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Fin 284 Yield Spreads S2004

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					       Yield Spreads

            Finance 298
Analysis of Fixed Income Securities




                              Drake Fin 284
                              DRAKE UNIVERSITY
                                           Drake
    Level of interest rates                Drake University

                                            Fin 284



We often refer to the “level of interest rates”
in the economy.
How is this measured?
What do we mean by a base rate?
What role does the Federal Reserve Play in
determining the level of interest rates?
What other factors play a role in determining
the level of interest rates?
                                         Drake
The “Level of interest rates”             Drake University

                                           Fin 284


Often interest rates are discussed with the
assumption that there is only one rate in the
economy. This is not true.
There is a structure of rates based upon
different risks and economic forecasts,
however the general level of each rate is
correlated with the others. Therefore interest
rates are tied to a base rate and then
differentiated by the risk premiums we
discussed at the beginning of the semester.
                                           Drake
            Base rates                      Drake University

                                             Fin 284


Given that risk differentiates interest rates
one place to start is a “risk free” rate. US
treasury securities are often used for this,
should we use short term of long term
treasuries?
A second place to start is with the availability
of borrowing for the banking sector,
especially short tem borrowing which is used
to cover shortages in reserves, the Federal
funds rate.
                                         Drake
      Federal funds rate                 Drake University

                                          Fin 284



The federal funds rate is the market rate for
short term lending between banks. The
substitute for borrowing in this market is
borrowing from the Federal Reserve through
the discount window. Therefore, the Federal
Reserve has a large influence on the level of
both rates. It does not however actually set
the Federal funds rate as we will show soon.
    Review of Key Factors               Drake
          Impacting                      Drake University

                                          Fin 284
    Interest Rate Volatility
Fisher Classical model of the Savings Market
Household saving (supplies funds) for
business (demands funds)
    Saving and Investment                      Drake
                                                Drake University

          Decisions                              Fin 284


Saving Decision
  Marginal Rate of Time Preference
  Trading current consumption for future consumption
  Expected Inflation
  Income and wealth effects
  Generally higher income – save more
  Federal Government
  Money supply decisions
  Business
  Short term temporary excess cash.
  Foreign Investment
                                          Drake
   Loanable Funds Theory                  Drake University

                                           Fin 284


Expands suppliers and borrowers of funds
includes business, government, foreign
participants and households.
Interest rates are determined by the total
demand for funds (borrowing) and the total
supply of funds (Savings).
Savings is positively related to the level of
interest rates. (upward sloping)
Borrowing is negatively related to the level of
interest rates (downward sloping)
                                     Drake
     Borrowing Decisions             Drake University

                                      Fin 284



Borrowing Decision
  Marginal Productivity of Capital
  Expected Inflation
  Other
                                                 Drake
     Equilibrium in the Market                   Drake University

                                                  Fin 284
Original Equilibrium           Decrease in Income
                S                           S’
                                                           S




             D                                        D


Increase in Marg. Prod Cap   Increase in Inflation Exp.
                                                 S’
                                                           S
             S



                                                          D’
                    D’                           D
            D
                                             Drake
 Liquidity Preference Theory                 Drake University

                                              Fin 284


Liquidity Preference
  Two assets, money and financial assets
  Equilibrium in one implies equilibrium in other
  Supply of Money is controlled by Central Bank
  and is not related to level of interest rates (A
  vertical line)
  Similar to Loanable Funds, changes in money
  supply and money demand cause a change in
  the equilibrium level of interest rates.
                                                  Drake
Equilibrium in Liquidity Theory                   Drake University

                                                   Fin 284


Three main effects of a change in the level of money
  Liquidity effect – change in level of money available
  (decreasing rate)
  Income Effect – in the longer run the increased
  economic activity may increase demand for money
  (increasing rates)
  Price expectations effect it producing close to full
  capacity, price increases may cause an increase in the
  demand for money (increasing rates)
                                         Drake
     Liquidity Preference                Drake University

                                          Fin 284



Money supply is controlled by the central
bank (the Federal Reserve for the US).
Monetary policy therefore plays a key role in
determining the level of interest rates and
corresponding level of economic activity.
  The Federal Reserve System          Drake
                                       Drake University

   Background and overview              Fin 284



12 Regional Banks
Fed board of Governors 7 members, 14 year
appointments
Federal Open market Committee (FOMC),
Board of Gov, Bank of NY Pres, 5 other Fed
bank pres.
Independence of the Fed
                                 Drake
Instruments of Monetary Policy   Drake University

                                  Fin 284



Reserve Requirements
Open Market Operations
Discount Window Lending
                                               Drake
    Reserve Requirements                       Drake University

                                                Fin 284


Setting of the % of required reserves in the banking
sector.
The reserves must either be cash on hand or on
deposit at the Fed.
If reserve requirements are increased banks hold
more money in reserve, decreasing the amount that
is available for lending.
If reserve requirements are decreased banks hold
less money in reserve, increasing the amount
available for lending.
                                                Drake
Monetary Control Act of 1980                    Drake University

                                                 Fin 284


Moved much of the responsibility of reserve
requirements from the Fed to the Congress.
Rules also expanded to include all depository
institutions. A basic ratio of 12% was established for
all checkable deposits. Likewise a basic rate of 3%
was set for time deposits.
Fed given ability to change the checkable deposit
rate between 8 and 14%.
                                        Drake
Using Reserve Requirements              Drake University

                                         Fin 284



Advantage is that reserve rules affect all
banks the same
Can have large impact because of multiple
deposit creation.
Can cause immediate liquidity problems for
banks with low excess reserves.
Is not used very often.
                                        Drake
  Open Market Operations                Drake University

                                         Fin 284



The buying and selling of US government
securities by the Federal Reserve on the open
market.
In other words, it is buying and selling the
securities at the market price and yield.
                                              Drake
   Open Market Operations                     Drake University

                                               Fin 284


When the Fed purchases securities on the “open
market” it must use its cash reserves (money which
was out of circulation), therefore the amount banks
have available to lend (excess reserves) will
increase.
When the Fed sells these securities on the “open
market” individuals and institutions pay for them
with cash which the Fed then holds in reserve, in
effect removing it from circulation, reducing the
amount of excess reserves in banks.
Open Market Operations and the                   Drake
                                                 Drake University

     Federal Funds Rate                           Fin 284


The goal of open market operations is to help
manage the Federal Funds Rate
  Fed Funds Rate – the interest rate charged on short
  term lending between banks
By effectively increasing and decreasing the
amount of funds available, the fed is impacting
the amount of funds that banks have available to
lend. As supply of funds increases, the rate
charged decreases.
                                           Drake
  Open Market Operations                   Drake University

                                            Fin 284



Dynamic
   intended to change the level of reserves and
  the monetary base
Defensive Open Market Operations
  Intended to offset movements in other factors
  that affect reserves and the monetary base.
  Only buys and sells US Treasury and
  government securities to avoid conflicts of
  interest
                                       Drake
 Daily Open Market Operations           Drake University

                                         Fin 284



Conducted at the trading desk, (at the New
York Fed), Both Dynamic and Defensive
Operations are undertaken.
                                             Drake
 A Day at the Trading Desk                   Drake University

                                              Fin 284


Review of developments in Fed Funds Market on the
previous day and check of actual amount of
reserves on the previous day.
Detailed Forecast developed by staff of short term
factors affecting reserves
(treasury deposits, float, publics holding of
currency…)
Monitor the current developments in the Fed Funds
Market
   A Day at the Trading Desk             Drake
                                         Drake University

           continued                      Fin 284



Use forecasts to decide if sales or purchases
need to be made to keep the Fed Funds rate
in its target range.
Call treasury to get updated info on planned
moves
   A Day at the Trading Desk             Drake
                                         Drake University

           continued                      Fin 284



Contact Monetary Affairs Division at the Board
of Governors in D.C. and
formulate a proposed course of action.
Midmorning Conference call with Director of
Monetary affairs and one of the
regional bank presidents to propose course of
action for the day
                                       Drake
 A Day at the Trading Desk              Drake University

                                         Fin 284


Execution of “temporary” Open Market
Operations mainly through the use of
repurchase agreements and reverse
repurchase agreements. The effect of these
changes are reversed at the maturity of the
agreement.
Conduct any “Outright” Open market
operations (purchase and sale of securities
directly)
    Open Market Repurchase                Drake
                                           Drake University

      Agreements (Repos)                    Fin 284



Used when the Fed believes that there will be
an event that is significant but not long lived.
An example may be a large payment from the
US treasury such as Tax Refunds or Social
Security payments (either would create a
temporary increase in the amount of reserves
available)
                                           Drake
   Repurchase Agreements                   Drake University

                                            Fin 284



The sale of a security with the promise of
repurchasing it in a very short time (usually
overnight) at a premium.
The seller is essentially borrowing money
from the other party and using a security
(usually issued by the treasury) as collateral.
                                           Drake
   Repurchase Agreements                   Drake University

                                            Fin 284



The difference in price represents the interest
rate paid on the loan (it is often referred to as
the repo rate).
Reverse Repo’s are just taking the opposite
side of the agreement (lending the money
today, agreeing to sell back the security it he
future).
  Advantages of Open Market               Drake
                                          Drake University

         Operations                        Fin 284



Conducted at the initiative of the Fed (with
the discount rate they can only encourage
banks to loan more or less)
Flexible and precise
Easily reversed
Implemented quickly
                                        Drake
         Discount Rate                  Drake University

                                         Fin 284



The Federal Reserve provides short- term
loans to banks to enable them to meet
depositors demands and reserve
requirements.
The Fed sets the discount rate which the rate
of interest changed on the loans.
                                         Drake
   Using the Discount Rate               Drake University

                                          Fin 284



When the Fed increases the discount rate it
discourages banks from borrowing, reducing
the money supply.
Increases in the discount rate raise the cost
of borrowing…
When the Fed decreases the discount rate
banks are more willing to borrow so the
money supply will increase
                                              Drake
 Discount Window Loans                        Drake University

                                               Fin 284


Adjustment Credit Loans – Most common type of
loan to cover short falls of reserves
Seasonal Credit – given to a limited number of banks
that operate in vacation and agriculture areas, rate
tied to the average of the monthly average Fed
Funds rate and CD rates.
Extended Credit – Banks with severe liquidity
problems. ½ point above the rate on seasonal credit
                                              Drake
Discount Window Disadvantages                 Drake University

                                               Fin 284


Disadvantages to using the discount window as a
source of funds:
Cost associated with Discount window lending:
Interest rate is high compared to other sources
Concerns that might be raised about the health of
the bank causing increased monitoring:
More likely to be turned down in the future.
           Problems with                   Drake
                                           Drake University

       The Discount Window                  Fin 284



The rate is set by the Fed, but it can’t control
the amount of lending.
It is difficult to revise.
It can cause large fluctuations in the spread
between rates in general and the discount
rate, causing unintended changes in the
volume of loan and hence the money supply.
                                         Drake
    A Big Picture Question               Drake University

                                          Fin 284



Do we need a lender of last resort if the FDIC
is in existence?
The Announcement Effect – Signal future
monetary policy moves.
The role of lender of last resort promotes
safety and soundness, but the lending
function is not very effective as a tool.
                                        Drake
        What is Money?                  Drake University

                                         Fin 284



 How is it measured and what functions does
it perform?
Does only cash count? What about easily
converted to cash like a treasury bill? What
about “hard assets” like gold?
                                                Drake
Functions Performed by Money                    Drake University

                                                 Fin 284


Medium of exchange -- Allows trade to occur, barter
is inefficient. Most be accepted by the individuals in
the economy.
Store of Value -- Can be used to hold wealth from
one period to the next as opposed to various goods
which might not be storable
Unit of account -- Basic unit for measuring economic
value. allows for comparison between different
consumption goods, prices wages and incomes.
         Measuring money                Drake
                                        Drake University

                                         Fin 284



There is no single measure of money in the
  economy, generally measured by a group of
  money aggregates. M1, M2, M3, and L are all
  aggregates established by the Fed.
                                          Drake
                M1                        Drake University

                                           Fin 284



             M1 = Currency
  + Traveler’s checks held by the public
   + demand deposits (pay no interest)
 + checkable deposits (pay some interest)

M1 is the most liquid measure of money and
 closest to the theoretical definition of money
                                              Drake
                  M2                           Drake University

                                                Fin 284


                    M2 = M1
   + Savings deposits including passbook saving
         + Time deposits of a fixed term
+ Money Market Mutual Funds (individuals, invest in
      short term securities, allow check writing)
            + Repurchase agreements

             M2 is not as liquid as M1
                                      Drake
             M3, L                     Drake University

                                        Fin 284


              M3 = M2
  + Large denomination time deposits
              (>100,000)
+ money market funds held by institutions

L = M3 + short term treasury securities
+ Commercial paper (short-term debt of
             corporations
        + US saving bonds
 Required Reserves and the Money         Drake
                                          Drake University

            Multiplier.                    Fin 284



When new money enters the banking system
it expands the money supply by a much
larger amount.
This is referred to as the “creation of money”
                                       Drake
            Example                    Drake University

                                        Fin 284



Assumes that the Fed purchases securities on
the open market (the total amount of money
as measured by the aggregates has not
changed).
 Fed purchases $10 Million dollars of US
securities from bank A.
Bank A now has an extra $10 million that it
wants to lend out (it is now cash).
                                         Drake
       Example Continued                 Drake University

                                          Fin 284



Assuming that the required reserve ratio is
12% the banks required reserves have
increased by $1.2 Million and the amount it
has in excess reserves has increased by $8.8
Million.
 Now assume it loans out the $8.8 Million to a
firm who uses it to buy parts and equipment
from a vendor who deposit is it in a second
bank (Bank B).
                                         Drake
      Example continued                  Drake University

                                          Fin 284



Bank B has an increase of ($8.8million)(1-.12)
in required reserves or $7.744 million.
This continues again and again until the total
change in demand deposits is equal to:
      DR+(1-REQ)DR+(1-REQ)2DR+(1-
           REQ)3DR+…. = DR/REQ
                                          Drake
         Quick Question 1                 Drake University

                                           Fin 284



 How does this impact the level of interest
rates?

Answer
  The increase in the amount of excess
  reserves causes banks to lower the
  amount they are charging on loans to
  attract new customers.
                                          Drake
       Quick Question 2                    Drake University

                                            Fin 284



Does the level of interest rates impact the
level of the money supply? (leakages)
It is assumed that the level of the money
supply impacts the level of interest rates, but
does the reverse also hold true?
                                       Drake
            Answers                    Drake University

                                        Fin 284



Yes, If banks do not lend out all of their
money. If rates are high there is a high
opportunity cost of not making loans.
No, However if rates are low, the firm may
be willing to have excess reserves.
                                        Drake
           Leakages                     Drake University

                                         Fin 284



Also we assumed that all of the money was
deposited and none held in the form of cash.
If some of the funds are held as cash, there
are foregone interest earnings for the
individual (an opportunity cost to the
investor).
Any lending that is less than the full amount
possible can be referred to leakages, These
cause the impact of the change in the money
supply to be less.
                                     Drake
           Leakages                  Drake University

                                      Fin 284



In an open economy foreign exchange can
also serve as a leakage.
                                          Drake
How is monetary policy determined?        Drake University

                                           Fin 284



 The Fed is attempting to attain a given set of
 macroeconomic goals.
                                      Drake
             Goals                    Drake University

                                       Fin 284


High employment – Full Employment and
Balanced Growth Act of 1978 (Humphrey
Hawkins). Committed the government (and
the Fed) to promoting high employment
consistent with a stable price level.
Key is how big should or can employment
be? The “natural rate of unemployment”
constrains the ability to always increase
employment.
                                       Drake
        Economic Growth                Drake University

                                        Fin 284



Growth is measured by increases in real GDP.
Biggest current question is why has growth
slowed in the last 20 years?
                                          Drake
          Price Stability                 Drake University

                                           Fin 284



Targeting inflation is the latest “fad” among
central banks. The belief is that keeping
prices stable can decrease uncertainty and
lead the economy toward the other goals.
                                        Drake
     Interest rate Stability –          Drake University

                                         Fin 284



Again the main idea is decreasing uncertainty
and promoting Stability in Financial Markets
  Stability in Foreign Exchange          Drake
                                         Drake University

              Markets                     Fin 284



Not always able to control Asian Financial
crisis is a good example.
                                         Drake
      Conflict among Goals.               Drake University

                                           Fin 284



The goals often interfere with each other, for
example stable prices and high employment.
If the Phillips curve is correct there is a
tradeoff between unemployment and
inflation. Often low unemployment has
resulted in high inflation ad vice versa.
                                          Drake
       Conflicts continued                Drake University

                                           Fin 284



Likewise since interest rates are linked to the
price level (fisher equation) Interest rate
stability and high employment are not always
compatible.
Which should a central bank target? How
should they set their objective?
                                        Drake
        Goals vs. Targets               Drake University

                                         Fin 284



Sets Goals (Employment, Inflation) then
establishes targets for key variables that
should be consistent with reaching the goals
The targets are the means of obtaining the
desired goals.
                                        Drake
       Operating Targets:               Drake University

                                         Fin 284



Variables that are directly effected by the
policy tools of the central bank.
Some examples include reserve aggregates,
the monetary base, federal funds rate,
borrowed reserves…
                                          Drake
      Intermediate Targets                Drake University

                                              Fin 284



Variables that have a direct effect on the
goals, but are not directly effected by the
central banks monetary tools.
Examples include M1, M2 etc…
                                          Drake
        Monetary Policy                   Drake University

                                           Fin 284



Since Targets are more long term in nature,
the central bank aims at the targets in an
attempt to steer the economy toward its
goals.
Often there is conflict in choosing the correct
target.
 For example in class we showed, choosing a
monetary aggregate lessens the ability of the
bank to control interest rates and vice versa.
                                                Drake
         Choosing Targets                       Drake University

                                                 Fin 284


Operating Targets should be:
  Measurable
  Central Bank has some control over changes
  in the variable
  Have an intermediate target as its goal.
Intermediate Targets should be:
  Measurable
  Central Bank has some control over changes in the
  variable.
  Have a predictable impact on the goal
                                                 Drake
A quick Historical Perspective of the Fed        Drake University

                                                  Fin 284


 Pre 1920’s Discount rate is the primary tool
 1920 – 1930 Expanded use of Open Market
 Operations
 1930’s The Great Depression
   The introduction of the Reserve Requirement
   (Thomas Amendment to the Agricultural Adjustment
   Act of 1933
   Pegging of Interest rate and war finance. Fed would
   make Open Market Purchases to keep the interest
   rates fixed to pre war levels.
                                            Drake
  Historical Perspective continued          Drake University

                                             Fin 284


1950’sand 60’s
 Money Market Conditions. Use of Free
 reserves as indicator resulting in procyclical
 monetary policy.
 1970’s Targeting Monetary Aggregates and
 the federal funds rate
   Widening of target range for Fed Funds Rate
   Specifically the Fed targeted the amount of
   non borrowed reserves (total reserves less
   those borrowed from the discount window)
                                               Drake
  Historical Perspective continued             Drake University

                                                Fin 284



1982-early 1990’s
 De-emphasis on monetary aggregates, return
 toward federal funds targeting
 Target became growth in borrowed reserves was
 kept to a specific range.
 Fed recognizes the need to target foreign exchange
 rate stability
 Stock market crash of 1987 forced Fed to think
 about stability in the financial markets which also
 became a point of emphasis.
                                         Drake
  Historical Perspective continued       Drake University

                                          Fin 284



Mid to late 1990’s
  Fed still used the fed funds rate as primary
  tool, but was more tolerant of growth than
  before.
  One explanation was a possible new paradigm
  of increased productivity. There has been
  debate about whether or not this new
  productivity growth actually exist.
                                                Drake
Base Interest Rates Revisited                   Drake University

                                                 Fin 284


Generally in the US, fixed income securities
are compared to the on - the – run treasury
with a similar maturity.
This represents a rate that is considered to as
close as risk free as possible.
Is the treasury actually risk free?
  No – there is still a possibility of default and it
  faced both price risk and reinvestment rate
  risk, but it is the closest to risk free.
      Yield Spreads and Risk                   Drake
                                               Drake University

             Premiums                           Fin 284


  The difference in yield between any two assets
  should represent differences in risk. The extra
  return earned on a riskier security is termed the
  risk premium.
  Generally the risk premium is quoted in basis
  points.
Yield Spread = Yield on Bond A – Yield on Bond B

     Where yield on bond B is being used as a
                    benchmark
                                              Drake
     Relative Yield Spreads                    Drake University

                                                Fin 284


Spreads are also measured relative to a base rate

relative
         yield on bond A - yield on bond B
 yield 
                  yield on bond b
spread

          yield yield on bond A
               
          ratio yield on bond B
                                        Drake
Factors impacting yield spreads             Drake University

                                             Fin 284



       1.   Type of issuer
       2.   Issuers creditworthiness
       3.   Maturity
       4.   Embedded options
       5.   Taxability
       6.   Liquidity
       7.   Other risks associated with
            previously discussed premiums
                                              Drake
         Type of Issuer                       Drake University

                                               Fin 284


Federal Government vs. Private vs. Muni
Intermarket Spread
  The spread in yield between bonds with the
  same maturity but offered in different sectors.
  Usually calculated using the Treasury
Intramarket Spread
  The spread between two bonds in the same
  sector.
  Often split by industry classification (banks vs.
  industrial) for example.
                                                                                                      Drake
    Corporate Yield Spreads 1994-2003                                                                  Drake University

                                                                                                           Fin 284
        10                                                                                                    6

        9
Yield




                                                                                                              5
        8

        7
                                                                                                              4
        6
                                   AAA
        5                          BBB                                                                        3
                                   Treas
        4
                                   AAA-Treas




                                                                                                                  Spread
                                   BBB-Treas                                                                  2
        3

        2
                                                                                                              1
        1

        0                                                                                                     0
        Jan-94   Nov-94 Sep-95   Jul-96    May-97 Mar-98 Jan-99   Nov-99 Sep-00   Jul-01   May-02 Mar-03

                                                       Date
                                            Drake
       Credit Worthiness                    Drake University

                                             Fin 284



Quality Spread – the difference in yield
between a treasury bond and another bond
that is identical except for issuer (also called
credit spread.
                                              Drake
              Options                         Drake University

                                               Fin 284



Call Option
  Benefits the issuer causing an increase in the
  spread

Put Option
  Benefits the investor lowering the spread
                                        Drake
           Taxability                   Drake University

                                         Fin 284



Having a tax break decreases the yield and
therefore the spread.

 equivalent     tax exempt yield
             
taxable yield 1 - marginal tax rate
                                         Drake
             Liquidity                   Drake University

                                          Fin 284



Greater liquidity lowers the yield and
therefore the spread
                                         Drake
            Maturity                     Drake University

                                          Fin 284



Bond yields will differ with the maturity of
bond.
Generally with all other constraints the same
the longer the term to maturity the higher the
yield. However, economic fluctuations may
impact that relationship.
The difference based upon maturity keeping
everything else the same is referred to the
term structure of interest rates. The
relationship is graphed in a “yield curve”
                                          Drake
     Treasury Yield Curve                 Drake University

                                           Fin 284



The most commonly investigated and used
term structure is the treasury yield curve.
Treasuries are used since they are considered
free of default, and therefore differ mainly in
maturity. Also the treasury is the benchmark
used to set base rates.
The treasury market is also very liquid so
there are no problems with liquidity
                                        Drake
Current Treasury Yield Curve             Drake University

                                          Fin 284



The most straightforward way to represent
the yield curve is by graphing the
combinations of yield and maturity
The problem with this measure is that it does
not account for differences in coupon rates
across bonds of similar maturities. Therefore
there are some alternative methods we need
to explore.
                                                   Drake
        Yield Curves Previous 6 Months              Drake University

                                                     Fin 284
        0.06


        0.05


        0.04
Yield




        0.03                                    7/31/2003
                                                8/29/2003
        0.02                                    9/30/2003
                                                10/31/2003
        0.01                                    11/28/2003
                                                12/31/2003
          0
           0.00   5.00        10.00     15.00      20.00

                         Maturity (Years)
                                                     Drake
Yield Curves Previous 5 quarters                      Drake University

                                                       Fin 284
        0.06




        0.05




        0.04
Yield




        0.03
                                                    12/31/2002
                                                    3/31/2003
        0.02
                                                    6/30/2003
                                                    9/30/2003
        0.01
                                                    12/31/2003

          0
           0.00   5.00        10.00         15.00       20.00

                         Maturity (Years)
                                                                                                   Drake
                            US Treas Interest Rates
                                                                                                   Drake University

                                                                                                    Fin 284
                              Jan 1990- Dec 2003
  0 .1


0 .0 9                                                                                                     1-mo
                                                                                                           3-mo
0 .0 8

                                                                                                           6-mo
0 .0 7
                                                                                                           1-yr
0 .0 6
                                                                                                           2-yr
0 .0 5
                                                                                                           3-yr
0 .0 4
                                                                                                           5-yr
0 .0 3
                                                                                                           7-yr
0 .0 2
                                                                                                           10-yr
0 .0 1                                                                                                     20-yr
   0                                                                                                       30-yr
 12 /8 /19 8 9   9 /3 /19 9 2    5/3 1/19 9 5   2 /2 4 /19 9 8   11/2 0 /2 0 0 0   8 /17/2 0 0 3
                                                                                        Drake
  US Treas Rates Jan 1990 Dec 2003                                                      Drake University

                                                                                         Fin 284
    0.1


  0.09

                                                   Downward sloping yield curve
  0.08



  0.07


  0.06                                                                                        3-mo
Yield




  0.05

                                                                                              1-yr
  0.04


  0.03
                                                                                              5-yr
  0.02

                                                                                              20-yr
   0.01


        0
   12/ 8/ 1989   9/ 3/ 1992   5/ 31/ 1995    2/ 24/ 1998   11/ 20/ 2000   8/ 17/ 2003
                                            Date
                                                                 Drake
                 Yield Curve 2000                                Drake University

                                                                  Fin 284
        0.07


   0.065


        0.06


   0.055
Yield




        0.05
                                                         12/31/1999
   0.045                                                 3/31/2000
                                                         6/30/2000
        0.04                                             9/29/2000
                                                         12/29/2000
   0.035
        0.00   5.00   10.00    15.00     20.00   25.00   30.00            35.00
                              Maturity (years)

				
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