Advanced Financial Economics
- Learning Objectives
- Course Outline
- Expectations: How to do well?
Why Advanced Financial Economics: Derivatives & Structured Products?
- Trends and historical growth
- Controversial—The Bad Rep!
- No Arbitrage Principle
- Standard Present Value Methodology
- Compounding, Interest rates/LIBOR, Term structure, yields & forward rates
- Day count conventions
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Who Am I?
B.A., Economics & Mathematics--University of Washington (Int’l Certificate)
Wall Street, New York: Lehman Brothers, Goldman Sachs
Main Street, Seattle: Bulge bracket to boutique independent wealth advisory
UW Lecturer (Econ 422, Econ 423, Econ 399/499/497)
Consultant: Financial services firms, primarily hedge funds
Finance: Behavioral Finance; Practical Applications of Finance Theory; Hedge Funds;
Derivative Securities & Structured Finance.
*Primary research is for non-public use.
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Economics 426 provides an introduction to the study of complex financial securities, with particular emphasis
on financial derivatives and structured products.
The course begins with an in depth study of futures and options, including economic theory, market and
institutional considerations, valuation methods, trading strategies, and hedging. More complex derivative
securities will be discussed, including exotics, index options, options on futures, callable and convertible bonds,
swaps, credit derivatives, and credit default swaps.
The process of securitization will be introduced as the basis for understanding structured financial products such
as asset backed securities and collateralized debt obligations.
Real world applications, recent events and ongoing developments in the economy and financial markets—
domestic and global--will be heavily emphasized throughout the course, in particular, discussion of the
subprime credit crisis, role of hedge funds, and real option analysis as an investment decision making
protocol for firms.
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Be able to understand, analyze, and value a variety of simple (‘plain vanilla’) to
complex securities from derivatives to structured products in the global economy.
- Course reading material: Required Hull text and supplementary course reading packet
- Regular problem sets (group work encouraged!)
Recognize and understand real world economic applications of such financial
securities—for good or for bad?!
- In class discussions
- Case studies: Required Marthinsen and supplementary course readings
Be conversant in current topics in the financial markets and the interplay in the
- Supplementary course reading packet
- Regular reading of financial sources
- In class discussions
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General Course Outline
May be fluid, ultimate moving target = subprime/financial crisis discussion
Part I: (2/3)
Both broader and more in depth coverage of derivative securities than that in Econ
- Math/Stat 492: presents stochastic calculus—the foundations for Black-Scholes--This
course is not meant as a substitute but as a complement to augment Math 492 with
the focus on application of derivatives in real world financial situations.
- Other great course complements:
464 Financial Crises
424 Computational Finance
Part II: (1/3)
With advanced coverage of derivatives securities the course will provide exposure
and basic understanding of ‘Structured Finance’ providing the framework within
which specific complex securities involved in the subprime/current financial crisis
can be discussed.
Specific Outline: See Syllabus
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Structured Finance: Structured Credit Meets Derivatives
RMBS CDS Swaps
MBS CDOs Options
Source: IMF Global Stability Report, October 2008.
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- website & email alias
Google group? – opt in (volunteer to establish?)
- Immediately following class 10:30 – 11:30 (noon)
- Condon 401E (in the Department office)
- By appointment, email email@example.com
- Econ 422 (Prereqs: Econ 300; Calculus (Math 124); Statistics (Stat 311 or 390; Qmeth 201))
- Hull’s Fundamentals of Futures and Options Markets (6th edition) (Available at U Bookstore or e-book)
- Lecture notes (Available for download from course website—password protected)
- Supplementary course packet of readings available at Ave Copy Center: 4141 University Way
- Marthinsen’s Risk Takers: Uses and Abuses of Financial Derivatives (Available at U Bookstore)
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Should I go out and buy a financial calculator?
- Midterm (30%)
- Final (30%)
- Homework: Problem Sets & Case Studies (40%)
No late work accepted. All assignments to be handed in at the beginning of
class. No emailed homework accepted unless pre-approved.
Zero tolerance for cheating or lack of academic integrity. University Policies strictly
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How to do well?
Invest time and effort:
- Come to class…lecture notes are ‘mad libs’ style!
- Read required readings/lecture notes
- Seek help (office hours or by appointment) if you do not understand lectures
Connect to the material
- Work in a group
- Engage in class discussion
- Take an interest in and keep current on developments in the financial markets & industry
- The Wall Street Journal, Barron’s, The Economist: Finance & Economics section
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Why study derivatives and structured products?
1. Together they represent largest and fastest growing segment of the global financial
- By the early 1980s, the volume of derivatives trading had grown so rapidly that the number of
shares underlying the option contracts traded daily exceeded the daily volume of shares traded on
- BIS Quarterly Review statistics
2. Derivatives can be useful for hedging, speculating, and arbitrage.
3. Structured products typically involve derivatives to provide customized, versatile
Source: Bank for International Settlements, 2008.
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Growth of Derivatives-Notional Terms
Notional amount: the Face Value or underlying value
upon which a contract is written, on which basis payments
Source: Bank for International Settlements, 2008. For historical data see: www.bis.org/statistics/derstats.htm
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Derivative Contract Volumes
Source: The Options Clearing Corporation, 2008.
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Sources: IMF Global Stability Report, Inside MBS & ABS, JP Morgan Chase & Co.; European Securitization Forum. IMF
Global Stability Report has bi-annual release: April and October. Next update will be April 2009.
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CFA Study Guide Derivative Markets & Instruments, #11:
The most likely reason derivative markets have flourished is that:
A. Derivatives are easy to understand.
B. Derivatives have relatively low transaction costs.
C. The pricing of derivatives is relatively straightforward.
D. Strong regulation ensures that transacting parties are protected from fraud.
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Reason 4. Controversial—
Is The Bad Rep Warranted?
Examples in the media:
Gerald Corrigan of Goldman Sachs:
“Derivatives, like NFL quarterbacks, probably get more credit and more blame than they deserve.”
Warren Buffet, Berkshire Hathaway Annual Report, 2002:
I view derivatives as time bombs, both for the parties that deal in them and the economic system . . .
Many people argue that derivatives reduce systemic problems, in that participants who can’t bear certain
risks are able to transfer them to stronger hands. These people believe that derivatives act to stabilize the
economy, facilitate trade, and eliminate bumps for individual participants. On a micro level, what they say is
often true. I believe, however, that the macro picture is dangerous and getting more so. Large amounts of
risk, particularly credit risk, have become concentrated in the hands of relatively few derivatives dealers, who
in addition trade extensively with one another. The troubles of one could quickly infect the others . . . In my
view, derivatives are financial weapons of mass destruction, carrying dangers that while now
latent, are potentially lethal. [emphasis mine]
“Structured Products Lose Their Appeal,” The Financial News, March 25, 2008:
“It was clear that this product was all about the firm’s investment bank shoveling c*** down its private banking distribution
channel. And the disclosure was appalling.”
Andrew Merricks, financial advisor at Skerritts Consultants, quoted by Telegraph.co.uk (6/19/08)
“ . . .structured products put a straitjacket around your investment decisions . . .”
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Why the Bad Rep:
Derivatives and Structured Products highly controversial:
1. High level of complexity.
2. Lack of transparency.
3. Derivatives often used improperly can lead to large losses.
- Derivatives can reduce many risks, except the human kind!*
- In particular: when things go awry, derivatives themselves take the blame, rather than the
users of derivatives. In many cases, the critics of derivatives do not understand them well.
Scapegoats for crises. Is it deserved? How to know?
Current financial crisis: structured products and derivatives (CMOs, MBSs, CDSs, TRSs, etc.) to blame
(???) for tipping an otherwise recessionary decline in the housing market into a full fledged systemic crisis
of global proportions.
Due to controversial nature, lack of transparency, and association/involvement in the
financial crises, much congressional and regulatory focus going forward will be on these
If they fail colossally does this mean they are not useful, if better understood??
*See “Financial WMD” The Economist, January 22, 2004.
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Review of concepts (primarily from 422) that will be important later on in the course.
As a contrast:
Traditional presented discounted cash flow analysis generally does not apply to the
derivative securities we will be considering; however, if the derivative security payoff
mimics that of a bond, we can use our PV framework.
What we will use heavily:
Interest rates and the term structure
And not so heavily, but occasionally:
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An arbitrage is any trading strategy which requires no cash input that has some
probability of making profits with potentially risk of loss:
- Pure arbitrage is risk-less and rare.
- Near arbitrage is risky and more relevant.
In an efficiently functioning financial market, arbitrage opportunities cannot persist
as individuals take advantage of arbitrage profits, reducing them in the process to
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Present Value Methodology
Recall (422) we used present value methodology for both simple stock and bond
The idea is that you value the security for its future expected cash flows such that what you are
willing to pay today for these cash flows is precisely the sum of the discounted value of these today.
For these simplest stock and bond cases we considered, the biggest challenge is
determining the appropriate discount rate(s).
We established the idea that the discount rate should mirror the risk of the cash flows, i.e., use a
risk-less rate (Treasury yields, a.k.a our term structure) to discount risk-less cash flows and use a
risk-adjusted discount rate (CAPM based as one example) to discount risky cash flows.
Dividend discount model:
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Interest rates are a factor in the valuation of virtually all derivatives.
An interest rate is the amount of money that a borrower promises Standard No. 138,
allows for the
to pay a lender; includes: mortgage rates, deposit rates, prime, etc. LIBOR/swap rate to be
used as one of only two
Treasury rates are the rates an individual earns on Treasury bills, market interest-rate
Notes, and bonds. Treasuries are the instruments used by a benchmarks in hedge
government to borrow in its own currency. Treasury securities are accounting. The other
deemed the least risky securities under the presumption that a allowable market
government would not default on an obligation denominated in its
benchmark is the U.S.
own currency.* Treasury curve. LIBOR
LIBOR (London Interbank Borrowing Offered Rate) rates are typically important in pricing
used for defining OTC derivatives payoffs such that LIBOR is the commercial credit and
more common benchmark among derivative traders. LIBOR is the even more important in
rate at which a bank is willing to offer on a large deposit pricing derivatives.
with other banks.
*Examples of defaults: Russia, Argentina…’never say never!’ **LIBID (London Interbank Bid
Rate) is the rate at which a bank is willing to accept deposits. See article “The LIBOR
Treasury rates, “ PBS Nightly Business Report, SeptemberDavis 2008
The day count determines the way in which interest accrues over time.
Typically we need to calculate the interest over a period of time different than the
reference period (i.e., the accrued interest on a bond owed when purchased in the
secondary market sometime in between coupon payments)
Accrued Interest =
Three day count conventions commonly used in the United States:
(‘clean prices’) do
2. 30/360 not include
3. Actual/360 accrued interest
Cash or ‘dirty’
price = quoted
price + accrued
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Day Count Matters!
Between February 28, 2009 and March 1, 2009 you have your choice between owning
a corporate bond paying 10% or a US Treasury bond paying 10%.
Which do you choose, based on interest payments alone?
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Suppose an amount A is invested for n years, compounded m times per year, at an annual
interest rate r per year.
If the rate is compounded once per annum (m = 1), then the future value of the
If the rate is compounded m times per year, then the future value of the investment is:
As m approaches infinity (continuous compounding), the future value of the investment
To convert a rate with a compounding frequency of m times per year (rm) to a
continuously compounded rate (rc):
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PV with Continuous Compounding
When interest rates are continuously compounded:
Dividend discount model:
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In Class Problem #1
A bank quotes you an interest rate of 14% per annum with quarterly compounding.
What is the equivalent rate with:
a. continuous compounding?
b. annual compounding?
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In Class Problem #2
Suppose the following continuously compounded zero rates:
What is the price of a bond with a FV of $1,000 that will mature in 30 months and
pays a coupon of 4% semi-annually?
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In Class Problem #3
An investor receives $1,100 in one year in return for an investment of $1,000 now.
Calculate the percentage return per annum with:
a. annual compounding
b. semi-annual compounding
c. monthly compounding
d. continuous compounding
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Yield to Maturity
A bond’s yield to maturity (YTM or yield) is the discount rate that equates the
discounted value of the bond’s promised cash flow to its market price.
r = Yield to Maturity:
Example: Suppose a Treasury zero bond that matures in three months is selling for
$97.50. Face value is $1,000. What is the bond’s yield to maturity?
Suppose we want to express the interest rate with continuous compounding. Using
equation 5 from the ‘compounding’ slide:
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For current term structure:
Term Structure finnace/debt-management/interest-rate/yield.html
Yield curves can have various shapes.
Increasing rates are most common---upward sloping yield curve, but the plot can show a decrease,
hump or flat region.
The benchmark yield curve plots the going ‘spot’ rates for various constant maturity Government
securities—T-bills, T-Notes and T-Bonds that have been stripped of coupons (Zeros). These yields
and their respective maturities are referred to as the Term Structure.
‘Normal’ yield curve
(Associated with ‘loose’ monetary
r0,30 policy, i.e., short term money is ‘easy’ r0,30 Inverted yield curve
(Associated with ‘tight’ monetary policy, i.e.,
r0,10 r0,10 shortage/high cost of short-term money.)
t1 t5 t10 t30 t1 t5 t10 t30
R.W. Parks/Davis 2008
Relationship Between Rates Along Yield Curve
In a world with certainty, in order for there to be no arbitrage, the return on
holding a 2 year Treasury investment must be the same as investing in a one year
Treasury today then rolling this forward into another one year Treasury in one year:
You can solve for r0,2:
A similar relationship will hold for the period T interest rate:
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Forward Interest Rates
In reality, we live in a world of uncertainty, such that in our previous example, r1,2 is
In reality, we do not know with certainty any future interest rates, i.e., rt-1,t for t >1.
We can use today’s term structure, combined with our No Arbitrage condition; however,
to infer something about future rates.
Future rates from today are referred to as forward interest rates.
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Forward Rates and Term Structure
Recall our No Arbitrage Condition under certainty:
We can infer what the market thinks r1,2 will be in the future. This is the implied forward rate
f1,2 the one period ahead rate implied by our no arbitrage condition:
The implied forward rate is
Note: This forward rate is entirely described by current term structure!
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Forward Rates and Term Structure
The following general formula allows us to determine the forward rate for any
future period between periods t-1 and t:
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In Class Problem #4
The term structure of interest rates is upward sloping. Put the following in order of
a. 5 year zero rate
b. yield on a 5 year coupon bearing bond
c. forward rate corresponding between 4.75 and 5 years
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Calculating Forward Rates
Forward interest rates are the rates of interest implied by the current zero rates for
periods of time in the future.
Suppose the following represent zero rates, continuously compounded:
Year (n) Zero rate for n-year investment
To determine the forward rate for year two, consider the future value of a two year
investment of $100:
If instead you invested one year at 3% then rolled the investment forward at f12, by our
no arbitrage condition, the value of this investment must equal $108.33:
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Calculating Forward Rates
Similarly, we can solve for the forward rates for n =3-5 as shown below:
Year (n) Zero rate for n-year investment fn
2 4.0 5.0
3 4.6 5.8
4 5.0 6.2
5 5.3 6.5
In general, if R1 and R2 are the zero rates for maturities T1 and T2, respectively, and RF
is the forward interest rate for the period of time between T1 and T2:
RF = (R2T2-R1T1)/T2-T1
RF = R2 + (R2 –R1)*[T1/(T2-T1)]
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Duration is an important concept in the use of interest rate futures for hedging.
The duration of a financial asset measures the sensitivity of the asset's price to
movements in the interest rate as expressed as a number of years, i.e. dV/dr .
Suggested by Frederick Macaulay in 1938.
The duration of a bond is a measure of how long on average the holder of
the bond must wait before receiving cash flows. (Also referred to as effective
A zero coupon bond that matures in n years has a duration of n years.
Coupon bearing bonds with maturity of n years will have a duration less than n
years because some of the cash payments (coupons) are received prior to year n.
Example: A bond with a higher coupon rate (10% or $100/year) will return a higher percentage of
the bond’s current market value over a given number of years when compared to a bond of similar
maturity but with a lower coupon rate say 8%.
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Bond Value = V = ΣCFt/(1+i)t t = 1 to T
CFt = cash flow per period t
= coupon payment for t = 1 to T-1 and coupon plus face for t = T
i = r/m = current annual market yield (r )adjusted by the compounding frequency m
t = time in compounding periods = mY where Y = number of years
To measure the sensitivity of the value (V) of the bond in response to changes in i:
Noting that 1/(1+i) is substantially ≈ 1, then:
Duration = the total weighted average time for recovery of the payments and principal in
relation to the current market price of the bond:
Duration = Duration varies
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Duration Calculation-continuous compounding
Current time is 0
Bond provides holder with payments ci at time ti for (1< i <T)
r represents the continuously compounded yield
Price of the bond, B
The duration, D, of the bond is defined as:
From this second notation we see that the duration is a weighted average of the times
when cash flows are received with the weights representing the proportion of
the bond’s total present value provided by the cash flow at time ti.
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Duration Calculation-continuous compounding
Three year, 6% coupon Treasury (semi-annual coupon!) with a FV of $1000. Assume a
yield of 4% continuously compounded.
-ti (yrs) Cash Flow Present Value Weight t * Weight
(CF) =CFe-r/2*t = CFt/B
Bond Value Duration
Note: Duration will be negative. However, you may not always see it being referred to with a negative sign!
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Relationship of Duration and % changes in Bond prices
What is the impact on the bond price of a change in yields?
Given: B = Σcie-rti for i = 1 to n
Want to know: ∂B/∂r = ?
Using our definition of duration, we can write this as:
Meaning: the percentage change in a bond’s price is equal to its duration (this will
be negative!) multiplied by the size of the parallel shift in the yield curve.
→ Approximate relationship between percentage changes in a bond’s yield and bond price.
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With reference to the previous example:
∆B = BD∆r
∆B = 1,054.85 * -2.796*∆r
∆B = -2,949.36*∆r
If ∆r = 0.001 (so that r increases to 0.041), we expect ∆B to be -2.95, i.e., we expect the
price of the bond to decrease: $1,054.85 – $2.95 = $1,051.90.
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In Class Problem #5
A five year bond with a yield of 11% continuously compounded pays an 8% coupon at
the end of each year.
a. What is the bond’s price?
b. What is the bond’s duration?
c. Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in
d. Recalculate the bond’s price on the basis of a 10.8% per annum yield and verify it is
in agreement with part c. above.
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Bond Portfolio Duration
The duration of a bond portfolio is a weighted average of the duration of the
individual bonds in the portfolio where the weights are proportionate to the value
of the respective bond in the portfolio.
When duration is used for bond portfolios there is an implicit assumption that the
yields of all bonds will change by the same amount (i.e., a parallel shift of the yield
- Note: this calculation relies on a specific type of change in the yield curve which if not realized can
lead to ‘slippage,’ i.e., losses from a hedge, etc. (More on this to come!)
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Importance of duration
Match duration of assets with duration of liabilities
Insurance firm issuing life insurance:
- Insurance firms will frequently invest in bonds with durations matched to the duration of
future projected death benefits.
- Will issue debt to purchase assets to lease. The lease payments and the debt each have a
- Leasing companies will typically structure debt financing so the duration of the debt
(liability) matches the duration of the leases (asset).
- Pension funds have obligations to retirees. These obligations have a duration.
- The pension fund can invest assets into fixed income securities.
- Pension fund managers commonly select pension assets with given duration that match the
pension fund liability duration.
- * Readings: “Company Pensions: Time for a Reality Check” and “Actuaries and the Pensions Crunch: When the Spinning Stops,” The
Economist, January 26, 2006; “
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