1. Chapter 6 The Structure of Interest Rates

2. 2  From One Interest Rate to Many From One Interest Rate to Many  Term to Maturity Term to Maturity  The Expectations Theory The Expectations Theory  Necessary Modifications to the Expectations Theory Necessary Modifications to the Expectations Theory  Credit Risk Credit Risk  Taxability Taxability

3. 3 From One Interest Rate to Many  Numerous types of financial claims are traded in financial markets  Interest rates generally move up and down together. All rates may not move the same amount.  However, occasionally some rates may not even move in the same direction as the rest.

4. 4 The purpose of chapter 6  To study the factors that are primarily responsible for determining the relationship among interest rates.

5. 5 From One Interest Rate to Many  There are four primary determinants of the relationships among interest rates  term to maturity  credit risk  liquidity  tax treatment

6. 6 Term to Maturity  The major characteristic distinguishing one type of Treasury security from another is the term to maturity  Treasury bills have short terms to maturity of one year or less  Treasury notes and bonds have long maturities of one year or more

7. 7 Term to Maturity  The pattern of relationships among interest rates and the time to maturity are referred to in financial markets as the term structure of interest rates  利率的期限结构：收益率和到期时间之间的 关系。

8. 8 The Yield Curve  A yield curve visually represents the term structure of interest rates  shows the relationship between interest rates (yields) on particular financial instruments (securities) and their terms to maturity  Each type of asset is represented on a single yield curve  controls for factors other than term to maturity 收益率曲线：描述某种证券的利率（收益率）与 其期限之间的关系的图形。

9. 9 Interest Rates on Treasury Securities

10. 10 Yield Curves

11. 11 The Expectations Theory  The expectations theory postulates that  the yield curve is determined by borrowers’ and lenders’ expectations of future interest rates  changes in the slope (shape) of the curve result from changes in these expectations 预期理论：该理论假设长期利率是当前短期利率及 预期短期利率的几何平均数。

12. 12 Example  Suppose you have funds to lend for a two- year period and the current yield on a one- year bill (i 1 ) is 5% and the current yield on a two-year note (i 2 ) is 5.99%  Suppose you expect that the yield on one- year securities (i e 1 ) will be 7% one year from now

13. 13  You have two options  buy a one-year security today and another one year from now  buy a two-year security today  Which option will give you a higher expected rate of return?

14. 14  To calculate the expected return of the first option, we find the geometric average of the two rates  we assume that the interest earned during the first year will earn interest during the second year 几何平均数：考虑了复利影响的平均数。

15. 15  The long rate (i 2 ) can be calculated as (1 + i 2 ) = [(1 + i 1 )(1 + i e 1 )] 1/2 i 2 = [(1 + i 1 )(1 + i e 1 )] 1/2 – 1 i 2 = [(1.05)(1.07)] 1/2 – 1 = 5.99%  This is the rate of the two-year security  You will be indifferent between the two options

16. 16 Hypothetical Yield Curve Term to Maturity Yield to Maturity (percent) 1 5 2 5.99 yield curve

17. 17 The Expectations Theory  Suppose that expectations about future rates change so that i e 1 rises from 7 to 9 percent (1 + i 2 ) = [(1 + i 1 )(1 + i e 1 )] 1/2 i 2 = [(1 + i 1 )(1 + i e 1 )] 1/2 – 1 i 2 = [(1.05)(1.09)] 1/2 – 1 = 6.98%

18. 18 The Expectations Theory  You will no longer be indifferent between the two options  you and others will want short-term securities  those who own long-term securities will want to sell them and buy short-term securities  the price of long-term securities will fall and their yields will rise  this will continue until the long rate rises to 6.98%

19. 19 The Expectations Theory  The interest rate changed as a result of a change in the interest rate expectations of the lender  affected the demand for securities  The expectations of the borrower are also important

20. 20 The Expectations Theory  When borrowers believe that the average rate of current and expected future short- term securities is greater than the rate on long-term securities, they will increase their supply of long-term securities  this will lower the price of existing long-term securities  this will raise the long-term interest rate

21. 21 The Expectations Theory  If expectations about future rates change such that future rates are expected to be higher, the yield curve will shift  the long rate will rise relative to the short rate and the yield curve will get steeper

22. 22 New Hypothetical Yield Curve Term to Maturity Yield to Maturity (percent) 1 5 5.99 original yield curve 2 new yield curve 6.98

23. 23 The Expectations Theory  We can solve for the interest rate expected to prevail in the future by looking at the current structure of interest rates (1 + i 2 ) = [(1 + i 1 )(1 + i e 1 )] 1/2 (1 + i 2 ) 2 = {[(1 + i 1 )(1 + i e 1 )] 1/2 } 2 (1 + i 2 ) 2 = (1 + i 1 )(1 + i e 1 ) (1 + i 2 ) 2 /(1 + i 1 ) = (1 + i e 1 ) i e 1 = [(1 + i 2 ) 2 /(1 + i 1 )] – 1

24. 24 Alternative Yield Curve Shapes  When a rising yield curve is observed in the market, the expected short-term interest rate (i e s ) is expected to rise above current short rates (i s )  A flat yield curve implies that interest rates are expected to remain constant (i e s = i s )  A negatively sloped yield curve implies that interest rates are expected to decline (i e s < i s )

25. 25 Alternative Yield Curve Shapes Yield to Maturity Term to Maturity Yield to Maturity Term to Maturity a.A Rise Expected in Interest Rates (i e s > i s ) Yield to Maturity Term to Maturity b.No Change Expected in Interest Rates (i e s = i s ) c.A Decline Expected in Interest Rates (i e s < i s )

26. 26 Determining Interest Rate Expectations  Remember that the interest rate is determined by several supply and demand factors  This must mean that the expected short-term interest rate must be determined by expectations of Y, M, and p e

27. 27 Determining Interest Rate Expectations  A positively-sloped yield curve reflects expectations of rising interest rates  future increases in income  rising inflation expectations  a reduction in the future growth rate of the money supply  Thus, a positively-sloped yield curve should occur at a business cycle trough and during the first half of the recovery

28. 28 Determining Interest Rate Expectations  A negatively-sloped yield curve reflects expectations of falling interest rates  future declines in income  falling inflation expectations  an increase in the future growth rate of the money supply  Thus, a negatively-sloped yield curve should occur at a business cycle peak and during the early part of a recession

29. 29 Necessary Modifications to the Expectations Theory  Over the last 50 years, yield curves have almost always been positively sloped  do financial market participants always expect short-term interest rates to rise?  Borrowers and lenders may not be indifferent between short- and long-term securities  many borrowers and lenders have preferred habitats 习惯性偏好：修正了的预期理论，假定大部分借贷 者都对预期有偏好，这在一定程度上将市场分成 了短期和长期。

30. 30 Necessary Modifications to the Expectations Theory  Research suggests that investors may be willing to switch preferred habitats from short-term to longer-term financial claims if they are provided a liquidity premium  an extra return required to induce lenders to lend long term rather than short term  the size of the premium is presumed to rise with the term to maturity 流动性补偿：吸引贷方提供长期而非短期资金的额外报 酬。

31. 31 Necessary Modifications to the Expectations Theory  Suppose that the current short rate and the expected short rate are both 5%  according to the expectations theory, the yield curve would be flat  If the issuer of long-term bonds must offer an interest premium to get investors to buy them, the yield curve is actually upward- sloping

32. 32 The Role of Liquidity Premiums Term to Maturity Yield to Maturity (percent) Yield Curve Based on Expectations (i e s = i s ) Liquidity Premium Observed Yield Curve = Expectations (i e s = i s ) + Liquidity Premium

33. 33 Necessary Modifications to the Expectations Theory  We can summarize the relationship between long-term interest rates (i l ), short-term interest rates (i s ), and the liquidity premium (l)

34. 34 Credit Risk  Credit risk refers to the probability of a debtor not paying the principal or interest due on an outstanding debt 信用风险：未偿还债务的借方不归还本金和利息的可 能性。  Three major credit-rating agencies evaluate a borrower’s credit risk and assign the borrower to a particular risk class  Standard & Poor’s  Moody’s  Fitch Investors Service

35. 35 Credit Risk  In the case of business firms, the credit- rating agencies examine several things  the pattern of revenues and costs  the degree of leverage (dependence on borrowed funds)  the past history of debt redemption  the volatility of the industry

36. 36 Credit Risk  In the case of state and local governments, the credit-rating agencies examine several things  the tax base  the level of outstanding debt  the current and expected budget condition  growth in spending

37. 37 Credit Ratings

38. 38 Credit Risk  Investors are generally risk averse  they must be rewarded or compensated with extra interest for accepting more risk  this extra return is called a risk premium  the size increases with the riskiness of the borrower 风险溢价：贷方承担风险的额外补偿或报酬。

39. 39 Taxability  Interest income earned from securities issued by state and local governments is exempt from federal income tax after-tax yield = i – it = i(1 – t) where t is the marginal tax rate  the rate paid on the last dollar of income the taxpayer earns 边际贡献：纳税人为其收入的最后一单位所支付的 税收。

40. 40 Taxability  In general, we would expect the substitution of securities to result in the yield on municipals being approximately equal to the yield on a similarly rated taxable corporate bond minus the portion that is taxed away

41. 41 Taxability  The market will gravitate to the rate that makes the “average” tax payer indifferent between municipals and similarly rated corporate bonds  individuals in high tax brackets will be especially attracted to municipals because they are subject to a tax rate above the average marginal rate

42. 42 Summary of Major Points  The yield curve is a graphical representation of the relationship between interest rates (yields) on a particular security and its term to maturity  a visual depiction of the term structure of interest rates  A unique curve exists for each type of financial asset

43. 43 Summary of Major Points  The most widely accepted explanation for the shape (slope) and position (level) of the yield curve is the expectations theory  postulates that the long-term rate is the geometric average of the current short-term rate and the short-term rates expected to prevail over the term to maturity of the security  takes compounding into effect

44. 44 Summary of Major Points  The slope of the yield curve depends on the interest rates expected to prevail on short- term securities in the future  a positively sloped curve reflects expectations of a rise in future short-term rates  a negatively sloped curve reflects expectations of a fall in future short-term rates

45. 45 Summary of Major Points  Expectations about future short-term rates depend on expectations about future income, the money supply and inflation  as expectations about these variables change, expected short-term rates will change, resulting in a change in the slope and level of the yield curve

46. 46 Summary of Major Points  The expectations theory is an incomplete explanation of the term structure of interest rates  it has been modified to take account of liquidity premiums  Long-term rates will be determined by current short-term rates, expected short- term rates, and liquidity premiums

47. 47 Summary of Major Points  Credit risk refers to the probability of a debtor defaulting  the three major credit-rating agencies evaluate a borrower’s probability of default and assign the borrower a risk classification  Since investors are risk averse, they must be offered a risk premium  the size will rise with the riskiness of the borrower

48. 48 Summary of Major Points  Financial investors care about the after-tax return of their investments  since interest earned on municipal securities is exempt from federal income tax, the yield on municipal securities are typically below the yields of other taxable securities with similar credit ratings and terms to maturity