Expectation hypothesis

The expectations hypothesis of the term structure of interest rates (whose graphical representation is known as the yield curve) 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 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.

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 ${\displaystyle d_{t}}$ at times ${\displaystyle t=1,2,...}$ and with risk-free rate ${\displaystyle r}$ then the price at time ${\displaystyle t}$ is given by

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