Money and Banking: Lecture 17

Money and
Banking

Lecture 17


Review of the Previous Lecture
• Bonds and Risk
• Default Risk
• Inflation Risk
• Interest Rate Risk

• Bond Ratings
• Bond Ratings and Risk


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


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


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).


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.


Term Structure of Interest Rates


Term Structure of Interest Rates
Term Structure of Treasury Interest Rates

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.


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


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)


i r ut a mot dl ei Y

Expectations Hypothesis

Yield curve when interest rates are
expected to rise
Time to maturity


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


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

(1 i2y )(1 i2y )
Return from one year bond and then another one year bond

e
1y

(1 i1y )(1 i )


Expectations Hypothesis
If one and two year bonds are perfect substitutes, then:

(1 i2y )(1 i2y ) (1 i1y )(1
Or

i2y

e

1y

)

2
1y

i1y i
2

Or in general terms

int

i1t

e
1t 1

i

e
1t 2

i

n

e
1t n 1

.... i


Expectations Hypothesis
•

•

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


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


Summary

• Bonds
• Tax Effect
• Term Structure of Interest Rate
• Expectations Hypothesis
• Liquidity Premium