The Yield Curve – The Expectations Hypothesis
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At any point in time there are a large number of
bonds that differ in yields….WHY?
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Risk Characteristics
Tax Characteristics
Liquidity Characteristics
Maturity
The Term Structure of interest rates refers to the yield
differences that are entirely due to maturity.
A plot of yields versus maturity is referred to as the
Yield Curve.
So: Yield Curve and Term Structure are two ways of
saying the same thing.
A recent plot of yields (from February 11) on Government
Securities
Historical plot of Long-Term and Short-Term
Rates
Figure 5.4
Short-Term and Long-Term Interest Rates
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18
14
Long-Term
Interest Rate
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10
8
6
4
Short-Term
Interest Rate
2
0
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Interest rate (percent)
16
Date
Note: Long rates are typically greater than short rates:
Yield curve is typically upward sloping.
The critical question: why do bonds with different
maturities have different yields?
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The most common answer: The Expectations
Hypothesis of the Term Structure.
The current yields on bonds with different maturities
reflects investors expectations of future interest rates.
Basic intuition: the yields on holding a long term bond
until maturity is equal to the expected yield from
purchasing a sequence of short bonds.
Consider a simple setting: just one- and two-year
bonds. And suppose there is no uncertainty. Then
arbitrage requires
Expectations hypothesis, continued
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The expectations hypothesis replaces the future rate
with its expected value
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Define the implied one-period forward rate as:
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The forward rate is an unbiased predictor of the future
spot rate:
One of the most tested relationships in finance!!
The forecasts of interest rates based on the expectations hypothesis
Figure 5.A
Forecasts of Short-Term Interest Rates
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10
8
Forecast made four quarters ago
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Forecast made one quarter ago
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2
Actual
Year
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0
1982
Interest Rate (percent)
12
Comparing the accuracy of the forecasts – short and long term
Figure 5.C
Scatter Plot of Actual Interest Rate
Versus Forecast Made One Year Earlier
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12
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10
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8
8
Forecast
Forecast
Figure 5.B
Scatter Plot of Actual Interest Rate
Versus Forecast Made One Quarter Ago
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2
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0
0
0
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Actual
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Actual
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A brief aside: Expectations Hypothesis belongs to a large
class of models. Expectations Based theories of asset pricing
What determines the price of stock (i.e. equity)? In a
world of certainty, it would be the present discounted
value of dividends:
With uncertainty in dividends, replace with expected
value:
A brief aside: Expectations Hypothesis belongs to a large
class of models. Expectations Based theories of asset pricing
What explains the difference in interest rates between
two countries? The expected change in the exchange
rate:
Let
denote the price of foreign currency in term of
domestic currency. Example Euros – then the
exchange rate is:
Note: an increase in the exchange rate is a devaluation in
the home currency
A brief aside: Expectations Hypothesis belongs to a large
class of models. Expectations Based theories of asset pricing
Consider two strategies: buy a dollar denominated bond
or use the dollar to buy euros, then buy a euro
denominated bond, then use the proceeds to buy
dollars at time t+1. If no uncertainty, then we must
have:
Or:
A brief aside: Expectations Hypothesis belongs to a large
class of models. Expectations Based theories of asset pricing
With uncertainty, replace future exchange rate with its
expected value (this is uncovered interest rate parity):
If the one-year interest rate in the US is 10% greater
than in Euroland, then this implies that the dollar is
expected to devalue by 10% over the next year.
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Spread (percent)
The yield curve seems to predict recessions
F ig u re 5 .1 5
T h e T e rm S p re a d a n d R e c e s s io n s
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1
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-1
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-3
D a te