# Money and Banking

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Money & Banking ­ MGT411
VU
Lesson 17
TAX EFFECT & TERM STRUCTURE OF INTEREST RATE
Tax Effect
Term Structure of Interest Rate
Expectations Hypothesis
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
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.
Figure: The U.S. Treasury Yield Curve
___Yesterday
6.0%
___1 month ago
___1 year ago
5.0
The figure plots the
4.0
yields on Treasury
bills and bonds for
3.0
August 27, 2004.
2.0
1.0
0
1
3
6
2
5
10
30
Months
Years
________ Maturity________
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Money & Banking ­ MGT411
VU
Figure: The Term Structure of Treasury Interest Rates
18
16
14
12
10
8
6
4
2
0
1979
1983
1987
1991 1995 1999
1971 11975
2003
___3 months T.Bills_____10 years T-Bonds
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
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)
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Money & Banking ­ MGT411
VU
Figure: Yield Curve
Yield curve when interest rates are expected to
rise
Time to maturity
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
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 + i  2y )(1 + i  2y )
Return from one year bond and then another one year bond
(1 + i  1y )(1 + i  1y )
e
If one and two year bonds are perfect substitutes, then:
(1 + i  2y )(1 + i  2y ) = (1 + i  1y )(1 +  1y )
e
Or
i1y + i1y
2
i  2y =
2
Or in general terms
i1 t + i1et + 1 + i1et + 2 + .... + i1et + n - 1
=
i  nt
n
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
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Money & Banking ­ MGT411
VU
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
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
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