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Chapter Fin 7 & pages 21-23: The Risk and Term Structure
of Interest Rates
Lecture 5
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Risk & Term Structure:
1. Why do different bonds have different yields?
1. The risk structure
2. Differences in tax status
3. The term structure
2. What information is there in the relative yield of
different bonds?
2
Bond Ratings
Bond Ratings Moodys and Standard and Poors
Ratings Groups
Investment Grade
Non-Investment
Speculative Grade
Highly Speculative
The government has acknowledged a few firms as
nationally recognized statistical rating
organizations (NRSROs)
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WSJ, August 6, 2011
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Bond Ratings:
BBB and Higher
The top four categories are considered investmentgrade bonds.
Very low risk of default.
Reserved for most government issuers and
corporations that are among the most financially
sound.
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Bond Ratings
BB and lower
Speculative grade bonds are companies and
countries that may have difficulty meeting their bond
payments but are not at risk of immediate default.
Highly speculative bonds includes debts that are in
serious risk of default.
Both speculative grades are often referred to as junk
bonds or high-yield bonds.
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Bond Ratings
Types of junk bonds:
Fallen angels - once investment-grade, but
issuers fell on hard times.
Cases in which there is little known about the
issuer.
Material changes in a firms or governments
financial conditions precipitate change in its dept
ratings.
Ratings downgrade - lower an issuers bond
rating.
Ratings upgrade - upgrade an issuers bond
rating.
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What is a subprime mortgage?
A residential mortgage is called subprime when
it does not meet the key standards of
creditworthiness that apply to conventional
prime mortgages.
Conventional mortgages are those that satisfy
the riles for inclusion in a collection or pool of
mortgages to be guaranteed by a U.S.
Government agency.
The standards cover the size of mortgage,
price of the home, and the ratio between the
two: the loan-to-value ratio (LTV ratio)
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Subprime loans may fail to meet some or all of
these standards for a qualifying mortgage.
Like other loans, subprime loans can be at a fixed
or variable rate (ARMs).
ARMs typically provide a low interest rate, or
teaser rate, for a couple of years and then the
interest resets to a higher rate.
This gives borrowers the ability to refinance
after the introductory rate is up.
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Although, at their peak, subprime mortgages
accounted for less than 15 percent of overall
residential mortgages, they helped trigger the
financial disruptions of 2007-2009.
The key reason is some large, highly leveraged
financial institutions held a sizable volume of MBS
backed by subprime mortgages.
These financial institutions had bet the house on
subprime mortgage securities.
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As the government sought to reform the financial
system after the financial crisis of 2007-2009, the
role of ratings agencies attracted great attention.
Investors around the world had relied on the high
ratings agencies had awarded to a large groups of
mortgage-backed securities (MBS).
As housing prices began to fall, agencies gave
sharp downgrades.
Downgrades lowered MBS prices
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What caused the ratings errors?
Data didnt have sufficient information.
Firms hire the agencies to consult on what
types of MBS have the highest ratings and
then rate them - conflict of interest.
Ratings agencies are compensated by the
issuers of the bonds.
Agencies used a single rating scale to
represent default probabilities, independent of
other characteristics, like liquidity.
May have led investors to underestimate
other important risks.
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Commercial Paper:
What is it?
Short-term (less than 270 days) bond
Unsecured.
Issued on a discount basis
Only most creditworthy borrowers can issue it.
More than one third is held by money-market mutual
funds.
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Commercial Paper
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Bond Ratings and Risk:
Impact of Ratings on Yields
Risk
Bond Demand
Bond Price
Bond Yield
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The Impact of Ratings on Yields
U.S. Treasury issues are the closet to risk-free and
are commonly referred to as benchmark bonds.
Yields on other bonds are measured in terms of the
spread over Treasuries.
Bond yield is the sum of two parts:
= U.S. Treasury yield + Default risk premium
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The Impact of Ratings on Yields
If bond ratings property reflect risk, then the lower the
rating if the issuer, the higher the default-risk
premium.
When Treasury yields move, all other yields move
with them.
We can see this from Figure 7.2 showing a plot of the
risk structure of interest rates.
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19
Tax Status and Bond Prices
Coupon Payments on Municipal Bonds are
exempt from Federal Tax Payments.
Interest income from bonds issued by one
government are not taxed by another
government
20
Tax Status and Bond Prices
Tax-Exempt Bond Yield
= (Taxable Bond Yield) x (1- Tax Rate).
21
Differences in Tax Status and
Municipal Bonds
What are the tax implications for bond yields?
Consider a one-year $100 face value taxable
bond with a coupon rate of 6 percent.
Par is $100, yield to maturity is 6 percent.
Government sees this at 6 percent taxable
income.
If tax rate is 30%, the tax is $1.80.
Bond yields $104.20 after taxes, equivalent of
4.2 percent.
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Asset-backed commercial paper (ABCP) is a
short-term liability with a maturity of up to 270
days.
ABCP is collateralized by assets that financial
institutions place in a special portfolio.
These played a special role in the housing boom
that preceded the financial crisis of 2007-2009.
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To lower costs and limit asset holding, some large
banks created firms (a form of shadow bank) that
issued ABCP and used the money to buy mortgages
and other loans.
The payment stream generated by the loans was
used to compensate the holders of the ABCP.
This also allowed banks to boost leverage and
take on more risk.
When mortgage volume surged, these shadow
banks issued more ABCP to finance expansion.
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When the ABCP matures, issuers have to borrow (or
sell underlying assets) to be able to return the
principal to the ABCP holders.
The risk was that the issuers be would unable to
borrow - they faced rollover risk.
If they were also unable to sell the long-term assets
easily, the shadow banks would face failure.
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The uncertainty in the value of mortgages lead
ABCP purchasers to realize the risk and ABCP
purchases halted.
Firms that has issued ABCP faced an immediate
threat to their survival.
Unable to sell assets or obtain other funding
caused many to fail.
Some banks rescued their shadow banks,
facing heightened liquidity needs and
pressures to sell assets during the worst time the middle of a crisis.
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Term Structure of Interest Rates:
Definition of the Term Structure:
The relationship among bonds with the same risk
characteristics but different maturities is called the
term structure of interest rates.
Yield Curve:
A plot of the term structure, with the yield to maturity
on the vertical axis and the time to maturity on the
horizontal axis.
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Term Structure of Interest Rates
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Term Structure of Interest Rates:
Facts to Explain
1.
Interest Rates of different maturities tend to move together
2.
Yields on short-term bond are more volatile than yields on
long-term bonds
3.
Long-term yields tend to be higher than short-term yields.
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The Expectations Hypothesis
Assumption:
Bonds of different maturities are perfect substitutes for each
other.
Implies:
Investor w/ a two-year horizon indifferent between:
1. A 2 yr bond for 2 yrs
2. A 1 yr bond and a second 1yr bond in 1 yr.
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The Expectations Hypothesis
If current interest rate is 5 percent and
future interest rate is 7 percent, then the
current two-year interest rate will be
(5+7)/2 = 6%.
When interest rates are expected to rise,
long-term interest rate will be higher than
short-term interest rates.
The yield curve will slope up.
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The Expectations Hypothesis
WSJ 9/20/11
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The Expectations Hypothesis
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The Expectations Hypothesis
If bonds of different maturities are perfect
substitutes for each other, then we can construct
investment strategies that must have the same
yields.
Options:
1. Invest in a two-year bond and hold it to maturity
i2t is interest rate - 2 year bond bought today,
t.
One dollar yields (1 + i2t)(1 + i2t) two years
later.
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The Expectations Hypothesis
2. Invest in two one-year bonds, one today and one
when the first matures.
One-year bond today has interest i1t.
One-year bond purchased in year 2 has
interest ie1t+1, where e is expected.
One dollar invested today returns (1 + i1t)(1 +
ie1t+1)
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The Expectations Hypothesis
The expectations hypothesis tells us investors will
be indifferent between the two options.
This means they must have the same return:
(1 + i2t)(1 + i2t) = (1 + i1t)(1 + ie1t+1)
We can now write the two-year interest rate as the
average of the current and future expected oneyear interest rates:
i t +i
i2t = 1
2
e
1+
t1
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The Expectations Hypothesis
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Expectations Hypothesis
General formula:
i nt =
i1t + i
e
1t +1
+i
e
1t + 2
+ .... + i
e
1t + n 1
n
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Expectations Hypothesis
Explains:
1. Interest Rates of different maturities tend to move
together
2.
Yields on short-term bond are more volatile than
yields on long-term bonds
BUT NOT
3. Long-term yields tend to be higher than short-term yields.
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Liquidity Premium Theory
The yield curves upward slope is explained by the
fact that long-term bonds are riskier than short-term
bonds.
Bondholders face both inflation and interest-rate risk.
The longer the term of the bond, the greater both
types of risk.
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Liquidity Premium Theory
Explaining the fact that the yield curve normally slopes
up:
Bondholders face both inflation and interest-rate
risk.
The longer the term of the bond, the greater both
types of risk.
The bigger the risk, the higher the risk premium
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The Liquidity Premium Theory
Together this forms the liquidity premium theory of
the term structure of interest rates.
We can add the risk premium to our previous
equation to get:
e
e
e
1t
1t +1
1t + 2
1t + n 1
nt
n
i = rp +
i +i
+i
+ .... + i
n
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Information Content of Interest Rates:
Risk Structure
When the economy starts to slow, it puts a strain on private
firms.
A slower economy means a higher default probability
Increased default risk is different across firms
Firms already doing poorly, do even worse
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During financial crises, people take cover.
They sell risky investments & buy safe ones.
An increase in the demand for government bonds
coupled with a decrease in the demand for
virtually everything else is called a flight to quality.
This leads to an increase in the risk spread.
The 1998 Russian default on its bonds lead to a
serious flight to quality causing the financial
markets to cease to function properly.
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Information Content of Interest Rates:
Term Structure
When the yield curve slopes down,
it is called inverted
An inverted yield curve
is a very valuable forecasting tool
It signals an economic downturn
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Question 3
Suppose the risk premium on bonds
increases. How would the change
affect your forecast of future
economic activity, and why?
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I. * G i ven t he data in the t able below, would you say that this economy is
heading for a boom or for a recessi on? Explain your choice.
3-month
10-y ear
Baa corporate
Treasury -bil l rate Treasury bond
10-year bond
January
1.0%
3%
7%
February
1.05%
3.5%
7.2%
March
1.1%
4%
7.6%
April
1.2%
4.6%
8%
May
1.25%
5%
8.2%
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Answer: Th e information in both the t erm structure and t he r isk st ructure point t o a
heal thy economy.
The t erm spread (t he gap bet ween the 3 month Treasury yield and t he 10 year Treasury
bond yiel d) is positive and widening. Th is tell s us that t he yiel d curve is upward sl oping
and gett ing more steeply upward sloping. This impli es that interest rat es are ex pected to
continue to rise in the futurea si gn t hat the economy is expect ed to do well.
The risk spread (the gap bet ween the Treasury and corporat e 10 year bonds) i s narrowing.
This is a sign of a heal thy eco nomy as people do not requi re such a high risk premi um on
corporate bonds.
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