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

2. Overview of Term Structure
Information on expected future short term rates can be implied from the 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. Figure 15.1 Treasury Yield Curves

4. Bond Pricing Yields on different maturity bonds are not all equal
Need to consider each bond cash flow as a stand-alone zero-coupon bond when valuing coupon bonds

5. Table 15.1 Yields and Prices to Maturities on Zero-Coupon Bonds ($1,000 Face Value)

6. Yield Curve Under Certainty
An upward sloping yield curve is evidence that short-term rates are going to be higher next year
When next year’s short rate is greater than this year’s short rate, the average of the two rates is higher than today’s rate

7. Figure 15.2 Two 2-Year Investment Programs

8. Figure 15.3 Short Rates versus Spot Rates

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

10. Example 15.4 Forward Rates 4 yr = 8.00% 3yr = 7.00% fn = ?
fn = or 11.06%

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

12. Forward Rates for Downward Sloping Y C Example
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] =

13. Interest Rate Uncertainty
What can we say when future interest rates are not known today
Suppose that today’s rate is 5% and the expected short rate for the following year is E(r2) = 6% then:
The rate of return on the 2-year bond is risky for if next year’s interest rate turns out to be above expectations, the price will lower and vice versa

14. Interest Rate Uncertainty Continued
Investors require a risk premium to hold a longer-term bond
This liquidity premium compensates short-term investors for the uncertainty about future prices

15. Theories of Term Structure
Expectations
Liquidity Preference
Upward bias over expectations

16. 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

17. Liquidity Premium Theory
Long-term bonds are more risky
Investors will demand a premium for the risk associated with long-term bonds
The 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

18. Figure 15.4 Yield Curves

19. Figure 15.4 Yield Curves (Concluded)

20. Interpreting the Term Structure
If the yield curve is to rise as one moves to longer maturities
A longer maturity results in the inclusion of a new forward rate that is higher than the average of the previously observed rates
Reason:
Higher expectations for forward rates or
Liquidity premium

21. Figure 15.5 Price Volatility of Long-Term Treasury Bonds

22. Figure 15.6 Term Spread: Yields on 10-Year Versus 90-Day Treasury Securities

23. Forward Rates as Forward Contracts
In general, forward rates will not equal the eventually realized short rate
Still an important consideration when trying to make decisions :
Locking in loan rates

24. Figure 15.7 Engineering a Synthetic Forward Loan