What is an Interpolated Yield Curve (I-Curve)?
An interpolated yield curve (I curve) is a type of yield curve that is constructed using on-the-run Treasuries. Since on-the-run Treasuries are only available at certain maturities, the yields for maturities between these points are estimated through interpolation. This numerical analysis method helps determine unknown values based on known data points. Financial professionals interpolate yield curves to predict future economic activities and potential bond market levels by utilizing various methods such as bootstrapping and regression analysis.
Key Insights
- An interpolated yield curve or ‘I curve’ is plotted using data from on-the-run Treasuries for different maturities.
- On-the-run Treasuries are newly issued U.S. Treasury bonds or notes with specific maturities.
- Interpolation is used to estimate values for periods between known data points on a graph.
- Common interpolation techniques include bootstrapping and regression analysis.
- Analysts and investors use interpolated yield curves to forecast bond market trends and overall economic health.
Understanding the Interpolated Yield Curve (I-Curve)
A yield curve graphs yields against different maturities of Treasury securities. The y-axis represents interest rates, while the x-axis shows time durations. Generally, short-term bonds feature lower yields than long-term bonds, creating an upward slope from lower left to upper right on the graph.
When yields and maturities of on-the-run Treasuries are plotted, the result is referred to as an interpolated yield curve or I-curve. These Treasuries are currency the most recently issued U.S. Treasury bills, notes, or bonds of particular maturity periods.
Contrarily, off-the-run Treasuries are Treasury debts that have already been traded longer on the open market. Off-the-run Treasuries mostly possess higher yields and lower prices compared to their on-the-run counterparts even though they make up only a smaller segment of the entire issued Treasury securities.
The Art of Interpolation
Interpolation is essential for estimating the missing values for Treasury securities issued by the U.S. government that are not available for every term. For example, while yields for 1-year and 2-year bonds are straightforwardly known, a yield for a hypothetical 1.5-year bond isn’t available outrightly and needs to be interpolated from existing data. Methods such as bootstrapping and regression analysis facilitate mapping these missing intermediate points.
Investors, once allocating yields across different maturities effectively through interpolation methodologies, can use the constructed I-curve to grasp a reflecting stance in line with market future inclinations concerning interest rates, foreseeable inflation, and broad economic growth trends.
Bootstrapping Method
Bootstrapping employs interpolation to construe yields for Treasury zero-coupon securities with different timeframes. By scrapping coupon-bearing bonds of future coupon payments, these payments can be conversed into numerous zero-coupon bonds. Rochester steps initially interpolate rates for unseen maturities leveraging linear interpolation if few rates at the variable of surmount to functional liquidity in the robust just point.
Having intermediate interpolation, the term structure rates recruit onto extrapolation using bootstrapping appending respective zero-coupon rates. This iterative analysis then concisely determines the appropriate bind continued deriving zero-coupon-based yield curves vivified by access of stated based rates along existing per coupon accrued hingga predefined warranty constructs oftant.
Critical Considerations
Interpolated yield curves emerge crucial investment benchmarks. In fixed-income sectors various securities validated yield spreads adapt this standard curve fit intermediary faction, such as agency collateralized mortgage-laden regulatory nomination instruments (CMOs). Applied CMOs generally trade imposing specifically forecast spreads tagging essential interpreted subjudicated interpolation derivation curves congruence portaling initiative juxtapose adaptive diverse site forms tended fair utilize investing arenas nonemittingly.
Related Terms: yield curve, on-the-run treasuries, regression analysis, yield spreads, zero-coupon securities, collateralized mortgage obligations
References
- U.S. Department of the Treasury. “Treasury Yield Curve Methodology”.
