Chapter 5

1. Chapter 5 Factors Affecting Bond Yields and the Term Structure of Interest Rates

2. U.S. Treasuries • Viewed as having zero default risk • Largest and most liquid market • Lowest rate (yield) • Rate (yield) is the base or benchmark rate

3. Treasury yields • Minimum yield investors will accept • Other bonds trade at spreads over the treasury yield • Examples of current U.S. Treasury rates

4. Risk Premium • Non-Treasury bonds trade at a spread above Treasuries: • Yield on non-Treasury=yield on Treasury + spread or • Yield on non-Treasury = yield on Treasury + risk premium • The spread is stated in basis points • The spread is compensation for risk. • Alternative spread measures include yield spreads and yield ratios

5. Spread determinants • Type of issuer • Issuer’s perceived credit risk • Maturity or term • Embedded options • Liquidity

6. Types of Issuers • U.S. Government • U.S. Government Agency • Municipal Government • Credit (domestic and foreign corporations) • Industrial, utility, finance, noncorporate • Foreign Government

7. Perceived credit worthiness • Default risk measure the probability that principal and interest will not be repaid • Higher default risk results in higher yields • The spreads between treasuries and corporates with the same maturity are called credit spreads

8. Embedded options • Spreads reflect any embedded options • Options include: • calls • puts • conversion options • Spreads will be: • lower if the option is good for the buyer • higher if the option is good for the seller

9. Taxability • Interest income is taxed at ordinary income rates • Some interest is exempt from federal taxes • After tax yield = pretax yield (1-tax rate) • Equivalent taxable yield =tax exempt yield/(1-Tax rate) • Qualified Municipal bonds are tax-exempt • Muni bonds types • general obligation (GO) • revenue bonds • AAA GO bond is benchmark for Munis

10. Liquidity and Financeability • Liquidity • Related to depth and breadth of market • Investors demand compensation for illiquidity • Financeability • demand by dealers to cover short positions • “On the run” vs. “Off the run” Treasuries • Corporate spreads • credit and liquidity driven

11. Term Structure • Maturity (or term) plays an important role in yield determination • Yield curve • Depiction of maturity and yield • Represent a specific risk class • Treasury yield curve is most common

12. Theoretical Spot Rate Curve • Treasury Bond valuation: • portfolios of zero coupon securities. • Each cash flow should be discounted by the appropriate yield • Cannot use yields on coupon bonds. • Need a zero coupon yield curve. • There are no zero coupon Treasuries with maturities > 1 year so a curve must be constructed

13. Constructing the Spot Rate Curve • Which securities? • On the run Treasuries • On the run and selected off the run Treasuries • All Treasuries • Treasury coupon strips • Must use increasingly rigorous methods as securities are added

14. Bootstrapping with “On the run” Treasuries • Use the “On the run” Treasury yields • 3 month, 6 month, 2, 5, 10, 30 par yields • Extrapolate to fill in curve every six months • Bootstrap starting with the six month yield • See example in class: • Problem: Big gaps between observed yields

15. Other methods • Bootstrapping with “Off the run” • Use all Treasuries • Sophisticated screening and statistical fitting techniques • Exponential splining • Most used method. • The theoretical spot yield curve is generated and provided for analysts.

16. Example using theoretical spot rates (exhibit 5-7)

17. Forward rates • Yield curve provides consensus estimate of future spot rates • Consider two alternatives • Buy a one year instrument • Buy two six month instruments consecutively • Investor should be indifferent between strategies

18. Exhibit 5-8: Two alternative one year investments

19. Calculating forward rates • Invest $100 in each strategy • Alternative 1 payoff at end of year • $100(1 + z2)2 • Alternative 2 payoff at end of year • $100(1 + z1)(1+f) • Investors are indifferent if: • $100 (1 + z2)2 = $100(1 + z1)(1+f) • f = ((1 + z2)2 /(1 + z1)) -1

20. Yield Curve Shapes

21. Yield curve theories • Pure Expectations • Liquidity • Preferred Habitat • Market Segmentation

22. Pure expectations • Forward rates = expected future rates • Term structure reflects expectations only • Upward sloping – rising future rates • Flat – rates won’t change • Downward sloping – falling future rates • Why? • Shortcomings

23. Interpretations of the Theory • broadest interpretation • local expectations form of the pure expectations theory • return to maturity interpretation

24. Liquidity • Considers issues other than expectations • Investors prefer shorter maturities • Demand a premium for longer terms • Forward rates reflect • Future expectations • Risk or liquidity premium • Changes interpretation of YC shapes

25. Preferred Habitat • Term structure influenced by • Expectations • Risk premiums • Risk Premiums influenced by • Relative supply and demand in different maturities • Can be positive or negative • Can explain all yield curve shapes

26. Market segmentation • Like PH supply/demand in maturity sectors influence rates • Investors/borrowers will not shift across maturities • YC shape influenced by supply/demand in maturity classes

27. Main yield curve influences • Ilmanen (1996) finds three main influences • Market expectations • Bond risk premiums • Convexity Bias