# Understanding the Interpolated Yield Curve: Definition and Application

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

An interpolated [yield curve](https://www.investopedia.com/terms/y/yieldcurve.asp) (I curve) is created using [on-the-run Treasuries](https://www.investopedia.com/terms/o/on-the-runtreasuries.asp). Since these Treasuries only cover specific maturities, yields for in-between maturities must be estimated. Interpolation, often using numerical analysis, helps in estimating these unknown values.

Financial analysts and investors use interpolated yield curves to predict economic activity and bond prices. They achieve this through methods like bootstrapping and [regression analysis](https://www.investopedia.com/terms/r/regression.asp).

### Key Takeaways

*   An interpolated yield curve, or "I curve," is derived using on-the-run Treasuries to estimate yields between known maturities.  
    
*   On-the-run Treasuries are the most recently issued U.S. Treasury securities of a specific maturity.  
    
*   Interpolation methods like bootstrapping and regression analysis help predict future economic activity and bond market levels.  
    
*   Yield curves can guide investment decisions by reflecting expectations on inflation, interest rates, and economic growth.  
    
*   Bootstrapping involves creating a zero-coupon yield curve from coupon-bearing bonds' rates and prices.

## How the Interpolated Yield Curve (I Curve) Works

A yield curve is plotted on a graph showing the [yields](https://www.investopedia.com/terms/y/yield.asp) and varying maturities of Treasury securities. 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 yields and maturities of on-the-run Treasuries are used, the plot is called an interpolated yield curve or I curve. On-the-run Treasuries are the most recently issued U.S. [Treasury bills](https://www.investopedia.com/terms/t/treasurybill.asp), notes, or bonds of a particular maturity.

Conversely, [off-the-run Treasuries](https://www.investopedia.com/terms/o/off-the-runtreasuries.asp) are marketable [seasoned issues](https://www.investopedia.com/terms/s/seasonedissue.asp). On-the-run Treasuries usually have lower yields and higher prices compared to similar off-the-run issues, but they represent a small portion of total Treasury securities.

## Methods of Interpolation in Yield Curves

Interpolation is used to find the unknown value of entities. U.S. Treasury securities aren't issued for every time period. For instance, you can find a yield for a 1-year bond but not a 1.5-year bond.

To find a missing yield or interest rate, interpolation methods like bootstrapping or regression analysis are used. Once the yield curve is derived, [yield spreads](https://www.investopedia.com/terms/y/yieldspread.asp) can be calculated since few bonds match the maturities of on-the-run Treasuries.

> **Important**
>
> Because yield curves reflect the bond market's opinion of future levels of inflation, interest rates, and overall economic growth, investors can use yield curves to help them make investing decisions.

## Using Bootstrapping in Yield Curve Analysis

The bootstrapping method uses interpolation to determine the yields for Treasury [zero-coupon securities](https://www.investopedia.com/terms/z/zero-couponbond.asp) with various maturities. Using this method, a coupon-bearing bond is stripped of its future cash flows—that is, [coupon payments](https://www.investopedia.com/terms/c/coupon.asp)—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, you can use inter-bank money market rates.

To recap, first interpolate rates for each missing maturity. You can do this using a [linear interpolation](https://www.investopedia.com/terms/i/interpolation.asp) method. Once you have determined all the term structure rates, 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.

## Important Considerations for Using the Interpolated Yield Curve

Various fixed-income securities trade at yield spreads to the interpolated yield curve, making it a key benchmark. For instance, some agency [collateralized mortgage obligations (CMOs)](https://www.investopedia.com/terms/c/cmo.asp) trade at a spread to the I curve, aligned with their weighted average lives. This average life usually falls within the on-the-run Treasuries, making the interpolated curve essential.

> **Article Sources**
>
> 1.  U.S. Department of the Treasury. "[Treasury Yield Curve Methodology](https://home.treasury.gov/policy-issues/financing-the-government/interest-rate-statistics/treasury-yield-curve-methodology)."