The expectations hypothesis of the
term structure of interest rates
In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or y ...
(whose graphical representation is known as the
yield curve
In finance, the yield curve is a graph which depicts how the Yield to maturity, yields on debt instruments - such as bonds - vary as a function of their years remaining to Maturity (finance), maturity. Typically, the graph's horizontal or ...
) is the proposition that the long-term rate is determined purely by current and future expected short-term rates, in such a way that the expected final value of wealth from investing in a sequence of short-term bonds equals the final value of wealth from investing in long-term bonds.
This hypothesis assumes that the various maturities are perfect substitutes and suggests that the shape of the
yield curve
In finance, the yield curve is a graph which depicts how the Yield to maturity, yields on debt instruments - such as bonds - vary as a function of their years remaining to Maturity (finance), maturity. Typically, the graph's horizontal or ...
depends on market participants' expectations of future interest rates. These expected rates, along with an assumption that arbitrage opportunities will be minimal, is enough information to construct a complete yield curve. For example, if investors have an expectation of what 1-year interest rates will be next year, the 2-year interest rate can be calculated as the compounding of this year's interest rate by next year's interest rate. More generally, returns (1 + yield) on a long-term instrument are equal to the geometric mean of the returns on a series of short-term instruments, as given by
:
where ''lt'' and ''st'' respectively refer to long-term and short-term bonds, and where interest rates ''i'' for future years are expected values.
This theory is consistent with the observation that yields usually move together. However, it fails to explain the persistence in the non-horizontal shape of the yield curve.
Definition
The expectation hypothesis states that the current price of an asset is equal to the sum of expected discounted future dividends conditional on the information known now. Mathematically if there are discrete dividend payments
at times
and with
risk-free rate
The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations.
Since the risk-free ra ...
then the price at time
is given by
: