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# Term structure of Interest Rates.docx

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Brock University

Economics

ECON 3P03

Zisimos Koustas

Fall

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Term structure of Interest Rates.
A bond’s term to maturity also affects interest rates.
A plot of the yields to maturity on bonds with different terms to maturity but the same default risk,
liquidity, and tax considerations is called a yield curve.
Yield-curve Stylized Facts to be Explained
1. Interest rates for different maturities move together (yield curves shift up and down).
1. Yield curves tend to have a steep slope when short rates are low and downward slope when short rates are
high.
2. The yield curve is typically upward sloping.
See Graph T7.7
Three theories of the term structure
1. The Expectations Hypothesis
2. The Segmented Markets Theory
3. The Preferred Habitat Theory
a) The Expectations Hypothesis
Key assumption: Bonds of different
Maturities are perfect substitutes (investors are “risk neutral”). Implication: investors expect the same
yield to maturity from a two-year bond as they do from a one-year bond that’s rolled over for a second year
(with interest reinvestment).
Investment strategies for a two-year holding period
1. Buy $1 of a two-year bond and hold it for two years.
2. Buy $1 of one-year bond. When it matures, buy another one-year bond (using principal plus interest)
Expected return (value at the end of holding period) form strategy 1
(1+i2t)(1+i2t)=(1+ 2t)^2 (1)
Expected return from strategy 2
(1+i1t)(1+I^ e 1t+1 ) (2)
From the implication mentioned above:
(1+i2t)^2=(1+i1t)(1+i^ e 1t+1 ) (3) or i2t=(1+i1t)(1+i^ e 1t+1 )]^(1/21 – (4)
The last relationship between the yield to maturity of a long-term bond and the current and expected one-
period yield can be generalized as follows:
iNt=[(1+i1t)(1+i^ e 1t+1 )+…+ (1+i^ e 1t+N )]^(1/N)1– (5)
In words, the yield to maturity on a long bond is equal to the geometric average of short rates that
are expected to occur over the life of the long bond.
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