1. Chapter 3 The Level and Structure of Interest Rates
Modern Financial Markets: Prices, Yields, and Risk Analysis Blackwell, Griffiths and Winters
Chapter 3
The Level and Structure of
Interest Rates

2. Loanable Funds Theory
Loanable funds theory states that short-run interest rates are determined by the supply and demand of loanable funds. (see Figure 3-2) The theory states that the equilibrium interest rate is a combination of a long-run base rate plus short-run supply/demand factors and current financial market risks.

3. Components of Market Interest Rates
The Level of Rates
Long-run base rate
Inflation (expected)
The Structure of Rates
Time to maturity
Default risk
Taxes
Marketability
Embedded options

4. Long-run Base Rate
The long-run base rate is referred to as the real rate of interest. Assuming individuals either consume or invest (delay consumption) and that individuals prefer consumption today, the real rate of interest is the rate necessary to get individuals to delay consumption. (see Figure 3-4)

5. Inflation (expected)
When we lend our money, we are delaying consumption. So, when we get our money back we want to be able to buy the same goods that our money would have bought before. Thus, we need to include expected inflation in all interest rates.

6. Fisher Effect
The Fisher Effect combines the real rate of interest and expected inflation to create a (risk-free) nominal interest rate. The nominal interest rate is a market interest rate. That is, it is the rate you either pay or earn.

7. Fisher Equation r = nominal interest rate R = real rate of interest
E(i) = expected annual rate of inflation
solving for r,

8. Example: Loan contract interest rate
If borrower and lender agree that R = 6% and E(i) = 7%,
then what would be the contract interest rate for a one-year loan?
Using the Fisher Equation, the contract rate is:

9. Approximate Fisher Equation
This equation is used as a “rule of thumb”

10. Treasury Inflation Protected Securities (TIPS)
Starting in 1997 the US Treasury has been issuing securities, called TIPS, that compensate investors for inflation, as is occurs.
Over the last year in the US, through July 2008, the annual rate of inflation based on the CPI was 5.6%.
This means an investor in a TIPS one year ago would get a real interest plus 5.6% compensation of inflation.
In other words, the stated interest rate on TIPS can be thought of as a real interest rate.

11. WSJ Quotes on Treasury securities
Quotes for “conventional” or nominal Treasury securities can be found at:
What is the interest rate on a five year to mature Treasury security today, then? Is this a real interest rate or a nominal interest rate? Why?
What is its coupon rate? What is its price?
Quotes for TIPS securities can be found at:
What is the interest rate on a five year TIPS today? Is this a real interest rate, or a nominal interest rate? Why?

12. Finding Expected inflation
Take the two different five year interest rates on Treasuries found for conventional and TIPS securities. Based on these yields, find what the market is expecting inflation to be given these two rates and the Fisher Effect.
Do you think this is a good estimate of inflation over the next five years or not? Why?
Which do you think would be a better five year investment today: a conventional Treasury or a TIPS? Why?

13. Inflation and Realized Real Rate

14. Impact of Changes in Inflation on Short-Term and Long-term Interest Rates

15. Time to Maturity Impacts Relation between Rates
The Structure of Interest Rates Historical Evidence – top of figure 3-7, used for yield curve plot
Time to Maturity Impacts Relation between Rates
Debt Security Yield
May 2000
April 2004
3-month Treasury bill
5.99%
0.91%
6-month Treasury bill
6.39
1.17
1-year Treasury bill
6.33
1.53
2-year Treasury note
6.81
2.21
3-year Treasury note
6.77
2.74
5-year Treasury note
6.69
3.52
7-year Treasury note
4.01
10-year Treasury note
6.44
4.43

16. The Structure of Interest Rates Historical Evidence (cont.)
Impact of Taxes and Default Risk
Aaa Municipal bonds (20 years)
4.89%
4.46%
Aaa Corporate bonds (20 years and above)
7.64
5.80
Aa Corporate bonds
7.82
6.04
A Corporate bonds
8.07
6.13
Baa Corporate bonds
8.40
6.51

17. Time to Maturity
The relationship between interest rates on similar securities with different times to maturity is referred to as the Term Structure of Interest Rates

18. Theories of the Term Structure
Expectations Theory
Liquidity Preference Theory
Preferred Habitat Theory
Each theory will be discussed in some detail in the following slides.

19. 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.

20. 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.

21. Expectations Theory and Slopes of the Yield Curve (cont.)
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.

22. 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.

23. 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

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

25. Example: Finding an expected future rate
Using data from May 2000 term structure (Figure 3.7 (Slide 17)), the expected one-year rate maturing at the end of Year 2 is:

26. Liquidity Preference Theory
Simply put, investors prefer liquidity. This theory extends expectations theory by assuming that investors are risk-averse and prefer short-term investments. If investors are asked to extend beyond their preferred short-term time to maturity, they demand a premium for the price risk created by going beyond their preferred time horizon.

27. Formula for the Long-term Rate under Liquidity Preference Theory
where
l = risk premium for increasing time to maturity
and

28. Liquidity Preference Theory and the Yield Curve
Liquidity Preference Theory explains why the yield curve slopes upward most of the time.

29. Yield Curve plots: Expectations Theory vs. Liquidity Premium Theory

30. 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.

31. Preferred Habitat Theory (cont.)
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.

32. Preferred Habitat Theory and Yield Curve Slopes
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.

33. Yield Curve of Treasury Data in Figure 3-7

34. 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.

35. Default Risk (cont.)
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.

36. 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.

37. Problems with credit rating agencies today
1. They have done a very poor job of assessing the default risk of MBS and new asset backed securities. Defaults have been much greater that suggested by the rating.
2. Many blame this on the fact that the rating agencies get their funding from the issuing firm, who has a vested interest in getting high ratings, since this lowers the interest expense for the issuer.
Conflict of interest.
What should be done?

38. Bond Ratings (Figure 3-11)

39. Cumulative Default Rates by Bond Rating

40. 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.

41. 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:

42. 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?

43. Marketability
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.

44. Marketability (cont.)
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

45. Embedded Options in Debt Contracts
Embedded call option allows the issuing firm (borrower) to retire the debt before maturity.
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.

46. Embedded Options (cont.)
2. 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.

47. Embedded Options (cont.)
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.