1. The Term Structure of Interest Rates
Chapter 15
The Term Structure of Interest Rates

2. Overview of Term Structure of Interest Rates
Relationship between yield to maturity and maturity
Information on expected future short term rates can be implied from yield curve
The yield curve is a graph that displays the relationship between yield and maturity
Three major theories are proposed to explain the observed yield curve

3. Yield Curves
Yields
Maturity
Upward Sloping
Downward Sloping
Flat

4. Expected Interest Rates in Coming Years (Table 15.1)
Expected One-Year Rates in Coming Years
Year Interest Rate
0 (today) 8%
1 10%
2 11%
3 11%

5. Pricing of Bonds using Expected Rates
PVn = Present Value of $1 in n periods
r1 = One-year rate for period 1
r2 = One-year rate for period 2
rn = One-year rate for period n

6. Long-Term Rates and Bond Prices using Expected Rates
Time to Maturity Price of Zero* Yield to Maturity
1 $ %
* $1,000 Par value zero

7. Forward Rates from Observed Long-Term Rates
fn = one-year forward rate for period n
yn = yield for a security with a maturity of n

8. Example of Forward Rates using Table 15.2 Numbers
4 yr = yr = fn = ?
(1.0993)4 = (1.0966)3 (1+fn)
( ) / ( ) = (1+fn)
fn = or 11%
Note: this is expected rate that was used in the prior example

9. Downward Sloping Spot Yield Curve
Zero-Coupon Rates Bond Maturity
12% 1
11.75% 2
11.25% 3
10.00% 4
9.25% 5

10. Forward Rates for Downward Sloping Yield Curve
1yr Forward Rates
1yr [(1.1175)2 / 1.12] =
2yrs [(1.1125)3 / (1.1175)2] - 1 =
3yrs [(1.1)4 / (1.1125)3] =
4yrs [(1.0925)5 / (1.1)4] =

11. Theories of Term Structure
Expectations
Liquidity Preference
Upward bias over expectations
Market Segmentation
Preferred Habitat

12. Expectations Theory
Observed long-term rate is a function of today’s short-term rate and expected future short-term rates
Long-term and short-term securities are perfect substitutes
Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates

13. Liquidity Premium Theory
Long-term bonds are more risky
Investors will demand a premium for the risk associated with long-term bonds
Yield curve has an upward bias built into the long-term rates because of the risk premium
Forward rates contain a liquidity premium and are not equal to expected future short-term rates

14. Liquidity Premiums and Yield Curves
Yields
Observed Yield Curve
Forward Rates
Liquidity Premium
Maturity

15. Liquidity Premiums and Yield Curves
Yields
Observed Yield Curve
Forward Rates
Liquidity Premium
Maturity

16. Market Segmentation and Preferred Habitat
Short- and long-term bonds are traded in distinct markets
Trading in the distinct segments determines the various rates
Observed rates are not directly influenced by expectations
Preferred Habitat
Modification of market segmentation
Investors will switch out of preferred maturity segments if premiums are adequate