What is an Interpolated Yield Curve?

Using on-the-run treasuries to make a yield curve gives us an estimated yield curve, or Interpolated Yield Curve. Since on-the-run Treasuries can only be bought at specific dates, the yield of maturities in between the on-the-run treasuries has to be calculated. The value of something that isn’t known can be estimated using interpolation, a way to determine what that thing is worth.

Investors and financial experts interpolate yield curves to help them guess how the economy will do and how much bonds will cost. Many methods, such as sampling and regression analysis, can help them do this.

How to Read the Interpolated Yield Curve (I Curve)

The yield curve is the shape made when you put the yield and different maturities of Treasury securities on a graph. As you move along the line, the y-axis shows interest rates, and the x-axis shows more extended periods. It goes up from the bottom left to the right because short-term bonds tend to have smaller yields than longer-term bonds.

It is called an interpolated yield curve, or I curve, when it is made using information about the yield and terms of on-the-run Treasuries. On-the-run Treasury is the U.S. Treasury bills, notes, or bonds with a particular maturity date released most recently.1

On the other hand, off-the-run Treasuries are marketable Treasury debt made up of older issues. The on-the-run Treasury will have a smaller yield and a higher price than an off-the-run issue of the same type. They also only make up a small part of all issued Treasury securities.

Using interpolation

Interpolation is just a way to figure out what something unknown is worth. You sometimes can’t get Treasury securities released by the U.S. government. It’s possible to find the return for a 1-year bond but not a 1.5-year bond.

There are several ways to interpolate missing information to find the value of a missing yield or interest rate and make a yield curve. These include bootstrapping, regression analysis, and others. It is possible to figure out yield spreads from the interpolated yield curve since few of the bonds have terms similar to those of the on-the-run Treasuries.

Investors can use yield curves to help them decide what to buy because they show how the bond market thinks inflation, interest rates, and general economic growth will change in the future.

Getting started

The bootstrapping method uses interpolation to find the yields for Treasury zero-coupon securities with different dates. With this technique, a coupon-bearing bond is stripped of its future cash flows, or coupon payments, and turned into several zero-coupon bonds. Most of the time, you’ll know some rates at the short end of the curve. You can use inter-bank money market prices for rates that aren’t known because there isn’t enough money in the short end.

To sum up, you should first interpolate rates for each missing age. A linear approximation method can help you do this. After you know all the rates for the term structure, use the bootstrapping method to get the zero curve from the par term structure. It is possible to get a zero-coupon yield curve from the rates and prices of bonds that bear coupons by going through several steps.

Unique Things to Think About

The interpolated yield curve is a valuable gauge because many fixed-income assets trade at yield spreads to it. In this case, some agency collateralized mortgage obligations (CMOs) trade at a spread to the I curve where their weighted average lives are equal to a point on the curve. A CMO’s weighted average life will likely fall within the on-the-run bonds. This is why the interpolated yield curve had to be made.

Conclusion

• There is a type of yield curve called an “I curve” that was made by plotting data on the yield and terms of on-the-run Treasuries.
• In a hurry, treasuries are the newest U.S. Treasury bonds or notes with a set expiration date.
• Interpolation is adding new, guesstimated data points to a graph between known data points.
• Bootstrapping and regression analysis are two of the most popular ways to get information from a yield curve.
• This is something that investors and financial experts do all the time to get a better idea of where the economy and bond markets might be going.