1. 1 Yield Curve flat descending (or inverted) ascending (includes steep and normal) humped

2. 2 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.

3. 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. 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. 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. 6 U-3 and U-6 Unemployment Rates Civilian Labor Pool = 157 million U-3 = 5.1% of civilian labor pool (5.9 last year, 7.2 year before). Those without jobs, who are available to work and who have actively sought work in the prior four weeks. ---------------------------------------------------------------------------- U-6 = 10.0% (11.8 last year, 13.6 year before) 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

7. 7 (1) 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. First of four theories used to explain shape of yield curve is expectation theory:

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

9. 9 Implied 1-Year Forward Rate Formula 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. This results in the implied forward rate formula for the n-th period coming up

10. Example 2: Calculating Forward Rates Assume following Treasury security quotes: yrs to maturityYTM 1201611-Nov0.8953 2201711-Nov1.3725 3201811-Nov1.8770 4201911-Nov2.3172 5202011-Nov2.6626 Find the 1-year implied forward rates during nth period (where n = 2,3,4,5) 10

11. 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: 4 th period starts 3 years from now, and ends 4 years from now.

12. 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. 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. 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. 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. 16 Bond Ratings Fitch, too

17. 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. 18 Default Rates AAA 0.52% AA 1.31 A 2.32 BBB 6.64 BB 19.52 B 35.76 CCC 54.38 Non-mortgage bond default history, when initially rated: History with recent mortgage securities entirely different.

19. 19 Default Risk Investors require a default risk premium. 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. 20 Call Options, Put Options Call option permits the issuer to call (refund) an obligation, under certain conditions, before maturity. Issuers will likely “call” in a bond from investors if interest rates decline. Difference in yields between callable and noncallable contracts is call interest premium. Put option permits a investor to terminate a contract, under certain conditions, before maturity. Investors are likely to “put” a bond back to its issuer if interest rates rise. Difference in yields between putable and nonputable contracts is put interest discount.

21. 21 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.