A yield curve is a graphical representation of the mathematical function in relation to the effective interest rate at a given instant of a zero-coupon based on maturity of the same class of fungible instruments such as swaps, expressed in the same currency.
By extension, it is used for instruments not fungible but nevertheless highly comparable, as the fixed rate debt of the same state. The yield is called flat if the interest rate is independent of the commitment period. However, this is an exception as they occur when long-running title (bond) interest rates are paid less than for short-term permits.
The yield is graphically demonstrated in the so-called yield curve. With the short end referring to the maturity of one year and with the long end of the period from about five years to ten years in some countries, and up to thirty years in the United States. A similar indicator is the interest rate spread.
The term structure is of a great importance to economic researchers in the assessment of future development of financial markets and the economy. The interest rate is generally dependent on the duration, the risk of the tax treatment and other properties of the corresponding financial instruments.
The pure expectation hypothesis follows from the assumption of full information efficiency of the market and the assumption of full risk-neutrality of the active subjects.
If the market expects rising interest rates, investors invest preferably in short term notes, that is, demand accumulates on the short end of the yield curve. This limits, increment of the return on short-term title and on the interest-rate curve (normal yield curve). And if the market expects interest rates to fall, investors in turn invest their capital on higher interest rates rather long term title. Through the interplay of supply and demand the inverted yield evolves.
The expectations hypothesis provides the conceptual basis for the calculation of forward rates and implied forward rates that correspond to the expected spot rates.
Only the swap market allows the drawing of a real yield curve. Unlike securities, they have no physical existence, and they are fully fungible and contractible to their discount factors. In addition, their stock is practically unlimited, their market prices can be much more consistent and mathematically less dependent on supply and demand of bond prices, even the most liquid of government bonds.
Furthermore, the swaps provide a curve at par, that is, the yield to maturity equals the coupon rate, without distortions due to the off-market coupon rate. The yield curve can be used in the valuation of fixed income securities, and can calculate the theoretical price and exchange rate. Thus the sensitivity of the fixed interest rate and price of the title to interest rate changes can be reliably measured.
Moreover, the yield curve is also suitable for the calculation of implied forward rates, scenario analysis and for the valuation of interest rate derivatives.