1. Money and Banking
Lecture 17

2. Review of the Previous Lecture
Bonds and Risk
Default Risk
Inflation Risk
Interest Rate Risk
Bond Ratings
Bond Ratings and Risk

3. Topics under Discussion
Tax Effect
Term Structure of Interest Rate
Expectations Hypothesis
Liquidity Premium

4. Tax Effect
The second important factor that affects the return on a bond is taxes
Bondholders must pay income tax on the interest income they receive from privately issued bonds (taxable bonds), but government bonds are treated differently
Interest payments on bonds issued by state and local governments, called “municipal” or “tax-exempt” bonds are specifically exempt from taxation

5. Tax Effect
A tax exemption affects a bond’s yield because it affects how much of the return the bondholder gets to keep
Tax-Exempt Bond Yield
= (Taxable Bond Yield) x (1- Tax Rate).

6. Term Structure of Interest Rates
The relationship among bonds with the same risk characteristics but different maturities is called the term structure of interest rates.
A plot of the term structure, with the yield to maturity on the vertical axis and the time to maturity on the horizontal axis, is called the yield curve.

7. Term Structure of Interest Rates

8. Term Structure of Interest Rates
Term Structure of Treasury Interest Rates

9. Term Structure of Interest Rates
Term Structure “Facts”
Interest Rates of different maturities tend to move together
Yields on short-term bond are more volatile than yields on long-term bonds
Long-term yields tend to be higher than short-term yields.

10. Expectations Hypothesis
The risk-free interest rate can be computed, assuming that there is no uncertainty about the future
Since certainty means that bonds of different maturities are perfect substitutes for each other, an investor would be indifferent between holding
a two-year bond or
a series of two one-year bonds
Certainty means that bonds of different maturities are perfect substitutes for each other

11. Expectations Hypothesis
Assuming that current 1-year interest rate is 5%. The expectations hypothesis implies that the current 2-year interest rate should equal the average of 5% and 1-year interest rate one year in future.
If future interest rate is 7%, then current 2-year interest rate will be (5+7) / 2 = 6%
Therefore, when interest rates are expected to rise long-term rates will be higher than short-term rates and the yield curve will slope up (and vice versa)

12. Expectations Hypothesis
Yield to maturity
Yield curve when interest rates are expected to rise
Time to maturity

13. Expectations Hypothesis
From this we can construct investment strategies that must have the same yield.
Assuming the investor has a two-year horizon, the investor can:
invest in a two-year bond and hold it to maturity
Interest rate will be i2y
Investment will yield (1 + i2y) (1 + i2y) two years later
invest in a one-year bond today and a second one a year from now when the first one matures
Interest rate will be iey+1
Investment will yield (1 + i1y) (1 + iey+1) in two years

14. Expectations Hypothesis
The hypothesis tells us that investors will be indifferent between the two strategies, so the strategies must have the same return
Total return from 2 year bonds over 2 years
Return from one year bond and then another one year bond

15. Expectations Hypothesis
If one and two year bonds are perfect substitutes, then: Or
Or in general terms

16. Expectations Hypothesis
Therefore the rate on the two-year bond must be the average of the current one-year rate and the expected future one-year rate
Implications would be the same old
Interest rates of different maturities tend to move together.
Yields on short-term bonds are more volatile than those on long-term bonds.
Long-term yields tend to be higher than short-term yields

17. Expectations Hypothesis
However, expectations theory can not explain why long-term rates are usually above short term rates
In order to explain why the yield curve normally slopes upward, we need to extend the hypothesis to include risk

18. Summary Bonds Tax Effect Term Structure of Interest Rate
Expectations Hypothesis
Liquidity Premium