How do risk and term structure
affect interest rates?
Yesterday, we examined interest rates, but
made a big assumption – there is only one
economy-wide interest rate. Of course,
that isn’t really the case.
Today, we will examine the different rates
that we observe for financial products.
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How do risk and term structure
affect interest rates?
• Understanding why interest rates differ
from bond to bond can help businesses
and private investors decide which bonds
to purchase as investments and which
ones to sell
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How do risk and term structure
affect interest rates?
We will first examine why bonds with the
same term to maturity have different
interest rates.
The price differences are due to the risk
structure of interest rates. We will
examine in detail what this risk structure
looks like and ways to examine it.
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How do risk and term structure
affect interest rates?
Next, we will look at the different rates
required on bonds with different maturities.
That is, we typically observe higher rates
on longer-term bonds.
This is known as the term structure of
interest rates.
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Risk Structure of Interest Rates
• To start this discussion, we first examine
the yields for several categories of longterm bonds over the last 85 years.
• You should note several aspects regarding
these rates, related to different bond
categories and how this has changed
through time.
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Risk Structure
of Long Bonds in the U.S.
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Risk Structure
of Long Bonds in the U.S.
The figure show two important features of
the interest-rate behavior of bonds.
•
Rates on different bond categories change
from one year to the next.
•
Spreads on different bond categories change
from one year to the next (The spread
between the interest rate on Baa corporate
bonds and U.S. government bonds is very
large during the Great Depression)
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Factors Affecting Risk Structure
of Interest Rates
To further examine these features, we will
look at three specific risk factors.
•
Default Risk
•
Liquidity
•
Income Tax Considerations
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Default Risk Factor
• One attribute of a bond that influences its
interest rate is its risk of default, which occurs
when the issuer of the bond is unable or
unwilling to make interest payments when
promised.
• U.S. Treasury bonds have usually been
considered to have no default risk because the
federal government can always increase taxes
to pay off its obligations (or just print money).
Bonds like these with no default risk are called
default-free bonds.
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Default Risk Factor (cont.)
• The spread between the interest rates on bonds
with default risk and default-free bonds, called
the risk premium, indicates how much
additional interest people must earn in order to
be willing to hold that risky bond.
• A bond with default risk will always have a
positive risk premium, and an increase in its
default risk will raise the risk premium.
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Exercise
• Consider a $1,000 par-bond paying a 20% annual
coupon (maturity date: year 2). The issuing company
has 20% chance of defaulting this year; in which
case, the bond would not pay anything.
• If the company survives the first year, paying the
annual coupon payment, it then has a 10% chance of
defaulting in the second year. If the company defaults
in the second year, neither the final coupon payment
nor par value of the bond will be paid.
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Increase in Default Risk
on Corporate Bonds
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Analysis of Figure 5.2: Increase in
Default on Corporate Bonds
• Corporate Bond Market
1. Re on corporate bonds , Dc , Dc shifts left
2. Risk of corporate bonds , Dc , Dc shifts left
3. Pc , ic 
• Treasury Bond Market
4. Relative Re on Treasury bonds , DT , DT shifts right
5. Relative risk of Treasury bonds , DT , DT shifts right
6. PT , iT 
• Outcome
– Risk premium, ic - iT, rises
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Default Risk Factor (cont.)
• Default risk is an important component of the
size of the risk premium.
• Because of this, bond investors would like to
know as much as possible about the default
probability of a bond.
• One way to do this is to use the measures
provided by credit-rating agencies: Moody’s and
S&P are examples.
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Bond Ratings
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Liquidity Factor
• Another attribute of a bond that influences
its interest rate is its liquidity; a liquid asset
is one that can be quickly and cheaply
converted into cash if the need arises. The
more liquid an asset is, the more desirable
it is (higher demand), holding everything
else constant.
• Let’s examine what happens if a corporate
bond becomes less liquid (Figure 1 again).
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Decrease in Liquidity
of Corporate Bonds
Figure 5.2 Response to a Decrease in the Liquidity of Corporate Bonds
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Analysis of Figure 5.1: Corporate Bond
Becomes Less Liquid
• Corporate Bond Market
1. Liquidity of corporate bonds , Dc , Dc shifts left
2. Pc , ic 
• Treasury Bond Market
1. Relatively more liquid Treasury bonds, DT , DT shifts right
2. PT , iT 
• Outcome
–
Risk premium, ic - iT, rises
• Risk premium reflects not only corporate bonds' default
risk but also lower liquidity
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Liquidity Factor (cont.)
• The differences between interest rates on
corporate bonds and Treasury bonds (that
is, the risk premiums) reflect not only the
corporate bond’s default risk but its liquidity
too. This is why a risk premium is
sometimes called a risk and liquidity
premium.
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5-19
Income Taxes Factor
• Another attribute of a bond that influences
its interest rate is its tax charge.
• For the investor it is important to measure
the after-tax expected return.
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Tax Advantages of Municipal Bonds
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Analysis of Figure 5.3:
Tax Advantages of Municipal Bonds
• Municipal Bond Market
1. Tax exemption raises relative Re on municipal
bonds,
Dm , Dm shifts right
2. Pm 
• Treasury Bond Market
1. Relative Re on Treasury bonds , DT , DT shifts left
2. PT 
• Outcome
im < iT
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5-22
Exercise
• What is the yield on a $1,000,000 municipal
bond with a coupon rate of 8%, paying
interest annually, versus the yield of a
$1,000,000 corporate bond with a coupon
rate of 10% paying interest annually?
• Assume that you are in the 25% tax bracket
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5-23
Sol
• Municipal bond coupon payments equal
$80,000 per year. No taxes are deducted;
therefore, the yield would equal 8%.
• The coupon payments on a corporate bond
equal $100,000 per year. But you only keep
$75,000 because you are in the 25% tax
bracket. Therefore your after-tax yield is
only 7.5%
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Case: Bush Tax Cut and Interest Rates
• The 2001 tax cut called for a reduction in
the top tax bracket, from 39% to 35% over
a 10-year period.
• This reduces the advantage of municipal
debt (interest payments on municipal
bonds are exempt from federal income
taxes) over T-securities since the interest
on T-securities is now taxed at a lower
rate.
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Term Structure of Interest Rates
Now that we understand risk, liquidity, and
taxes, we turn to another important
influence on interest rates – maturity.
Bonds with different maturities tend to have
different required rates, all else equal.
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Term Structure of Interest Rates
• A plot of the yields on bonds with differing
terms to maturity but the same risk,
liquidity, and tax considerations is called a
yield curve
• It describes the term structure of interest
rates for particular types of bonds, such as
government bonds
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The WSJ: Following the News
For example, the WSJ publishes a plot of the
yield curve (rates at different maturities) for
Treasury securities.
Yield curves can be classified as upwardsloping, flat, and downward-sloping
(inverted yield curve)
When yield curves slope upward, the most
usual case, the long-term interest rates are
above the short-term interest rates.
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Case: Interpreting Yield Curves
• The picture on the next slide illustrates
several yield curves that we have observed
for U.S. Treasury securities in recent years.
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Case: Interpreting Yield Curves, 1980–
2008
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Chapter Summary
• Risk Structure of Interest Rates: We
examined the key components of risk in
debt: default, liquidity, and taxes.
• Term Structure of Interest Rates: We
examined the various shapes the yield
curve can take, theories to explain this, and
predictions of future interest rates based on
the theories.
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