1. The Structure of Interest Rates (a) The Term Structure of Interest Rates (b) Risk Premiums and Quality Spreads Blackwell, Griffiths and Winters, Chapter 3, and other material

2. The Yield Curve and the Term Structure of Interest Ratesto
Maturity 14 14 16 16

3. Expectation Hypothesis The Yield Curve for Default Free, Very Liquidity Instrument with Virtually No Information Costs
Yield to
Maturity
Effect of Expectations over a horizon of “M” Months
Real Risk-Free Rate
Maturity in Months 14 14 16 16

4. Expectations Theory
Current long-term interest rates are based on investors expectations of future interest rates…
which means that
Current long-term rates are combinations of current and expected future short-term rates.

5. Expectations Theory and Slopes of the Yield Curve
The yield curve plots yield against time to maturity for default-free securities Expectations theory can explain three shapes of the yield curve: upward-sloping, downward-sloping, and flat.
Rates expected to rise in the future, then yield curve is upward sloping.
Rates expected to fall in the future, then yield curve is downward sloping.
Rates expected to remain constant in the future, then the yield curve is flat.

6. Definition of Long-term Rate under Expectations Theory
Under expectations theory, a long-term rate is the geometric average of current and expected future short-term rates.

7. Formula for the Long-term Rate
where
r = spot rate
f = one-period expected future short-term rate
t = number of time periods in the long-term rate
and
prescript is beginning of time period covered by the rate
postscript is ending of the time period

8. Example for a three-year rate
Timeline of three-year rate

9. Solving for an Expected Future Short-term Rate
then, solving for t-1ft is

10. Example: Finding an expected future rate
Using data from May 2000 term structure (Figure 3.7 ), the expected one-year rate for Year 2 is:

11. Graphic Portrayal of the Liquidity Premium Hypothesis
Yield to
Maturity
Observed Yield Curve
Term Premium
Yield Curve Excluding Term Premium 28 28 30 30

12. Graphic Portrayal of the Liquidity Premium Hypothesis
Yield to
Maturity
Observed Yield Curve
Term Premium
Yield Curve Excluding Term Premium 29 29 31 31

13. Graphic Portrayal of the Liquidity Premium Hypothesis
Yield to
Maturity
Observed Yield Curve
Term Premium
Yield Curve Excluding Term Premium 30 30 32 32

14. Graphic Portrayal of the Segmented Market Hypothesis (Explaining the Slope of the Yield Curve)to
Maturity 24 24 26 26

15. Graphic Portrayal of the Preferred Habitat Hypothesis
Observed Yield Curve
Yield to
Maturity
Other premiums
Term Premium
Yield Curve Excluding Term Premium 28 28 30 30

16. Preferred Habitat Theory
The preferred habitat theory is a corollary of the market segmentation theory. Market segmentation theory assumes that investors have specific maturity preferences that they will not leave regardless of the additional compensation. This assumption is too restrictive. The preferred habitat theory assumes that investors have a desired time to maturity for investment (a preferred habitat), but if adequately compensated for the additional risk of moving from their desired maturity, they will move to other maturities.
The preferred habitat theory is the only theory that allows for ‘humps’ or ‘twists’ in the yield curve. In other words, it allows for a change in the direction of the slope of the yield curve. This is important because this frequently occurs in plots of market yields.

17. The Basic Rate: The Nominal Risk Free Rate
The nominal risk free rate is the rate on a relatively short-term asset that has essentially two components:
The real risk free rate (krf,t), and
The inflation premium (IPm,t) for an investment maturity of m periods,
This may expressed as
For the risk free rate, the maturity m would be a very short horizon and the inflation risk premium would be close to zero
The nominal risk free rate can be approximated by a very short-term Treasury bill rate
It has no credit risk
It has a very high degree of liquidity
It has no term premium
The superscript T in the previous equation represents a Treasury security

18. Beyond the Risk Free Rate
However, once one considers an asset longer than a very short-term Treasury bill rate, other forms of risk emerge
Some affect all debt contracts in an equal manner for a given maturity--general risks
General risk seem to have a term structure
This means that its size varies with an assets maturity
However, for a given maturity, it affects all debt contracts by the same magnitude
Other risks depend upon the specific characteristics of the debt contract--instrument specific risks
Its size depends upon the asset under consideration; and the magnitude may also have a term structure
Maturity risk premium
Term Structure
Impact of Business Cycle:
Inflation premium
Inflation risk premium

19. General Risks and the Yield on Treasury Securities
The yield on a Treasury security (an instrument lacking instrument specific risks) may be expressed as
The nominal risk free rate would have a zero maturity risk premium and no inflation risk premium
Supply premium (SPm,t): the shortage of Treasury securities could lead to a scarcity value for Treasury securities

20. The Term Structure of Inflation Forecasts Survey of Professional Forecasters

21. The Composition of Treasury Yields and the Four Theories of the Yield Curve
Pure Expectations
The expectation embodied in the yield curve at time t is the inflation premium (expected inflation rate) over a horizon of m periods
Liquidity Premium Hypothesis
The pure expectation hypothesis is expanded by adding the maturity risk premium demanded for an instrument with a maturity of m periods
Preferred Habitat
Segmented Market Hypothesis

22. Instrument Specific Risks
The risk that is unique to the asset under consideration
These risks affect each instrument differently
It is generally assumed that Treasury securities posses general risks but are free of the instrument specific risks
As a result, Treasury securities are often used as a benchmark against which the magnitude of instrument specific risk might be gauged
Instrument Specific Risks
Default/Credit Risk
Liquidity Risk
Supply shifts
Management Risk
Call Risk
Convertibility Risk
Political Risk
Sovereign
Industry Risk
Legal Risk
Operations Risk 23 22

23. More on Default Risk
Default on a debt contract occurs when the borrower violates any of the conditions of the contract. When examining default risk, a lender is concerned with how a default will impair the expected cash flows from the debt contract. So, the lender is concerned about the expected losses from a default and builds those expected losses into the debt contract rate through a default risk premium. There is a wide range of possible losses from default, so we need a way to measure default risk.
Bond Rating Proxies for Default Risk Credit rating agencies provide bond ratings The two primary rating agencies are Moody’s and Standard & Poor’s. A bond rating is the agency’s opinion on a company’s ability to meet its financial obligations. To determine a company’s bond rating, the rating agency does an in-depth analysis of the company, which includes a complete analysis of the company’s financial statements.

24. Bond Ratings (Figure 3-11)

25. Cumulative Default Rates by Bond Rating

26. Taxes
Investors look at after-tax returns because taxes are a cash outflow for investors.
Investors pay federal taxes on interest received from corporate debt, but not on interest received from municipal debt.

27. Taxes (cont.)
Accordingly, municipal bonds can compete with corporate bonds of similar risk while paying lower interest rates.
The formula used to make the comparison is:

28. Example: Municipal debt interest rate
Assume a AAA corporate bond has a rate equal to 4.65%
and an investor has a marginal tax rate of 28%. Then
what rate would a AAA muni have to pay to
compete?

29. Marketability (Liquidity)
Less marketable securities are harder to sell, so investors demand higher interest rates. Long-term debt securities are often assumed to be less marketable than similar short-term debt securities, but we feel it is dangerous assumption to make.
Marketability refers to the speed and cost with which an investor can sell a security.
The costs to consider are:
Price concession necessary for the sale
The cost of executing the trade
Search costs
Information costs

30. Embedded Options in Debt Contracts
Embedded call option allows the issuing firm (borrower) to retire the debt before maturit An embedded call provides a valuable right to the borrower and creates additional risk for the investor (lender), so callable debt pays higher interest rates than similar non-callable debt. Embedded put option allows the investor to sell the bond back to the issuing firm (borrower) before maturity. An embedded put provides a valuable right to the investor and creates additional risk for the issuer, so putable debt pays lower interest rates than similar non-putable debt.
Embedded conversion option allows the investor to convert the debt contract into other type of security (typically stock) from the issuing firm (borrower) before maturity. The investor acquires the valuable right by paying a higher price for the convertible debt than similar non-convertible debt, which results in a lower yield on the convertible debt.

31. Required Return Conventional Bonds
Represented by corporate bonds
DPc,m,t default premium on the corporate (c) security at maturity m.
LPc,m,t liquidity premium on the corporate bond at maturity m
OPc,m,t all other premiums assigned to this security at maturity m
CRPm,t the call risk premium
SPc,mt supply premium for the corporate bond

32. Quality Spreads Corporate Bonds
The quality for any given non-Treasury security is measured as the spread between that security and the Treasury security with the corresponding maturity
Substituting the equations for both the Treasury and the corporate bond yields

33. The Magnitude of Instrument-Specific Risk
The magnitude of instrument specific risk faced by securities may be affected by
Term structure of instrument specific risk
The business cycle and instrument specific risk
Industry characteristics instrument specific risk
Market segmentation
Event risk 25 24

34. Credit or Default Risk

35. The Term Structure of Credit/Default Risk

36. The Business Cycle and Credit/Default Risk

37. The Business Cycle and Credit/Default Risk

38. Industry Risk

39. Sovereign Risk An Illustration

40. Sovereign Risk Continued
Care must be exercised in measuring sovereign risk
Previous example used instruments denominated in dollars held in US and in the UK
Same conclusions cannot be reached using yields ob assets expressed in different currencies
Difference factor other than sovereign risk
See illustration in right panel
U.S.
Germany
Brazil
3-Month
0.02%
0.01%
6-Month
0.05%
12-Month
0.08%
11.10%
2-Year
0.42%
0.00%
11.47%
3-Year
11.44%
5-Year
1.54%
0.22%
11.53%
7-Year
0.49%
10-Year
2.36%
0.99%
11.65%
30-Year
3.18%
1.84%
bloomberg.com August 18, 2014
investing.com August 19, 2014

41. Liquidity The TED Spread

42. Tax Exempt Securities Implicit Tax Rate