Interpolated Yield Curve (I Curve)

An interpolated yield curve (I curve) is a yield curve derived by using on-the-run Treasuries. Because on-the-run treasuries are limited to specific maturities, the yield of maturities that lies between the on-the-run treasuries must be interpolated. It can be accomplished by a number of methodologies, including bootstrapping and regressions.

The yield curve is the curve that is formed on a graph when the yield and various maturities of Treasury securities are plotted. The graph is plotted with the y-axis depicting interest rates, and the x-axis showing the increasing time durations. Since short-term bonds typically have lower yields than longer-term bonds, the curve slopes upwards from the bottom left to the right.

When the yield curve is plotted using data on the yield and maturities of on-the-run Treasuries, it is referred to as an interpolated yield curve, or I curve. Note that on-the-run Treasuries are the most recently issued U.S. Treasury bills, notes, or bonds, of a particular maturity. Conversely, off-the-run Treasuries are marketable Treasury debt consisting of more seasoned issues. The on-the-run Treasury will have a lower yield and higher price than a similar off-the-run issue, and they only make up a small percentage of the total issued Treasury securities.

Interpolation is simply a method used to determine the value of an unknown entity. Treasury securities issued by the U.S. government are not available for every period of time. For example, you will be able to find the yield for a 1-year bond, but not a 1.5-year bond. To determine the value of a missing yield or interest rate to derive a yield curve, the missing information can be interpolated using various methods including bootstrapping or regression analysis. Once the interpolated yield curve has been derived, yield spreads can be calculated from it, as few of the bonds have maturities comparable to those of the on-the-run Treasuries.

The bootstrapping method uses interpolation to determine the yields for Treasury zero-coupon securities with various maturities. Using this method, a coupon-bearing bond is stripped of its future cash flows, that is, coupon payments, and converted into multiple zero-coupon bonds. Typically, some rates at the short end of the curve will be known. For rates that are unknown due to insufficient liquidity at the short end, inter-bank money market rates can be used.

To recap, first interpolate rates for each missing tenor. It can be done using a linear interpolation method. Once all the term structure rates have been determined, use the bootstrapping method to derive the zero curve from the par term structure. It is an iterative process that makes it possible to derive a zero coupon yield curve from the rates and prices of coupon-bearing bonds.

Several different types of fixed-income securities trade at yield spreads to the interpolated yield curve, making it an important benchmark. For example, certain agency Collateralized Mortgage Obligations (CMOs) trade at a spread to the I curve at a spot on the curve equal to their weighted average lives. A CMO's weighted average life will most likely lie somewhere within the on-the-run treasuries, which makes the derivation of the interpolated yield curve necessary.