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Historical Savings Account Interest Rates

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									Interest Rates


    Fin 200




                 Drake Fin 200
                 DRAKE UNIVERSITY
                                        Drake
      The Cost of Money
                                        DRAKE UNIVERSITY


                                        Fin 200


The interest rate is the price paid to borrow
debt capital (the required return of the
bondholder). Likewise equity holders expect
a return (the required return of the
shareholder). What impacts the level of
interest rates?
Production Opportunities
Time Preference for Consumption
Risk
Inflation
                                        Drake
Review of Key Factors Impacting         DRAKE UNIVERSITY



     Interest Rate Volatility           Fin 200


  Federal Reserve and Monetary Policy
    Discount Window

    Reserve Requirements

    Open Market Operations
     Review of Key Factors                   Drake
           Impacting
                                             DRAKE UNIVERSITY


                                             Fin 200
     Interest Rate Volatility
Fisher model of the Savings Market
Two main participants: Households and Business
Households supply excess funds to Businesses who
are short of funds.
Loanable funds theory expands this to allow
individuals, business and governments to both
borrow and save.
The Saving or supply of funds is upward sloping
(saving increases as interest rates increase)
The investment or demand for funds is downward
sloping (demand for funds decease as interest rates
increase)
                                               Drake
    Saving and Investment                     DRAKE UNIVERSITY



          Decisions                            Fin 200

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 Decisions
  Short term temporary excess cash.
  Foreign Investment
                                     Drake
     Borrowing Decisions
                                     DRAKE UNIVERSITY


                                     Fin 200


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


                                    Fin 200


Interest
  Rate                       S




                             D


                                 Dollars
                                             Drake
     Equilibrium in the Market
                                             DRAKE UNIVERSITY


                                             Fin 200
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
         Multiple Markets
                                                DRAKE UNIVERSITY


                                                Fin 200


The market for investment capital is not one single
demand and supply relationship. It can be thought
of as being separated by the amount of risk in the
borrowing (the chance that the firm will repay the
debt) and the length of time for the debt (bond).
The different markets are interrelated.
If the risk free cost of borrowing increases, the rate
paid on more risky borrowing also increases.
Generally the higher the risk, the higher the return.
                                       Drake
    Differences in Return
                                      DRAKE UNIVERSITY


                                       Fin 200


The differences in return paid between two
different types of borrowing (low risk
corporate vs. high risk corporate with the
same maturity for example) is the risk
premium or yield spread.
                                         Drake
Yield Spreads and Risk Premiums
                                         DRAKE UNIVERSITY


                                         Fin 200


Yield Spreads and Risk Premiums
  The difference in required return between two
  assets, the difference in required return
  represents the difference in risk.
  Often bonds that are the same except for the
  possibility of default are compared, implying
  that the yield spread is a measure of the
  default risk
                                                       Drake
      Long Term Average Yearly Yields                  DRAKE UNIVERSITY



           Over Time (Moody’s)                         Fin 200

 18

 16

 14

 12
(%)




 10

      8

      6

      4
      1980    1985         1990    1995         2000
                     Aaa      Aa   A      Baa
   Bond Ratings and Average         Drake
Yield Spreads vs. US Treasuries
                                   DRAKE UNIVERSITY


                                    Fin 200
       (long term bonds)

    Rating   Spread   Rating   Spread
    AAA      .20%     B+       2.5%
    AA       .50%     B        3.25%
    A+       .80%     B-       4.25%
    A        1.0%     CCC      5.00%
    A-       1.25%    CC       6.00%
    BBB      1.5%     C        7.5%
    BB       2.0%     D        10.0%
                                                 Drake
            Yield Spread Monthly Data            DRAKE UNIVERSITY



         Jan 1919 – June 2004 (Moodys)           Fin 200

    20
    18
    16
    14
    12
%




    10
     8
     6
     4
     2
     0
    9/8/1913     1/24/1941    6/11/1968   10/28/1995
                Aaa   Baa    Date
                                                                                         Drake
             Yield Spreads 1994 - 2003
                                                                                        DRAKE UNIVERSITY


                                                                                         Fin 200
        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
       Impact of Maturity
                                           DRAKE UNIVERSITY


                                           Fin 200


It is often the case that the return on similar
assets that differ only in their maturity differ
also have a interconnected relationship.
Usually the long term asset has a higher
return than the short term asset. However
this is not always the case.
                                         Drake
General Model of Interest Rates
                                        DRAKE UNIVERSITY


                                         Fin 200


 The relationship between assets of different
 riskiness and maturity can be broken down
 into a very general idea.
 The return paid on an asset that matures I t
 years, rt should be thought of being a
 combination of its riskiness and maturity
 compared to a risk free asset.
                                         Drake
     Quoted Interest Rate
                                         DRAKE UNIVERSITY


                                         Fin 200


The quoted interest rate is then equal to a
base rate, the real risk free rate of interest,
plus premiums that account for differences in
maturity and riskiness.
                                            Drake
          The quoted rate
                                            DRAKE UNIVERSITY


                                            Fin 200


         r = r*+ IP + DRP + LP + MRP
Where:
 r* = The real risk free rate of interest
 IP = The inflation premium
 DRP =The default risk premium
 LP = The liquidity premium
 MRP = the Market Risk Premium
                                         Drake
The real risk free rate of interest
                                         DRAKE UNIVERSITY


                                         Fin 200


 r* is the rate that would be paid on an asset
 with zero default risk, and an expected
 interest rate of zero.
 It is the actual increase in purchasing power
 you should expect to receive. It depends on
 the productivity of the borrowers assets and
 the marginal time preference mentioned
 earlier.
                                           Drake
   Nominal Risk Free Rate and             DRAKE UNIVERSITY



     the Inflation Premium                 Fin 200


The nominal, or risk free rate of interest is
then the real rate plus a premium (IP) added
to account for expected inflation in the
future.
rRF = r*+ IP
Ideally the premium should be based upon
expected inflation over the life of the security.
Usually these are based on historical rates of
inflation and the current economy.
                                        Drake
     The other premiums
                                        DRAKE UNIVERSITY


                                        Fin 200


DFR = The extra return associated with a
higher chance of default (BBB corporate
bonds vs. treasury bonds for example)
LP = Liquidity Premium The extra return
associated with the market for an asset being
less liquid making it harder to sell the asset
for cash
                                         Drake
     The other premiums
                                        DRAKE UNIVERSITY


                                         Fin 200


MRP = Market Risk Premium A longer term
bond has higher interest rate risk (TVM says
the impact of a change in interest rates will
be larger on a cash flow received further in
the future). Therefore, the longer the
maturity of the bond the higher the quoted
interest rate.
                                        Drake
          Yield Curves
                                        DRAKE UNIVERSITY


                                        Fin 200


Graph of maturity (horizontal axis) vs. yield
(vertical axis) for a group of bonds with
similar risk.
Often represented using US gov’t bonds, it is
usually upward sloping, implying that the
longer the commitment the higher the
required return for the investor (the higher
the opportunity cost of capital).
                                                        Drake
                Recent Yield Curve
                                                        DRAKE UNIVERSITY


                                                        Fin 200
    0.055

    0.053

    0.051

    0.049

    0.047
Yield




    0.045

    0.043

    0.041
                12/30/2005   1/31/2006     2/28/2006   3/31/2006
    0.039
                4/28/2006    5/31/2006     6/30/2006
    0.037
                                   Maturity (Years)
    0.035
         0.00        5.00        10.00         15.00         20.00
                                                                                       Drake
  Long Term vs. Short Term Interest                                                    DRAKE UNIVERSITY



                rates                                                                  Fin 200

0.09
                                                             Downward Sloping
0.08                                                           Yield Curves
0.07


0.06


0.05


0.04
       Yield




0.03


0.02


0.01
               3-mo          6-mo        10-yr     20-yr     Date
  0
 12/8/1989        9/3/1992          5/31/1995    2/24/1998    11/20/2000   8/17/2003     5/13/2006
                                              Drake
    Why does the Yield Curve                  DRAKE UNIVERSITY



     usually slope upwards?                   Fin 200


Three things are observed empirically concerning the
    yield curve:
1. Rates across different maturities move together
2. More likely to slope upwards when short term rates
    are historically low, sometimes slope downward
    when short term rates are historically high
3. The yield curve usually slope upward
                                  Drake
Three Explanations of the Yield   DRAKE UNIVERSITY



            Curve                 Fin 200


The Expectations Hypothesis
Segmented Markets Theory
Preferred Habitat Theory
                                                Drake
   Expectations Hypothesis
                                               DRAKE UNIVERSITY


                                                Fin 200


Long term rates are a representation of the short
term interest rates investors expect to receive in the
future
Assumes that bonds of different maturities are
perfect substitutes
In other words, the expected return from holding a
one year bond today and a one year bond next year
is the same as buying a two year bond today.
                                          Drake
     Expectations Hypothesis
                                          DRAKE UNIVERSITY


                                          Fin 200


Let
Rt = today’s time t interest rate on a one
      period bond
Ret+1 = expected interest rate on a one period
      bond in the next period
R2t = today’s (time t) yearly interest rate on
      the two period bond
                                          Drake
  The One Period Return Twice
                                          DRAKE UNIVERSITY


                                          Fin 200


If the strategy of buying an one period bond in
   two consecutive years is followed the return
   is:
       (1+Rit)(1+Ret+1) – 1 which reduces to
                       Rt+Ret+1
              (Rt)(Ret+1) can be dropped
                                           Drake
       The 2 Period Return
                                           DRAKE UNIVERSITY


                                           Fin 200


If the strategy of investing in the two period
   bond is followed the return is:
       (1+R2t)(1+R2t) - 1 = 1+2R2t+(R2t)2 - 1
                   This simplifies to
                         2R2t
      (R2t)2 is small enough it can be dropped.
                                          Drake
Set the two equal to each other
                                         DRAKE UNIVERSITY


                                          Fin 200


               2R2t = Rt+Ret+1
              R2t = (Rt+Ret+1)/2

In other words, the two period interest rate is
    the average of the two one period rates
                                              Drake
   Expectations Hypothesis
                                             DRAKE UNIVERSITY


                                              Fin 200

When the yield curve is upward sloping it is expected
that short term rates will be increasing (the average
future short term rate is above the current short
term rate).
Likewise when the average yield curve is downward
sloping the average of the future short term rates is
below the current rate. (Fact 2)
As short term rates increase the long term rate will
also increase. (Fact 1)
This however does not explain Fact 3
                                          Drake
 Segmented Markets Theory
                                         DRAKE UNIVERSITY


                                          Fin 200


Interest Rates for each maturity are determined
by the supply and demand for bonds at each
maturity.
Different maturity bonds are not perfect
substitutes for each other.
Longer term bonds have a higher interest rate
risk (and associated Market Risk Premium),
therefore they should have a higher return
Implies the yield curve usually slopes up.
                                         Drake
  Preferred Habitat Theory
                                         DRAKE UNIVERSITY


                                         Fin 200


Combines the other two – The interest rate on
the long term bond will equal an average of the
short term rates, plus a liquidity premium and
market risk premium, that responds to the supply
and demand for that bond.
In other words the bonds are substitutes, but
savers might have a preference for one maturity
over another (they are not perfect substitutes)
                                               Drake
   Preferred Habitat Theory
                                               DRAKE UNIVERSITY


                                               Fin 200


The long term rate should include a premium
associated with them. To attract savers who prefer
a shorter maturity, the long term bond will need to
pay an additional amount (or market risk and
liquidity premiums).
Thus according to the theory a rise in short term
rates still causes a rise in the average of the future
short term rates. Therefore the long and short rates
move together (Fact 1).
                                               Drake
   Preferred Habitat Theory
                                               DRAKE UNIVERSITY


                                               Fin 200


The explanation of Fact 2 from the expectations
hypothesis still works. In the case of a downward
sloping yield curve, the term premium (interest rate
risk) must not be large enough to compensate for
the currently high short term rates (Current high
inflation with an expectation of a decrease in
inflation). Since the demand for the short term
bonds will increase, the yield on them should fall in
the future.
                                          Drake
  Preferred Habitat Theory
                                         DRAKE UNIVERSITY


                                          Fin 200


Fact three is explained since it will be unusual
for the term premium to be so small that the
yield curve slopes down.
                                              Drake
Predicting Future Short Term                  DRAKE UNIVERSITY



 Interest Rates Movements                     Fin 200


Steep Yield Curves
  Short term interest rates are expected to increase
Flat Yield Curves
  Short term interest rates are expected to decrease
  slightly
Downward sloping Yield Curves
  Short term interest rates are expected to
  decrease.
                                                Drake
 Changes in the Yield Curve
                                               DRAKE UNIVERSITY


                                                Fin 200

These ideas can also be used to analyze changes in
the shape of the yield curve. As the yield curve
starts to become more steep it indicates that the
average future short term rate is starting to increase.
The current short term rate is to low.
A shift in the Yield curve that remains approximately
the same slope is indicating that future expectations
about both short term and long term rates are
moving together (the real rate of interest is
increasing and not just short term rates are
changing)

								
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