1. 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.

2. Yield Curve flat descending (or inverted)
ascending (includes steep and normal)
humped

3. 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)

4. 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?

5. 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?
Always true that:
Geometric Average ≤ Arithmetic Average

6. 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”
neither working nor looking for work, but say they want a job, and
want to work full-time but are working part-time because that is best they can find.
11/7

7. (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 short-term securities.

8. Term Structure Formula
Long-term interest rates are the geometric average of future period rates.
where:
0Rn observed YTM on n-year bond
t fq forward rate on q-year bond that starts at
time t (where t = 0 is now)

9. Implied 1-Year Forward Rate Formula
This results in the implied forward rate formula for the n-th period coming up
Example of how to apply:
Want implied yield of a 1-year security that starts 6 years from now.
Look up yields on 6-year security and 7-year security.
Use formula above with n = 7.

10. Example 2: Calculating Forward Rates
Assume following Treasury security quotes:
yrs to maturity
YTM 1
2015
11-Nov
0.8953 2
2016
1.3725 3
2017
1.8770 4
2018
2.3172 5
2019
2.6626
Find the 1-year implied forward rates during nth year (where n = 2,3,4,5) using

11. Example 3: Another Example
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.

12. (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.

13. (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.

14. (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.

15. 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.

16. Bond Ratings
Fitch, too

17. 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.

18. Default Rates Non-mortgage bond default history, when initially rated:
AAA % AA A
BBB BB B
CCC
History with recent mortgage securities entirely different.

19. 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.

20. 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

21. 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

22. 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