THE STRUCTURE OF

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CHAPTER 6

• THE STRUCTURE OF
• INTEREST RATES

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Interest Rate Changes Differences Between
Interest Rates Can Be Explained by Several
Variables

• Term to Maturity.
• Default Risk.
• Tax Treatment.
• Marketability.
• Call or Put Features.
• Convertibility.

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Need to Understand Yields

• Individual and institutional investors must
  understand why quoted yields vary so they can
  determine whether the extra yield is worth the
  risk.
• Financial managers of corporations or government
  agencies in need of funds must understand why
  quoted yields vary, so they can estimate the
  yield they would have to offer in order to sell
  new debt securities.

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Selected Rates of Interest,February 9, 2005
(Wall Street Journal)
Financial Security Interest Rate () Dealer
Commercial Paper, 3 months 2.70 GE Capital
Commercial Paper, 90 to 119 days 2.68 Bankers
Acceptances, 90 days 2.70 U.S. Government
Securities 13 weeks Treasury bills 2.480 26
weeks Treasury bills 2.710 10 year Treasury
notes 4.03
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Selected Rates of Interest,February 9, 2005
(Wall Street Journal)
Financial Security Interest Rate() AA
Municipals (General Obligations) 7-12
year 3.35 AA Municipals (General Obligations)
12-22 year 3.65 High Quality Corporate Bonds
1-10 year 4.10 Medium Quality Corporate Bonds
1-10 year 4.46 High Quality Corporate Bonds 10
years 5.14 Medium Quality Corporate Bonds 10
years 5.49 High Yield Corporate Bonds
6.88
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Yield Curve

• The Term to Maturity of a financial claim is the
  length of time until the principal amount becomes
  payable.
• The relationship between yield and Term to
  Maturity on securities that differ only in length
  of time to maturity is called the Term Structure
  of Interest Rates. Shown by the Yield Curve.
• The Yield Curve is the graph of the relationship
  between interest rates on particular securities
  and their yield to maturity. Same default risk.

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Term (Maturity) Structure

• May Be Studied Visually by Plotting a Yield Curve
  at a Point in Time
• The yield curve may be ascending, flat, or
  descending.
• Several theories explain the shape of the yield
  curve.

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Yield Curves in the 2000s
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Yield Curve (February 10, 2005)
Source Bloomberg Web Site http//www.Bloomberg.c
om/markets/C13.html
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The Expectations Theory of the Term Structure

• The slope of the yield curve reflects investors
  expectations about future interest rates.
• Ascending future interest rates are expected to
  increase.
• Descending future interest rates are expected to
  decrease.
• Long-term interest rates represent the geometric
  average of current and expected future (implied,
  forward) interest rates.

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The Expectations Theory of Term Structure
(concluded)

• Investors are assumed to trade in a very
  efficient market with excellent information and
  minimal trading costs.
• Other theories discussed later presume less
  efficient markets.

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Expectations Theory Notations
R
The actual market rate of
interest on a one year security today
(time t)
t
R
The current rate of interest for a 10 year
security
t
f
1
The one year interest rate one year in the
future
t 1
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Term Structure Formula from Expectation Theory
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An Implied One Year Forward Rate From the Term
Structure Formula
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Finding a One-Year Implied Forward Rate

• Using term structure of interest rates from
  January 29, 1999, find the one-year implied
  forward rate for year three.
• 1-year Treasury bill 4.51
• 2-year Treasury note 4.58
• 3-year Treasury note 4.57

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Expectations Theory Calculations
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Liquidity Premium Theory

• Long-term securities have greater risk and
  investors require greater premiums to give up
  liquidity.
• Long-term securities have greater price
  variability.
• Long-term securities have less marketability.
• The liquidity premium explains an upward sloping
  yield curve.
• Investors are not indifferent between purchasing
  long-term vs. short term securities

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Liquidity Premium Theory (Concluded)

• Todays long-term rates reflect the geometric
  average of intervening short-term rates plus a
  premium that investors demand for holding
  long-term securities instead of a series of
  short-term risky investments.
• The liquidity premium increases as maturity
  increases, because the longer the maturity of a
  security, the greater its price risk.
• Thus, an investor would not be indifferent
  between a 5-year bond and a series of five 1-year
  bonds.

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Market Segmentation Theory

• Maturity preferences by investors may affect
  security prices (yields), explaining variations
  in yields by time
• Market participants have strong preferences for
  securities of particular maturity and buy and
  sell securities consistent with their maturity
  preferences.
• If market participants do not trade outside their
  maturity preferences, then discontinuities are
  possible in the yield curve.

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Market Segmentation Theory (Concluded)

• For instance, commercial banks may prefer
  short-term investments while pension funds and
  life insurance companies make generally long-term
  investments that coincide with their long-term
  liabilities.

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Preferred Habitat Theory

• The Preferred Habitat Theory is an extension of
  the Market Segmentation Theory.
• The Preferred Habitat Theory allows market
  participants to trade outside of their preferred
  maturity if adequately compensated for the
  additional risk.
• The Preferred Habitat Theory allows for humps or
  twists in the yield curve, but limits the
  discontinuities possible under Segmentation
  Theory.

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Which Theory is Right?

• Day-to-day changes in the term structure are most
  consistent with the Preferred Habitat Theory.
• However, in the long-run, expectations of future
  interest rates and liquidity premiums are
  important components of the position and shape of
  the yield curve.

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Yield Curves and the Business Cycle

• Interest rates are directly related to the level
  of economic activity.
• An ascending yield curve notes the market
  expectations of economic expansion and/or
  inflation.
• A descending yield curve forecasts lower rates
  possibly related to slower economic growth or
  lower inflation rates.
• Security markets respond to updated new
  information and expectations and reflect their
  reactions in security prices and yields.

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Interest-rate and Yield-curve Patterns Over the
Business Cycle
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Default Risk Is the Probability of the DSU Not
Honoring the Security Contract

• Losses may range from interest a few days late
  to a complete loss of principal.
• Risk averse investors want adequate compensation
  for expected default losses.
• Measured as the difference paid on a risky
  security and the rate paid on a default-free
  security, all other factors held constant.

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Default Risk, cont.

• Investors charge a default risk premium (above
  riskless or less risky securities) for added risk
  assumed
• DRP i - irf
• The default risk premium (DRP) is the difference
  between the promised or nominal rate and the
  yield on a comparable (same term) riskless
  security (Treasury security).
• Investors are satisfied if the default risk
  premium is equal to the expected default loss.

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Risk Premiums (2/02)Exhibit 6.5
Notice that as bond rating quality declines, the
default risk premium increases.
SECURITY YIELD EQUIVALENT RISK-FREE
RATEa RISK PREMIUM
SECURITY
(PERCENT) (PERCENT) (PERCENT)
Corporate bonds Aaa 6.51 5.61
0.90 Corporate bonds Aa 6.95 5.61
1.34 Corporate bonds A 7.37
5.61 1.76 Corporate bonds Baa 7.89
5.61 2.28
aTwenty-year Treasury bond yield. Source
Federal Reserve Statistical Release H.15 and Dow
Jones Market Data
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Default Risk, Cont.

• Default Risk Premiums Increase (Widen) in Periods
  of Recession and Decrease in Economic Expansion
• In good times, risky security prices are bid up
  yields move nearer that of riskless securities.
• With increased economic pessimism, investors sell
  risky securities and buy quality widening the
  DRP.
• Flight to Quality during periods of recession

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Default Risk, cont.

• Credit Rating Agencies Measure and Grade Relative
  Default Risk Security Issuers
• Cash flow, level of fixed contractual cash
  payments, profitability, and variability of
  earnings are indicators of default riskiness.
• As conditions change, rating agencies alter
  rating of businesses and governmental debtors.

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Corporate Bond-Rating Systems
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Tax Effects on Yields

• The Taxation of Security Gains and Income Affects
  the Yield Differences Among Securities
• The after-tax return, iat, is found by
  multiplying the pre-tax return by one minus the
  marginal tax rate.
  iat ibt(1-t)
• Municipal bond interest income is currently tax
  exempt. (See footnote 4, on page 147.)
• Capital gains for individuals are taxed
  differently than ordinary income such as
  corporate bond interest.
• Maximum rate of 15 for gains on securities held
  by individuals for more than one year (effective
  May 5, 2003).

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Should you buy a municipal or a corporate bond?
CORPORATE AFTER-TAX INVESTORS
MARGINAL TAX RATE MUNICIPAL YIELD
YIELD
0 7 10(1 - 0.00) 10.0 10 7 10(1 -
0.10) 9.0 20 7 10(1 - 0.20)
8.0 30 7 10(1 - 0.30) 7.0 40 7 10(1 -
0.40) 6.0 50 7 10(1 - 0.50) 5.0
Tax Equivalent Yield (TEY) is a useful concept,
especially for wealthy individuals and
fully-taxed corporations.
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Differences in Marketability Affect Interest
Yields

• Marketability -- The costs and rapidity with
  which investors can resell a security.
• Cost of trade.
• Physical transfer cost.
• Search costs.
• Information costs.
• Liquidity.
• Securities with good marketability have higher
  prices (in demand) and lower yields.

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Contract Options and Yields

• Varied Option Provisions May Explain Yield
  Differences Between Securities
• An option is a contract provision which gives the
  holder the right, but not the obligation, to
  buy,sell, redeem, or convert an asset at some
  specified price within a defined future time
  period.

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Contract Options and Yields

• A Call Option Permits the Issuer (Borrower) to
  Call (Refund) the Obligation Before Maturity
• Borrowers will call if interest rates decline.
• Investors in callable securities bear the risk of
  losing their high-yielding security.
• With increased call risk, investors demand a call
  interest premium (CIP).
• CIP ic inc 0
• A callable bond, ic, will be priced to yield a
  higher return (by the CIP) than a noncallable,
  inc, bond.

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Call Option on Bonds

• Most corporate and municipal bonds and some U.S.
  Government bonds contain a call option in their
  contracts.
• Similar to a Mortgage
• Many corporate bonds have a Deferred Call
  provision rather than an Immediate Call
  provision.
• With corporate bonds, the premium initially set
  is usually one years interest above the par
  value. A municipality may be able to call its
  bonds without any premiums being paid.

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Contract Options and Yields

• A put option permits the investor (lender) to
  terminate the contract at a designated price
  before maturity
• Investors are likely to put their security or
  loan back to the borrower during periods of
  increasing interest rates. The difference in
  interest rates between putable and nonputable
  contracts is called the put interest discount
  (PID).
• PID ip inp
• The yield on a putable bond, ip, will be lower
  than the yield on the nonputable bond, inp, by
  the PID.

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Contract Options and Yields

• A Conversion Option Permits the Investor to
  Convert a Security Contract Into Another Security
• Convertible bonds generally have lower yields,
  icon, than nonconvertibles, incon.
• The conversion yield discount (CYD) is the
  difference between the yields on convertibles
  relative to nonconvertibles.
• CYD icon incon lower yield on convertible bonds because they
  have an opportunity for increased rates of return
  through conversion.

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Conclusion

• Term Structure of Interest Rates
• Expectations
• Liquidity Premium
• Market Segmentation
• Preferred Habitat
• Use of Yield Curve
• Default Risk
• Tax Equivalent Yield
• Options
• Put
• Call
• Convertible