1. The Structure of Interest Rates
Risk Structure

2. Risk Structure in Interest Rates
The risk structure of interest rates refers to difference in the yields on instruments that have the same term to maturity.
Why do securities with the same term to maturity have different interest rates?
Default risk
Liquidity
Tax considerations

3. Interest Rate Differences
Yields differ because of differences in default risk, liquidity, and tax treatment
Default risk
You lose your asset.
Liquidity
Your ability to convert your asset into cash is less than that of another asset.
Tax treatment
Favorable tax treatment for your security results in lower interest rates.

4. Default Risk
Default occurs when there is a failure to fully meet the terms of a contractual agreement.
Failure to pay the full interest specified.
Failure to redeem the bond at face value at maturity.
Delay in the receipt on interest.
A premium for default risk is embedded in a security’s yield.

5. Default Risk Risk Premium Corporate Bond Market U.S. Treasury Bond
Price
Yield
Price
Yield S S
i2t
i1t
P2t
P1t
P1c
P2c
i1c
i2c
D2t
Risk
Premium
D1t
D2c
D1c
Quantity of Corporate Bonds
Quantity of Treasury Bonds
Corporate Bond
Market
U.S. Treasury Bond
Market

6. Default Risk Premium Let the default risk on corporate bonds rise.
The demand for corporate bonds falls from D1c to D2c.
The price of corporate bonds falls from P1c to P2c, and the yield on corporate bonds rises from i1c to i2c.
Simultaneously, the demand for Treasury bonds increases from D1t to D2t.
The price of Treasury bonds rises from P1t to P2t, and the yield on Treasury bonds falls from i1t to i2t.
The risk premium is i2c - i2t.

7. Liquidity
Liquidity is defined as the ability of an asset to be quickly and cheaply converted into cash.
Other things remaining the same, the more liquid an asset is the more attractive it is.
U.S. Treasury bonds are the most liquid of all long term bonds because they are the easiest and least costly of all bonds to sell.
They are widely traded.
Corporate bonds are less liquid.

8. Liquidity Risk Premium U.S. Treasury Bond Corporate Bond Market Market
Price
Yield
Price
Yield S S
i2t
i1t
P2t
P1t
P1c
P2c
i1c
i2c
D2t
Risk
Premium
D1t
D2c
D1c
Quantity of Corporate Bonds
Quantity of Treasury Bonds
U.S. Treasury Bond
Market
Corporate Bond
Market

9. Liquidity
Assume that corporate bonds and Treasury bonds are equally liquid and that all their other attributes are the same.
Equilibrium prices and yields are identical.
Let the liquidity of the corporate bond decrease because it is less widely traded.

10. Liquidity Let the liquidity on corporate bonds fall.
The demand for corporate bonds falls from D1c to D2c.
The price of corporate bonds falls from P1c to P2c, and the yield on corporate bonds rises from i1c to i2c.
Simultaneously, the demand for Treasury bonds increases from D1t to D2t.
The price of Treasury bonds rises from P1t to P2t, and the yield on Treasury bonds falls from i1t to i2t.
The risk premium is i2c - i2t.

11. Income Tax Considerations
Price
Yield
Price
Yield S S
P1m
P2m
i2m
i1m
P1t
P2t
i1t
i2t
D2m
D1t
D1m
D2t
Quantity of Municipal Bonds
Quantity of Treasury Bonds
Municipal Bond
Market
U.S. Treasury Bond
Market

12. Income Tax Considerations
Let municipal bonds be given tax-free status.
The demand for municipal bonds increases from D1m to D2m.
The price of municipal bonds rises, and the yield falls.
The demand for Treasury bonds falls from D1t to D2t.
The price of Treasury bonds falls, and the yield rises.

13. Tax Considerations
Assume a 50% income tax bracket. You own a bond that sells for $1,000 and pays a $100 coupon. Since half of your coupon is taxed away, your after tax yield is $50 or 5%.
Assume you own a tax-free municipal. It sells for $1,000 and pays an $80 coupon. Since it is tax-free, you receive the full coupon payment, and your after-tax yield is 8%.

14. Summary: Risk Structure of Interest Rates
The risk structure of interest is explained by:
Default risk, liquidity, and tax treatment.
As a bond’s default risk increases and/or its liquidity decreases, its price falls and its interest rate rises.
If a bond receives favorable tax treatment, its price rises, and its interest rate falls.

15. Interest Rate Determination Becomes...
Nominal Rate = Real Rate
+ Expected Inflation
+ Risk Premium

16. The Structure of Interest Rates
Term Structure

17. The Term Structure of Interest Rates
The term structure of interest rates refers to difference in the yields on instruments that are identical except for term to maturity.
Term structure is represented graphically by a yield curve.
Yield curves consider only the relationship between maturity or term of a security and its yield at a moment in time, otrs.

18. Term Structure Time to maturity affects interest rates because
Time increases exposure to risk, causing investors to demand higher yields on securities with longer maturities.

19. Yield Curves Shapes: Upward sloping Downward sloping Horizontal
Interest rates on securities with longer maturities exceed interest rates on shorter term securities.
Downward sloping
Interest rates on securities with longer maturities are less than interest rates on shorter term securities.
Horizontal
Interest rates on long and short term securities have approximately the same interest rates.

20. Treasury Yield Curve
February 4, 2005

21. Treasury Yield Curve Yields as of 4:30 p.m. on Wednesday 4.50
Feb 7, 2002
3.00
Jan 30, 2002
Dec 6, 2001
3.00
1.50
3mo 6mo 2yr yr 10yr 30yr
Maturities

22. Treasury Yield Curve Yields as of 4:30 p.m. on Wednesday 6.00
Jan 17, 2000
5.50
Jan 10, 2000
Dec 9, 1999
5.00
4.50
3mo 6mo 1yr 2yr 5yr 10yr 30yr
Maturities

23. Understanding the Yield Curve
Any theory that is used to analyze term structure should be able to explain the following:
Why interest rates on bonds of different maturities move together over time.
Why yield curves slope up when short term interest rates are low and down when short term interest rates are high.
Why yield curves almost always slope up.

24. Yield Curve Theories Expectations hypothesis
Explains facts 1 and 2, but not 3.
Segmented markets hypothesis
Explains facts 3, but not 1 and 2.
Preferred habitat and liquidity hypotheses
Explains facts 1, 2, and 3.

25. Expectations Hypothesis
Assumptions:
All investors are wealth maximizers.
No investor has a specific preference about the maturity or term of a security.
Bonds of different maturities are perfect substitutes.
Investors try to achieve the highest possible rate of return from holding one or more securities and are willing to move freely from one maturity to another.

26. Expectations Hypothesis: Example
Assume investors have only two options for investing over a three year period.
Option 1 is to buy a bond that matures in one year, reinvest the proceeds from the bond at the end of the year in another one year bond, and follow the same procedure at the end of the second year.
Option 2 is to purchase a security that matures in three years and hold it to maturity.

27. Expectations Hypothesis: Example
To make a decision between option 1 and option 2, an investor needs to know:
The rate currently earned on one year bonds and the expected rates on year 2 and year 3 bonds.
Assume the following:
A one year bond yields 4%
One year bonds are expected to yield 5% in year 2 and 6% in year 3.

28. Expectations Hypothesis: Example
What is the minimum accepted yield on a three year security?

29. Expectations Hypothesis: Example
Yield .
The yield curve slopes up when
expectations of future yields are rising
because long term interest rates equal
the average of short term interest rates
expected to occur over the life of the
long term bond. 5 4 .
1 3
Time

30. The Shape of the Yield Curve
The expectations hypothesis can explain why the yield curve changes shape.
Expectations of rising yields mean that investors expect bond prices to fall.
Since long-term bond prices fall by more than short- term bond prices, wealth maximizing investors sell long-term bonds and move into cash equivalents or short-term bonds.
The decrease in demand causes long-term bond prices to fall and long term yields to rise.
The yield curve slopes up and/or becomes steeper.

31. Expectations of Rising Rates
Price
Yield
Price
Yield S S i2 i1 P2 P1 P1 P2 i1 i2 D2 D1 D2 D1
Quantity of Long Term Bonds
Quantity of Short Term Bonds
Upward Sloping Yield Curve

32. The Shape of the Yield Curve
The expectations hypothesis can explain why the yield curve changes shape.
Expectations of falling yields mean that investors expect bond prices to rise.
Since long-term bond prices rise by more than short-term bond prices, wealth maximizing investors buy long-term bonds and move out of cash equivalents and short-term bonds.
The increase in demand causes long-term bond prices to rise and long-term yields to fall.
The yield curve slope flattens or inverts

33. Expectations of Falling Rates
Price
Yield
Price
Yield S S i1 P1 P1 i1 D1 D1
Quantity of Long Term Bonds
Quantity of Short Term Bonds
Downward Sloping Yield Curve
Your turn

34. Expectations Hypothesis: Summary
The expectations hypothesis can explain why….
Interest rates on bonds with different maturities move together over time.
A rise in short-term rates raises people’s expectations of future short term rates.
Long-term rates are an average of expected short rates so they rise when short-term rates rise.

35. Expectations Hypothesis: Summary
The expectations hypothesis can explain why…
Yield curves tend to have an upward slope when short term rates are low.
When short term rates are low, people expect them to rise in the future. This causes the average of future expected short rates to be high relative to current short term rates. Consequently, long rates will rise, and the the yield curve will slope up.

36. Expectations Hypothesis: Summary
The expectations hypothesis cannot explain why…
Yield curves usually slope upward.
In reality, interest rates are just as likely to fall as to rise, so the yield curve if determined by expectations should be flat.

37. Segmented Markets Hypothesis
Assumptions:
All investors are wealth maximizers.
Investors have specific preferences about the maturity or term of a security.
Investors do not stray from their preferred maturity.
Investors try to achieve the highest possible rate of return from holding one or more securities, but they do not move from one maturity to another.

38. Segmented Markets Hypothesis
The slope of the yield curve is explained by different demand and supply conditions for bonds of different maturities.
If the yield curve slopes up, it does so because the demand for short term bonds is relatively greater than the demand for long term bonds.
Short term bonds have a higher price and a lower yield as a result of the relatively greater demand. So the yield curve slopes upward.

39. Segmented Markets Hypothesis
Price
Yield
Price
Yield S S
P2s
P1s
i2s
i1s
P1l
P2l
i1l
i2l
D2s
D1l
D1s
D2l
Quantity of Short-term Bonds
Quantity of Long-term Bonds
Upward Sloping Yield Curve

40. Segmented Markets Hypothesis
The slope of the yield curve is explained by different demand and supply conditions for bonds of different maturities.
If the yield curve slopes down, it does so because the demand for short term bonds is relatively less than the demand for long term bonds.
Therefore, short-term bonds have a lower price and a higher yield. So the yield curve slopes down.

41. Segmented Markets Hypothesis
Price
Yield
Price
Yield S S
P1s
i1s
P1l
i1l
D1l
D1s
Quantity of Short-term Bonds
Quantity of Long-term Bonds
Your turn!
Downward Sloping Yield Curve

42. Segmented Markets Hypothesis
The segmented markets hypothesis explains why….
Yield curves typically slope upward.
On average investors prefer bonds with shorter maturities that have less interest rate risk.
Therefore, the demand for short term bonds is relatively greater than the demand for long-term bonds

43. Segmented Markets Hypothesis
The segmented markets hypothesis cannot explain why…
Interest rates on different maturities move together.
The segmented markets hypothesis assumes that short and long markets are completely segmented.
Yield curves slope up when interest rates are low and down when interest rates are high.
It is not clear how demand and supply for short versus long term bonds changes with the level of short term interest rates.

44. Preferred Habitat Hypothesis
Assumptions:
All investors are wealth maximizers.
Bonds of different maturities are treated as substitutes, but not perfect substitutes.
Investors prefer one maturity over another
Short-term bonds are preferred to long-term bonds because investors are risk averse.

45. Preferred Habitat Hypothesis
Investors try to achieve the highest possible rate of return from holding one or more securities.
Investors are willing to move from one maturity to another, but they have a preferred habitat.

46. Preferred Habitat/Liquidity Premium Hypothesis
Preferred Habitat Hypothesis
Interest rates on long-term bonds equal an average of short-term rates that are expected to occur over the life of the bond plus a term premium that responds to supply and demand conditions for that bond.
Liquidity Premium Hypothesis
A positive term (liquidity) premium must be offered to buyers of longer term bonds to compensate them for their increased risk.

47. Preferred Habitat/Liquidity Premium
The preferred habitat and liquidity premium theories can explain why…
Interest rates on different maturity bonds move together over time.
A rise in short-term interest rates indicates that short-term rates will, on average, be higher in the future.
The liquidity premium on long-term bonds ensures an upward sloping yield curve.

48. Preferred Habitat/Liquidity Premium
The preferred habitat and liquidity premium theories can explain why…
Yield curves tend to have a steep upward slope when short term interest rates are low.
When short-term interest rates are low, investors expect them to rise to some normal level.
Therefore, the average of future expected short-term rates will be high relative to the current short rates.
Given the existence of a liquidity premium, long rates must be substantially above current short rates.

49. Preferred Habitat/Liquidity Premium
The preferred habitat and liquidity premium theories can explain why….
Yield curves tend to slope down when short term interest rates are high.
When short-term interest rates are high, investors expect them to fall to some normal level.
Therefore, the average of future expected short-term rates will be low relative to the current short rates.
Given the existence of a liquidity premium, long rates will be below current short rates, if rates are expected to fall by more than the liquidity premium.

50. Preferred Habitat/Liquidity Premium
The preferred habitat and liquidity premium theories can explain why…
Yield curves typically slope upward.
The term premium rises with a bond’s maturity because of investors’ preferences for short term bonds.

51. Yield Curves Conclusions:
A steeply rising yield curve indicates that short-term interest rates are expected to rise in the future.
A moderately rising yield curve indicates that short-term interest rates are not expected to rise or fall much in the future.
A flat yield curve indicates that short-term rates are expected to fall moderately in the future.
An inverted yield curve indicates that short-term interest rates are expected to fall sharply in the future.

52. Interest Rate Determination Becomes...
Nominal Rate = Real Rate
+ Expected Inflation
+ Risk Premium
+ Maturity Premium
+ Liquidity Premium