# What Is an Interpolated Yield Curve (I Curve)?

An interpolated yield curve, also known as an "I curve," is a graphical representation of the yields and maturities of the latest U.S. Treasury bonds or notes, called on-the-run Treasuries. Interpolation is the process of estimating new data points between known data points on a graph. Two common methods for interpolating a yield curve are bootstrapping and regression analysis. By interpolating yield curves, investors and financial analysts can better understand the future direction of the bond markets and the economy.

## Basics

Yield curves, specifically the Interpolated Yield Curve (I curve), are constructed using on-the-run Treasuries. These Treasuries, limited to specific maturities, necessitate interpolating yields for maturities lying between them. Interpolation, a numerical analysis technique, is employed to ascertain the value of unknown entities.

Financial professionals, such as analysts and investors, employ yield curve interpolation to anticipate future economic trends and bond market prices. Various methodologies, including bootstrapping and regression analysis, are utilized in this predictive process.

## Exploring Interpolated Yield Curves in Treasury Securities

The graphical representation of Treasury security yields across different maturities gives rise to the yield curve, a fundamental tool for understanding market dynamics. This graph positions interest rates on the y-axis against time durations on the x-axis, manifesting an upward slope due to the typical yield hierarchy of shorter-term versus longer-term bonds.

When the focus shifts to on-the-run Treasuries, the resulting yield curve earns the title of an Interpolated Yield Curve (I Curve). On-the-run Treasuries denote the latest issuances of U.S. Treasury bills, notes, or bonds, specifically of a given maturity.

In contrast, off-the-run Treasuries represent more mature debt issues within the market. Notably, on-the-run Treasuries command lower yields and higher prices compared to their off-the-run counterparts, constituting a minority among the total Treasury securities in circulation.

Interpolation is a pivotal method to deduce values for unavailable data points, an essential need when dealing with gaps in the Treasury security spectrum. To bridge these gaps in yield and interest rate information, methodologies such as bootstrapping and regression analysis come into play. The resultant interpolated yield curve facilitates the calculation of yield spreads, which is particularly pertinent given the scarcity of bonds with maturities aligning closely with on-the-run Treasuries.

Crucially, as yield curves encapsulate the market's outlook on future inflation, interest rates, and overall economic growth, investors leverage these insights for informed decision-making in their investment strategies.

## Yield Curve Generation Through Bootstrapping Technique

In financial methodologies, bootstrapping employs interpolation to ascertain yields for Treasury zero-coupon securities across various maturities. This technique converts a coupon-bearing bond into multiple zero-coupon bonds. Initial rates at the short end of the curve are typically available, with inter-bank money market rates stepping in for short-end gaps caused by liquidity constraints.

To summarize, the process begins by linearly interpolating rates for absent maturities. Subsequently, utilizing the bootstrapping method, the zero curve is derived from the par term structure. This iterative procedure enables the extraction of a zero-coupon yield curve from the amalgamation of rates and prices associated with coupon-bearing bonds.

## Yield Spread Dynamics in Fixed-Income Securities

Within the fixed-income market, diverse securities exhibit yield spreads relative to the interpolated yield curve, underscoring its significance as a benchmark. Notably, specific agency collateralized mortgage obligations (CMOs) are observed trading at spreads aligned with the interpolated yield curve. This alignment occurs at a specific point on the curve corresponding to their weighted average lives. Given that a CMO's weighted average life typically falls within the realm of on-the-run Treasuries, the imperative need for deriving the interpolated yield curve becomes evident.

## Conclusion

The interpolated yield curve, represented as the "I curve," is a vital financial tool, revealing insights into on-the-run Treasuries' yields and maturities. Techniques like bootstrapping and regression analysis enhance our understanding, bridging data gaps and predicting economic trends. The importance of this benchmark is further emphasized in exploring yield spread dynamics, particularly in agency-collateralized mortgage obligations. These analyses contribute to informed decision-making in the ever-evolving financial landscape.