Chapter 3: Structure of
Interest Rates
Objectives
■ describe how characteristics of debt
securities cause their yields to vary
■ demonstrate how to estimate the
appropriate yield for any particular debt
security
■ explain the theories behind the term
structure of interest rates (relationship
between the term to maturity and the yield
of securities)
Why Debt Security Yields Vary
The yields on debt securities are affected:
Credit (default) risk
Liquidity
Tax status
Term to maturity
Special contract provisions such as
embedded options
Factors Affecting Security Yields
⚫Risk-averse investors demand higher
yields for added riskiness
⚫Risk is associated with variability of
returns
⚫Increased riskiness generates lower
security prices or higher investor required
rates of return
Default Risk
1. Credit (Default) Risk
⚫ Credit risk: Risk that borrower may not made payments
at specified time
⚫ Default premium: Higher credit risk, the higher default
premium (in terms of higher interest rate
⚫ Benchmark—risk-free treasury securities for given
maturity
⚫ Default risk premium = risky security yield – treasury
security yield of same maturity
⚫ Default risk premium = market expected default loss
rate
⚫ Rating agencies set default risk ratings
Default Risk
⚫ Rating Agencies - Rating agencies charge the
issuers of debt securities a fee for assessing
default risk (Conflict of interest)
⚫ Accuracy of Credit Ratings - The ratings issued
by the agencies are useful indicators of default
risk but they are opinions, not guarantees.
⚫ Oversight of Credit Rating Agencies - The
Financial Reform Act of 2010 established an
Office of Credit Ratings within the Securities and
Exchange Commission in order to regulate credit
rating agencies. Rating agencies must establish
internal controls
Rating Classification by Rating Agencies
Liquidity Risk
⚫The Liquidity of a security affects the
yield/price of the security
⚫A liquid investment is easily converted to
cash at minimum transactions cost
⚫Investors pay more (lower yield) for liquid
investment
⚫Liquidity is associated with short-term, low
default risk, marketable securities
Tax Status
⚫Tax status of income or gain on security
impacts the security yield
⚫Investor concerned with after-tax return or
yield
⚫Investors require higher yields for higher
taxed securities
Tax Status
Yat = Ybt(1 – T)
Where:
Yat = after-tax yield
Ybt = before-tax yield
T = investor’s marginal tax rate
⚫Break-even tax rate
Te = 1 – Ytax-free/Ytax-bearing
Tax Status
⚫Example: a taxable security that offers a
before-tax yield of 14 percent. The
investor’s tax rate is 20 percent. Calculate
the after-tax yield.
Yat = 14%(1 – 0.2)
= 11.2%
⚫The fully taxable pre-tax equivalent
corporate bond for a 11.2% municipal
bond is:
Ybt = 11.2%/(1 – 0.2) = 14%
Special Provisions
⚫Call Feature: enables borrower to buy
back the bonds before maturity at a
specified price
Call features are exercised when interest rates
have declined
Investors demand higher yield on callable
bonds, especially when rates are expected to
fall in the future
Special Provisions
⚫Convertible bonds
Convertibility feature allows investors to convert
the bond into a specified number of common
stock shares
Investors will accept a lower yield for
convertible bonds because investor returns
include expected return on equity participation
Estimating the Appropriate Yield
⚫The appropriate yield to be offered on a
debt security is based on the risk-free rate
for the corresponding maturity plus
adjustments to capture various security
characteristics
Yn = Rf,n + DP + LP + TA + CALLP + COND
Estimating the Appropriate Yield
Yn = Rf,n + DP + LP + TA + CALLP + COND
Where:
Yn
Rf,n
= yield of an n-day security
= yield on an n-day Treasury
(risk-free) security
DP
= default premium (credit risk)
LP
= liquidity premium
TA
= adjustment for tax status
CALLP = call feature premium
COND = convertibility discount
Yield Differentials on Money Market
Securities
⚫The yield differential is the difference between
the yield offered on a security and the yield on
the risk-free rate.
⚫Treasury bills have the lowest yield because
of their low default risk and high liquidity
⚫Yields on commercial paper and negotiable
CDs are only slightly higher than T-bill rates to
compensate for lower liquidity and higher
default risk
⚫Market forces cause the yields on all
securities to move in the same direction
Yield Differentials on Capital Market
Securities
⚫Municipal bonds have the lowest beforetax yield because they are free of tax at
federal level but their after-tax yields are
typically higher than Treasury bonds
⚫Treasury bonds have the lowest yield
because of their low default risk and high
liquidity
Term to maturity
⚫Interest rates typically vary by maturity.
⚫The term structure of interest rates
defines the relationship between maturity
and yield.
The Yield Curve is the plot of current interest
yields versus time to maturity
Yield Curve
Yield
%
Time to Maturity
An upward-sloping yield curve indicates that
securities with longer maturities offer higher annual yields
Yield Curve Shapes
Normal
Level or Flat
Inverted
Theories Explaining the Shape of
Yield Curve
⚫Pure expectations theory
⚫Liquidity premium theory
⚫Segmented markets theory
Pure Expectations Theory
⚫Long-term rates are average of current shortterm and expected future short-term rates
⚫Yield curve slope reflects market
expectations of future interest rates
⚫An expected increase in rates leads to an
upward sloping yield curve
⚫An expected decrease in rates leads to a
downward sloping yield curve
⚫Investors select maturity based on
expectations
Pure Expectations Theory
⚫Algebraic Presentation
2 year: (1+ti2)2 = (1+ti1)(1+t+1F1)
n year: (1+tin)n = (1+ti1)(1+t+1F1)…(1+t+n-1F1)
tin: known annualized interest rate of n-year
security as of time t
ti1 r: known annualized interest rate of a onesuất hàng năm của chứng khoán một năm tại
year security as of time t Lãi
thời điểm t
t+iF1: one-year interest rate that is anticipated
as of time t+i
The Term Structure of Interest Rates
Đường cong lợi
suất dốc lên
UpwardSloping
Yield Curve
⚫ Expected higher
interest rate levels
⚫ Tight monetary policy
Chính sách tiền tệ thắt chặt
⚫ Expanding economy
DownwardSloping
Yield Curve
Đường cong lợi
suất dốc xuống
⚫ Expected lower
interest rate levels
⚫ Expansive monetary
policy Chính sách tiền tệ nới lỏng
⚫ Recession soon?
Liquidity Premium Theory
⚫Pure expectation theory cannot explain the
fact that yield curve is normally upwardsloping
⚫Investors prefer short-term, more liquid,
securities
⚫Long-term securities and associated risks are
desirable only with increased yields
⚫Explains upward-sloping yield curve
⚫When combined with the expectations theory,
yield curves could still be used to interpret
interest rate expectations
Liquidity Premium Theory
⚫Estimation of Forward Rates Based on
Liquidity Premium
(1+ti2)2 = (1+ti1)(1+t+1F1) + LP
Liquidity Premium Theory
Segmented Markets Theory
⚫Theory explaining segmented, broken yield
curves
⚫Investors choose securities with maturities
that satisfy their forecasted cash needs
⚫Explains why rates and prices vary
significantly between certain maturities
Limitations of the theory:
Some borrowers and savers have the
flexibility to choose among various maturities
Preferred Habitat Theory
Implications: Preferred Habitat Theory
Although investors and borrowers may normally
concentrate on a particular maturity market,
certain events may cause them to wander from
their “natural” or preferred market, for example
higher interest rates.
Research on the Term Structure
Theories
⚫ Interest rate expectations have a strong
influence on the term structure of interest rates.
⚫ However, the forward rate derived from a yield
curve does not accurately predict future interest
rates, and this suggests that other factors may
be relevant.
⚫ General Research Implications - Although the
results differ, there is evidence that expectations,
liquidity premium, and segmented markets
theories all have some validity.
Integrating the Theories of the Term
Structure
⚫If we assume the following conditions:
Investors and borrowers currently expect interest
rates to rise.
Most borrowers need long-term funds, while most
investors have only short-term funds to invest.
Investors prefer more liquidity to less.
⚫Then all three conditions place upward
pressure on long-term yields relative to short
term yields leading to upward sloping yield
curve.
Integrating the Theories of the Term
Structure
Use of Term Structure
⚫Forecasting Interest Rates
 The shape of the yield curve can be used to
assess the general expectations of investors
and borrowers about future interest rates.
 The curve’s shape should provide a
reasonable indication (especially once the
liquidity premium effect is accounted for) of
the market’s expectations about future
interest rates.
⚫Forecasting Recessions - Some analysts
believe that flat or inverted yield curves
indicate a recession in the near future.
Use of Term Structure
⚫Making Investment Decisions - If the yield
curve is upward sloping, some investors may
attempt to benefit from the higher yields on
longer-term securities even though they have
funds to invest for only a short period of time.
⚫Making Decisions about Financing - Firms
can estimate the rates to be paid on bonds
with different maturities. This may enable
them to determine the maturity of the bonds
they issue.
Potential Impact of Treasury Shift from
Long-Term to Short-Term Financing
Yield Curves at Various Points in Time
Yield Curves among Different
Countries (as of May 2011)