Editing Yield curve (section)

===Market expectations (pure expectations) hypothesis===
{{main|Expectations hypothesis}}

This [[hypothesis]] assumes that the various maturities are [[Substitute good|perfect substitutes]] and suggests that the shape of the yield curve depends on market participants' expectations of future interest rates. It assumes that market forces will cause the interest rates on various terms of bonds to be such that the expected final value of a sequence of short-term investments will equal the known final value of a single long-term investment. If this did not hold, the theory assumes that investors would quickly demand more of the current short-term or long-term bonds (whichever gives the higher expected long-term yield), and this would drive down the return on current bonds of that term and drive up the yield on current bonds of the other term, so as to quickly make the assumed equality of expected returns of the two investment approaches hold.

Using this, [[futures contract|futures rates]], along with the assumption that [[arbitrage]] opportunities will be minimal in future markets, and that futures rates are unbiased estimates of forthcoming spot rates, provide enough information to construct a complete expected yield curve. For example, if investors have an expectation of what 1-year interest rates will be next year, the current 2-year interest rate can be calculated as the compounding of this year's 1-year interest rate by next year's expected 1-year interest rate. More generally, returns (1+ yield) on a long-term instrument are assumed to equal the [[geometric mean]] of the expected returns on a series of short-term instruments:

: <math>(1 + i_{lt})^n=(1 + i_{st}^{\text{year }1})(1 + i_{st}^{\text{year }2}) \cdots (1 + i_{st}^{\text{year }n}),</math>

where ''i''<sub>''st''</sub> and ''i''<sub>''lt''</sub> are the expected short-term and actual long-term interest rates (but <math>i_{st}^{\text{year}1}</math> is the actual observed short-term rate for the first year).

This theory is consistent with the observation that yields usually move together. However, it fails to explain the persistence in the shape of the yield curve.

Shortcomings of expectations theory include that it neglects the [[interest rate risk]] inherent in investing in bonds.