Structured Finance Cash Flow Collateralized Debt Obligations

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					             Advanced Financial Economics


                                       Econ 426

Discussion Outline
Course Mechanics
- Learning Objectives
- Course Outline
- Expectations: How to do well?
Why Advanced Financial Economics: Derivatives & Structured Products?
- Trends and historical growth
- Controversial—The Bad Rep!
Finance Essentials
- No Arbitrage Principle
- Standard Present Value Methodology
- Compounding, Interest rates/LIBOR, Term structure, yields & forward rates
- Day count conventions
- Duration

2                                       Davis 2008
    Who Am I?
          B.A., Economics & Mathematics--University of Washington (Int’l Certificate)
          Ph.D., Economics--MIT

    Career Experience
          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

    Research Interests*
    Finance: Behavioral Finance; Practical Applications of Finance Theory; Hedge Funds;
             Derivative Securities & Structured Finance.

    *Primary research is for non-public use.

      3                                                Davis 2008

    Course Mechanics
   Course website

   Course Description
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.

      4                                                Davis 2008
Learning Objectives
      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.
      -   Lectures
      -   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
      global economy.
      -   Supplementary course reading packet
      -   Regular reading of financial sources
      -   In class discussions

  5                                              Davis 2008

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
  6                                              Davis 2008
Structured Finance: Structured Credit Meets Derivatives

                    Structured Credit

                                                                    Credit Derivatives

                                     RMBS                                     CDS                   Swaps
                        MBS                             CDOs                                       Options

Source: IMF Global Stability Report, October 2008.

  7                                                  Davis 2008

Course Mechanics
 - website & email alias

 Google group? – opt in (volunteer to establish?)

 Office hours
 -    Immediately following class 10:30 – 11:30 (noon)
 -    Condon 401E (in the Department office)
 -    By appointment, email

 -    Econ 422 (Prereqs: Econ 300; Calculus (Math 124); Statistics (Stat 311 or 390; Qmeth 201))

 Required readings
 - 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)

  8                                                  Davis 2008
Course Mechanics
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
adhered to.

9                                              Davis 2008

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

10                                             Davis 2008
 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
    the NYSE.

    - 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.

  11                                                    Davis 2008

Growth of Derivatives-Notional Terms
                                                             Notional amount: the Face Value or underlying value
                                                              upon which a contract is written, on which basis payments
                                                             are calculated.

    Source: Bank for International Settlements, 2008. For historical data see:

  12                                                    Davis 2008
 Derivative Contract Volumes

                                      Source: The Options Clearing Corporation, 2008.

   13                                                  Davis 2008

 Structured Finance

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.

   14                                                  Davis 2008
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.

       15                                                  Davis 2008

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 (6/19/08)
            “ . . .structured products put a straitjacket around your investment decisions . . .”

       16                                                  Davis 2008
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.
  17                                                    Davis 2008

Finance Essentials
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:
    No-arbitrage principle
    Interest rates and the term structure

And not so heavily, but occasionally:
    Bond Duration

  18                                                    Davis 2008
No-Arbitrage Principle
  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.

No-Arbitrage Principle;

  In an efficiently functioning financial market, arbitrage opportunities cannot persist
  as individuals take advantage of arbitrage profits, reducing them in the process to


 19                                           Davis 2008

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.
  Investment valuation:

  Bond valuation:

  Dividend discount model:

 20                                           Davis 2008
     Interest rates
     Interest rates are a factor in the valuation of virtually all derivatives.
                                                                                            Financial     Accounting
     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
                                                                                            interest              rate
     government would not default on an obligation denominated in its
                                                                                            benchmark is the U.S.
     own currency.*                                                                         Treasury curve. LIBOR
                                                                                            is            increasingly
     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
                                                              14, 2007.
Treasury rates, “ PBS Nightly Business Report, SeptemberDavis 2008

     Day Count
     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:
                                                                                                   Quoted prices
1.   Actual/Actual
                                                                                                (‘clean prices’) do
2.   30/360                                                                                         not include
3.   Actual/360                                                                                  accrued interest

                                                                                                  Cash or ‘dirty’
                                                                                                 price = quoted
                                                                                                 price + accrued

      22                                                Davis 2008
  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?

    23                                  Hull/Davis 2008

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
   investment is:
   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
   grows to:
   To convert a rate with a compounding frequency of m times per year (rm) to a
   continuously compounded rate (rc):

    24                                    Davis 2008
PV with Continuous Compounding
When interest rates are continuously compounded:

  Investment Valuation:

  Bond Valuation:

  Dividend discount model:

   25                                  Davis 2008

 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?

   26                                Hull/Davis 2008
     In Class Problem #2
     Suppose the following continuously compounded zero rates:

                            Maturity           Rates
                                6                4%

                                12              4.2%

                                18              4.4%

                                24              4.6%

                                30              4.8%

     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?

      27                                    Davis 2008

     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

      28                                  Hull/Davis 2008
 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:

  29                                                     Davis 2008

                                                                           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
            or cheap.)
                                                                             (Associated with ‘tight’ monetary policy, i.e.,
  r0,10                                                       r0,10          shortage/high cost of short-term money.)

  r0,5                                                        r0,5

  r0,1                                                        r0,1

           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:

  31                                  R.W. Parks/Davis 2008

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.

  32                                  R.W. Parks/Davis 2008
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!

    33                                   R.W. Parks/Davis 2008

 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:


    34                                   R.W. Parks/Davis 2008
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

 35                                        Hull/Davis 2008

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

                 1                            3.0
                 2                            4.0
                 3                            4.6
                 4                            5.0
                 5                            5.3

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:

 36                                        Hull/Davis 2008
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

               1                        3.0

               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

or equivalently:
                                  RF = R2 + (R2 –R1)*[T1/(T2-T1)]

 37                                           Hull/Davis 2008

   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.

Bond Duration
   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%.

 38                                             Davis 2008
  Bond Duration
           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:
           dV/di =
           dV/di =
Noting that 1/(1+i) is substantially ≈ 1, then:
           dV/di ≈
            dV/di ≈
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
                                                                                inversely with
    39                                            Davis 2008

  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.

    40                                            Davis 2008
  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!
    41                                                            Davis 2008

  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.

    42                                                            Davis 2008
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.

     43                                       Davis 2008

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
      its yield.
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.

     44                                     Hull/Davis 2008
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!)

 45                                                        Davis 2008

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.
  Leasing company
  -   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*
  -   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; “

 46                                                        Davis 2008

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