futures hedge that was used to control the interest rate
risk inherent in the underwriting. In our review, we did some risk analysis
and applied a commonly used measure of risk often used in fixed income
analysis known as duration. We will use duration, modified duration (MD) and
convexity throughout the course as well as related concepts such as DV01 (an
industry term that refers to the dollar value of a 1 basis point interest
rate movement and is computed according to DV01 = MD x Price x .0001).
(2) At our next class we will begin by reviewing homework no. 1. Also,
in our next class, we will continue with the "why" of risk management during
which we will discuss various alternatives and substitutes for reducing the
demand for derivatives. Included will be a discussion of the importance of
identifying natural hedges. Then, as we transition to the "how" of risk
management, we will develop a understanding of the institutional environment
for derivatives including their regulatory framework, documentation,
margining and daily resettlement, and reporting conventions. We will
continue with our discussion of the two derivative building blocks: the
futures/forward contract and the option contract. We will discuss
similarities and differences between futures and forward contracts. We will
cover reading and interpreting futures price quotes and related terms of
trade. We will conclude by discussing concepts related to the valuation of
futures and forward contracts. Specifically, we will develop a useful
pricing model that is based on noarbitrage principles.
(3) Finally, please review homework No. 2 prior to the next class (see
posted under "Assignments") so that you can more easily pick up on key
thoughts during the lecture. Also, please make a note to yourself that to
be prepared to get the data for the assignment in a timely manner; you will
need to access market information available at the online WSJ (see wsj.com,
and click on 'Market Data Center') for the close of trading on Tuesday,
August 28. The WSJ and CMEGroup websites should be updated sometime late
that Tuesday or early Wednesday to reflect this information.
As you work the assignment, I look forward to seeing your summaries of the
risk management practices of your selected firm, its specific uses of
derivatives if any, and most importantly your thoughts rationalizing or
disapproving of their risk management practices based on the economic
rationales that we discussed. Be sure to avoid simply saying that
because your selected firm faces lots of risk that they can benefit from
managing risks. This is not the necessarily so and in some cases can lead to
destroying firm value. Rather, take some time to analyze the firms capital
structure and get a sense for the amount of debt they have outstanding. Is
the firm wellpositioned to service the debt or could a shortfall in cash
flow or earnings create potential problems? Also, is the firm growing or
have growth opportunities that could be impaired due to adverse movements in
interest rates, exchange rates, commodity prices, etc?


August 2, 2018

Welcome all to FI 4200
"Introduction to Derivative Markets"!
I hope that you will find this course to be a superb and one of your
most beneficial experiences at GSU. I am
looking forward to seeing each of you at the first class on August 20. As a
reminder, our class meets at 4:30pm in Room 323 of the Aderhold Learning
Center.
Please check back here for
updates throughout the term. Also, I will be communicating with you through
your student.gsu.edu email account so please get in the habit of
checking it regularly. (If you prefer to receive your messages at another email
address, please link your gsu student address to it as this is the only email
address that is officially recognized by the university for communication to
students.)
Please do the following prior to the first day of class:
(1) Review and download the Fall 2018 syllabus (see the "Syllabus/Readings" link)
(2) The textbook is entirely optional, but if you want to get one the ISBN number
is 9781405150491. Note that any used/older edition
will
also work fine.
(3) Go to www.cmegroup.com, shade
"Education" and click on the Education Home link. This will take you to
www.cmegroup.com/education.html and you will see a set of tutorials/presentations that provide a nice introduction
to derivatives, exchanges, and futures. At a minimum please take a few
minutes to watch
the following video group at:
(i) Managing Risk at CME Group  How it All Works (there are
about 8 chapter videos, each only about 12 minutes long).
http://www.cmegroup.com/education/managingriskcmegrouphowitworks.html
(ii) And then at
https://www.futuresfundamentals.org , go quickly through the various links
under "Get the Basics", "See the Impact", and "Explore the Marketplace".
(4) Important: Please begin to build a spread sheet that will compute duration and
modified duration. Along these lines, you should also go ahead and begin working on
Assignment No. 1. I will
send it to you via a separate email with instructions. Note that I will
attempt to post all homework exercises under "Assignments" on the course
website. For more information on this, I will send you an email with a
couple of short articles attached that provide an excellent primer on calculating duration with
examples. As you have time, please also:
(5) Give a quick review to the assigned chapters for the first day of class
and begin reading articles 2 and 3 that are posted under the
Syllabus/Readings link.
(6)
Here is a brief summary of what we will discuss at our first lecture:
We
will begin by developing a working definition of a derivative, and then
consider a number of common derivative structures as well as identify their
market venue (both OTC and exchangetraded instruments). We will look at
some recently released statistics regarding global market size, including
breakdowns according to product and instrument type, and maturity.
In our
inspection of the various types of derivatives, we will see that basically
all derivatives can be viewed as one or a combination of two basic building
blocks: the futures/forward contract and the option contract.
To illustrate both types of contracts, we will review two case studies. In
the first, we will review an early case study regarding the use of financial
futures for hedgingthe Salomon Bros/Merrill Lynch underwriting of IBM's
first public debt offering. This event is sometimes credited with being the
true motivating birth of the financial futures markets. In the second case
study, we will look a structured debt security. Using basic financial
engineering techniques, we will identify and value embedded options in the
product and show how the overall security was priced from a yield
perspective.
We will subsequently explore the "why" of financial risk management in which
we examine the various channels through which financial risk management can
potentially enhance shareholder value. We will discuss how and under what
conditions hedging can reduce financial distress and related business
disruption costs, reduce underinvestment incentives and adverse selection
problems, and reduce taxes.
See all at our first class and please do not hesitate to call me or stop by
at any time!
