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Market Interest Rates


Nominal rates include inflation ... It is difficult to measure expected inflation rates. Expected and realized rates of inflation usually differ ... – PowerPoint PPT presentation

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Title: Market Interest Rates

Market Interest Rates
  • Chapter 20

  • When people discuss market interest rates
  • Usually mean a bonds yield to maturity (YTM)
  • Market-determined rate that fluctuates

Bonds YTM are positively correlated3-month and
10-year T-bonds have a ? 0.90.
T-bond yield moves in tandem with inflation.
  • Market interest rates fluctuate due to
  • Undiversifiable factors
  • Impact all bonds
  • Include factors such as inflation, sovereign
    risk, and supply/demand for credit
  • Diversifiable factors
  • Unique to the bond issuer
  • Include changes in issuers default risk, and
    embedded options

Fishers Theory About Interest Rate Levels
  • Fisher (1930) pointed out that market interest
    rates move in tandem with inflation
  • In a world of certainty
  • Nominal rates include inflation
  • Example If inflation is expected to be 10 a
    year and a lender desires a 3 rate of return
    after inflation, they should charge 13
  • If they lend 100 they will be repaid 113 after
    one year
  • This will offer the lender a real return of 2.72
    or 113/110 1
  • So, to maintain their purchasing power, lenders
    need to raise their nominal rates to adjust for
  • Fishers theory included a positive, constant
    real rate

Is Fishers Theory Valid?
  • Evidence supports the Fisher effect
  • Positive correlation between inflation and
    Treasury rates
  • Can test statistically by the following regression

Represents the impact inflation has on the market
interest rateif Fishers theory is correct, ?
Represents the real rate.
Research suggest the results are sufficiently
close to Fishers theoretical values to support
the Fisher effect.
Realized Real Returns
  • Fishers effect uses the expected rate of
    inflation rather than the realized rate of
  • It is difficult to measure expected inflation
  • Expected and realized rates of inflation usually
  • Because of these problems researchers use this
    equation to test Fishers theory

Realized Real Returns
  • Differs from Fishers original equation
  • Uses the actual inflation rate rather than an
    expected inflation rate
  • Time subscripts are added to all three variables
  • However, the following equation is a bit more
  • Both equations yield almost identical realized
    real rates

Conclusions About Prices and Interest Rates
  • Conclusions of financial economists
  • Level of nominal market interest rate tends to
    vary directly with large movements in the general
    price level
  • However, during a short-run period the level of
    market interest rates may not respond to
    movements in the general price level
  • Possible to find periods of years when Fishers
    equation explains movements in nominal market
    interest rates very well
  • Also possible to find periods when Fishers
    equation doesnt explain movements very well

Conclusions About Prices and Interest Rates
  • The constant real rate Fisher assumed is an
  • Fishers theory is a valuable tool
  • Other explanatory factors also impact market
    interest rates
  • Most economists agree that inflation is usually
    the most important explanatory factor

Other Factors Influence Market Interest Rates
  • The business cycle
  • Represents fluctuations in the economy
  • Recessions are periods of slowing business
  • GDP falls during a recession (as does the rate of
    growth in real consumption expenditures)

Shaded bands represent recessions.
Other Factors Influence Market Interest Rates
  • Stock market is a leading economic indicator
  • Usually collapses several months prior to a
  • However, sometimes the stock market collapses and
    no recession occurs
  • Federal government borrowing and crowding out
  • When governments and businesses compete for a
    limited supply of loanable funds
  • Bids up interest rates even though inflation may
    be declining

Other Factors Influence Market Interest Rates
  • National monetary policy
  • A nations central bank controls the countrys
    monetary policy, interest rates and inflation
  • The U.S.s central bank, the Federal Reserve,
    sets economic targets
  • Has considerable influence on the movement of
    market interest rates

Measuring Yield Spreads
  • Measures the difference between two market
    interest rates
  • Quality spread (AKA credit spread, default risk
  • The yield spread between a U.S. T-bond and
    another (more risky) bond of the same time to
  • Measures the additional yield investors require
    to compensate them for higher risk

Measuring Yield Spreads
  • Horizon spread (AKA maturity risk premiums)
  • The yield spread between two bonds of equal
    quality with different terms to maturity
  • Rarely negative
  • Investors normally require a positive premium to
    encourage them to make long-term commitments

Yield Spreads Open and Close With The Business
  • Quality spreads vary predictably over the
    business cycle
  • All risk premiums tend to be larger at economic
    troughs than at peaks
  • Unemployment, fear of job-loss and risk aversion
    are higher during recessions
  • Corporate bond issuers experience decrease in
    sales and profits during recessions
  • Causes investors to desire higher risk premiums
  • Horizon spreads expand at the trough of business
  • Reflects expectation that inflation and interest
    rates will rise during business expansion ahead

Term Structure of Interest Rates (Yield Curve)
  • Refers to the relationship between maturity and
    YTM for bonds by a single issuer
  • Usually U.S. Treasury bonds

Yield curves shift dailyusually extremely small
Term Structure of Interest Rates (Yield Curve)
  • Fishers equation can be expanded
  • Different yield curves exist at each level of
    default risk

Theories About Yield Curves
  • Theories about what determines the shape of the
    yield curve
  • Horizon premium theory (AKA liquidity premium
  • Investors pay a price premium for short
  • To avoid higher interest rate risk inherent in
    investing in bonds with longer maturities
  • Segmentation theory
  • Yield curve is composed of a series of
    independent maturity segments and yields are
    determined by supply and demand conditions
    peculiar to a segment
  • For example pension funds tend to buy long-term
  • Expectations theory
  • Long-term yields are the average of expected
    short-term yields

Horizon Premium Theory
  • Long-term interest rates fluctuate less than
    short-term interest rates
  • Long-term bonds prices fluctuate more than
    short-term bond prices
  • Provides the basis for the horizon premium
  • On average, the yield curve exhibits an upward

Horizon Premium Theory
  • Why might the horizon premium theory not hold?
  • Short-term rates fluctuate continuously
  • Investors face reinvestment risk as a series of
    fluctuating future interest rates
  • There are increased transaction costs required in
    frequently changing investments in the short-term
  • Investors with a longer time horizon can hedge
    their risk
  • Investors could expect lower interest rates in
    the future

Market Segmentation Theory
  • Lenders and borrowers confine themselves to
    certain segments of the bond market because
  • Legal lists limit the types of investments
    certain institutional investors are allowed to
  • Investors may specialize in a certain segment due
    to the high cost of obtaining information
  • Investors may need to hedge liabilities with a
    fixed maturity
  • Human beings may have preferences not dependent
    upon theories or planning

Expectations Theory
  • Interest rates on a long-term bond equals the
    average of a series of expected short-term future
    interest rates
  • For example If the interest rate on a one-year
    bond is 10 and rates on a one-year bond next
    year are expected to be 12, then the rate on a
    current two-year bond should be about 11 (10
    12) ? 2 years
  • To properly discuss the expectations theory we
    need to understand
  • Forward rate tFtn
  • Yield expected to exist in the future (with the
    maturity date represented as tn)
  • Spot rate 0St
  • Market rates for bonds that currently exist at
    time 0 and are expected to mature at time t

Expectations Theory
  • The expectations theory exists when the following
    equations are all true simultaneously
  • (1 0S1)1 (1 0F1)
  • (1 0S2)2 (1 0F1)(1 1F2)
  • (1 0S3)3 (1 0F1)(1 1F2) (1 2F3)
  • (1 0Sn)n (1 0F1)(1 1F2) (1 2F3)…(1
  • Spot rates exist and can be observed
  • Forward rates are implicit rates on bonds that do
    not yet exist
  • It is possible to determine implicit forward
    rates using spot rates

Expectations Theory
  • For example
  • It is currently 2010
  • 2010S2013 is known
  • 2010S2014 is known
  • We may wish to know what interest rates will be
    on a one-year loan 3 years from now, or 2013F2014
  • Solve by

Arbitrage Maintains the Expectations Model
  • Perhaps something causes the following inequality
    to occur
  • (1 0ST)T gt (1 0F1)(1 1F2)…(1 T-1FT)
  • Profit-seekers would then buy the existing
    long-term bond yielding 0ST
  • Drives up its price leading to a decrease in
    yield or 0ST until the inequality no longer
  • If expectations theory is true, the yield curve
    should slope up preceding economic expansions and
    down preceding recessions
  • Market interest rates support this

The Bottom Line
  • YTM are market-determined interest rates that
    fluctuate continuously
  • Empirical data supports each of the three
    theories concerning the term structure of
    interest rates
  • However, a combination of the three theories
    probably best explains what actually determines
    the term structure of interest rates

The Bottom Line
Horizon premiums are added to the unobservable
expectations yield curve.
Feds interaction with the market provides supply
and demand forces that work on the short-term end
of the yield curve.
The Bottom Line
  • The Fisher effect explains how inflation has a
    positive impact on nominal interest rates
  • But nominal interest rates are also impacted by
  • Changes in the supply/demand for credit
  • Changes in risk-premiums (yield curves)

Appendix Alternative Formulations of the Yield
  • A bonds present value may be represented in
    terms of its YTM, spot rates or forward rates
  • Spot rate is the geometric mean of forward rates
  • (1 0St)t (1 0F1)(1 1F2)…(1 t-1Ft)
  • A bonds YTM is the weighted average of forward
  • Weights are determined based on size of cash flows

Appendix Alternative Formulations of the Yield
  • For example A 1,000 par bond has 3 years
    remaining until maturity with an annual coupon of
  • CF1 100
  • CF2 100
  • CF3 1,100
  • Assume the forward rate structure is
  • 0F1 0.10
  • 1F2 0.11
  • 2F3 0.15
  • The current one-year spot rate is the same as the
    0F1 rate, or 10
  • The second periods spot rate is
  • (1.10)(1.11) 1½ 0S2 10.4989
  • The third periods spot rate is
  • (1.10)(1.11)(1.15) 11/3 0S3 11.9793

Appendix Alternative Formulations of the Yield
  • We can calculate the present value of the bond
    using the spot or forward rates
  • Using this price we can derive the bonds YTM

Appendix The Term Structure of Interest Rates
  • Term structure of interest rates should be
    formulated in terms of spot or forward rates
  • YTM changes if the size of the coupon changes

Most commonly graphed term structurebut least
informative and ambiguousdepends on the CF
Forward and spot rate yield curves are
independent of the CFs.