Chapter 5

Factors Affecting Bond Yields and the Term Structure of Interest Rates

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

Treasury yields

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

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

Spread determinants

  Type of issuer Issuer’s perceived credit risk  Maturity or term  Embedded options  Liquidity

Types of Issuers

 U.S. Government  U.S. Government Agency  Municipal Government  Credit (domestic and foreign corporations)  Industrial, utility, finance, noncorporate  Foreign Government

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

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

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

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

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

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

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

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

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.

Example using theoretical spot rates (exhibit 5-7) 12 13 14 15 16 17 18 19 20 Period 1 2 3 4 5 8 9 6 7 10 11 6 6.5

7 7.5

8 8.5

9 9.5

10 Year 0.5

1 1.5

2 2.5

3 3.5

4 4.5

5 5.5

Cash Flow 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 105 5 5 5 5 Spot Rate (%) 5.25

5.5

5.76

6.02

6.28

6.55

6.82

6.87

7.09

7.2

7.26

7.31

7.43

7.48

7.54

7.67

7.8

7.79

7.93

8.07

PV of $1 at 0.974421

0.947188

0.918351

0.888156

0.856724

0.824206

0.790757

0.763256

0.730718

0.701952

0.675697

0.650028

0.622448

0.597889

0.573919

0.547625

0.521766

0.502665

0.477729

0.453268

PV of CF 4.872107

4.735942

4.591756

4.440782

4.283619

4.12103

3.953783

3.81628

3.653589

3.509758

3.378483

3.250138

3.112238

2.989446

2.869594

2.738125

2.608831

2.513325

2.388643

47.59317

Theoretical Value = 115.4206

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

Exhibit 5-8: Two alternative one year investments

Calculating forward rates

 Invest $100 in each strategy   Alternative 1 payoff at end of year  $100(1 + z 2 ) 2 Alternative 2 payoff at end of year   $100(1 + z 1 )(1+f) Investors are indifferent if:   $100 (1 + z 2 ) 2 = $100(1 + z 1 )(1+f) f = ((1 + z 2 ) 2 /(1 + z 1 )) -1

Yield Curve Shapes

Yield curve theories

 Pure Expectations  Liquidity  Preferred Habitat  Market Segmentation

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

Interpretations of the Theory

 broadest interpretation  local expectations form of the pure expectations theory  return to maturity interpretation

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

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

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

Main yield curve influences

 Ilmanen (1996) finds three main influences  Market expectations  Bond risk premiums  Convexity Bias