Transcript Definitions • Term structure of interest rates: relationship between the yields on bonds and their terms to maturity. • Yield curve: graphical portrayal.

Definitions
• Term structure of interest rates: relationship between
the yields on bonds and their terms to maturity.
• Yield curve: graphical portrayal of the term
structure of US Treasuries.
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Yield Curve
flat
descending (or inverted)
ascending (includes steep and normal)
humped
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Factors Influencing Bond Yields
•
•
•
•
•
•
General level of interest rates
Default risk
Term to maturity
Tax treatment
Marketability
Call or Put features
–
–
Call: issuer can retire bond early
Put: holder can retire bond early
• Convertibility (for instance to stock)
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Example 1: Geometric Average
Over the past 4 years your investment advisor says he
grew your money at 10%, 50%, -60%, 40%. Should
you be happy?
10  50  60  40
Arith Ave 
 10%
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Example 1: Geometric Average
Over the past 4 years your investment advisor says he
grew your money at 10%, 50%, -60%, 40%. Should
you be happy?
10  50  60  40
 10%
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Geom Ave  4 (1  .10)(1  .50)(1  .60)(1  .40)  1
Arith Ave 
 4 (1.1)(1.5)(.4)(1.4)  1
 .98043  1
 1.967%
Always true that:
Geometric Average ≤ Arithmetic Average
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U-3 and U-6 Unemployment Rates
Civilian Labor Pool = 156 million
U-3 = 5.9% of civilian labor pool (7.2 last year) Those
without jobs, who are available to work and who have
actively sought work in the prior four weeks.
----------------------------------------------------------------------------
U-6 = 11.8% (13.6 last year) Includes “marginally attached
workers”
(1) neither working nor looking for work, but say they want
a job, and
(2) want to work full-time but are working part-time
because that is best they can find.
11/7
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(1) Expectation Theory
First of four theories used to explain shape of yield
curve is expectation theory:
• Shape of yield curve determined by expectations
about future rates.
• This theory assumes investors are indifferent
between a long-term security and a series of shortterm securities.
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Term Structure Formula
• Long-term interest rates are the geometric average of
future period rates.
1  0 f1 1  1 f1  1  n2 f1 1  n1 f1   1  0 Rn 
n
1  0 Rn 

1  n1 f1  
1  0 f1 1  1 f1  1  n2 f1 
n
substituting
1  0 Rn 

1  n1 f1  
1  0 Rn1 1  1 Rn1 
n
1  n2 Rn1 
where:
0Rn
t fq
observed YTM on n-year bond
forward rate on q-year bond that starts at
time t (where t = 0 is now)
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Implied 1-Year Forward Rate Formula
This results in the implied forward rate formula for the
n-th period coming up
1  0 Rn 

1
n 1 f1 
n 1
1  0 Rn1 
n
Example of how to apply:
1. Want implied yield of a 1-year security that starts 6
years from now.
2. Look up yields on 6-year security and 7-year security.
3. Use formula above with n = 7.
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Example 2: Calculating Forward Rates
Assume following Treasury security quotes:
yrs to
maturity
YTM
1
2015
11-Nov
0.8953
2
2016
11-Nov
1.3725
3
2017
11-Nov
1.8770
4
2018
11-Nov
2.3172
5
2019
11-Nov
2.6626
Find the 1-year implied forward rates during nth
year (where n = 2,3,4,5) using
f 
n 1 1
1  0 Rn 
1  0 Rn1 
n
n 1
1
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Example 3: Another Example
 1  0 Rn n 
1
n 1 f1  
n 1 
 1  0 Rn1  
find the 1-year implied forward rate for the period that
begins 2 years from now where
1-year Treasury bill 1.9%
2-year Treasury note 2.4%
3-year Treasury note 2.7%
When doing, note for example: 4th period starts 3 years
from now, and ends 4 years from now.
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(2) Liquidity Premium Theory Says…
• Long-term securities have greater price risk, and
generally less marketability.
• Liquidity premiums contribute to an upward
tendency of a yield curve.
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(3) Market Segmentation Theory Says…
• Market participants may have strong preferences
for particular maturities, and buy and sell securities
consistent with these preferences.
• Can theoretically lead to discontinuities in yield
curve.
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(4) Preferred Habitat Theory Says…
• Preferred Habitat Theory (an extension of Market
Segmentation Theory) allows market participants to
trade outside of their preferred maturities if
adequately compensated.
• Preferred Habitat Theory allows for humps in the
yield curve.
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Which Theory is Right?
• Each has its point.
• Day-to-day changes in the term structure seem
consistent with the Preferred Habitat Theory.
• Many economists also feel that Expectations and
Liquidity Premiums are important, too.
• Market Segmentation Theory appears to be least
realistic of the four.
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Bond Ratings
Fitch, too
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NRSROs
• Nationally Recognized Statistical Rating Organizations
• NRSROs are credit-rating agencies authorized by the
SEC and banking regulators. Currently 10 (best known
Moody’s, Standard & Poor’s, Fitch).
• BBB- (Baa3) and above are investment-grade, below are
speculative-grade or “junk.”
• Issuers pay to have their bonds rated. Banks, insurance
companies, pension funds, many mutual funds can only
hold investment-grade bonds.
• As conditions change, rating agencies change their
ratings. Bad when an issue’s rating drops below cutoff.
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Default Rates
Non-mortgage bond default history, when initially rated:
AAA
AA
A
BBB
BB
B
CCC
0.52%
1.31
2.32
6.64
19.52
35.76
54.38
History with recent mortgage securities entirely different.
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Default Risk
• Investors require a default risk premium.
• DRP = i – irf > 0
• Default risk premiums tend to increase in periods of
recession (when people scared) and decrease in periods
of economic expansion (when people overconfident).
• “flight-to-quality”
• Bond ratings are only for default risk.
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Call Options
• Call option permits the issuer to call (refund) the
obligation before maturity.
• Issuers will “call” if interest rates decline.
• investors demand a call interest premium.
• CIP = ic – inc > 0
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Put Options
• Put option permits the investor to terminate the
contract at a designated price before maturity.
• Investors are likely to “put” their bond back to the
issuer during periods of high interest rates.
• Difference in interest rates between putable and
nonputable contracts is called the put interest discount.
• PID = ip – inp < 0
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Conversion Options
• Permits the investor to convert a security contract
into another security
• Conversion yield discount is the difference between
the yields on convertibles relative to
nonconvertibles.
• CYD = icon – incon < 0
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