What Is an Interpolated Yield Curve (I Curve)?
Let me explain what an interpolated yield curve, or I curve, really is. It's a yield curve that we derive by using on-the-run Treasuries. Since these Treasuries are only available at specific maturities, we have to interpolate the yields for the maturities that fall in between. Interpolation is essentially a mathematical way to estimate the value of something unknown, often through numerical analysis.
As a financial analyst or investor, you'll find that interpolating yield curves helps you predict future economic activity and bond market prices. You can use various methods for this, like bootstrapping and regression analysis.
Key Takeaways
- An interpolated yield curve or 'I curve' refers to a yield curve plotted using data on the yield and maturities of on-the-run Treasuries.
- On-the-run Treasuries are the most recently issued U.S. Treasury bonds or notes of a specific maturity.
- Interpolation refers to the methods used to create new estimated data points between known data points on a graph.
- Two of the most common methods to interpolate a yield curve are bootstrapping and regression analysis.
- Investors and financial analysts often interpolate yield curves to gain a better understanding of where the bond markets and the economy might be going in the future.
Understanding the Interpolated Yield Curve (I Curve)
The yield curve is what you get when you plot the yields and various maturities of Treasury securities on a graph. You put interest rates on the y-axis and increasing time durations on the x-axis. Typically, short-term bonds have lower yields than longer-term ones, so the curve slopes upward from the bottom left to the right.
When you plot this using data from on-the-run Treasuries, that's your interpolated yield curve or I curve. These on-the-run Treasuries are the newest U.S. Treasury bills, notes, or bonds for a given maturity. In contrast, off-the-run Treasuries are older issues. An on-the-run Treasury usually has a lower yield and higher price than a similar off-the-run one, and they represent only a small portion of all issued Treasuries.
Interpolation
Interpolation is a straightforward method to figure out the value of an unknown entity. U.S. government Treasury securities aren't issued for every possible time period. For instance, you can find a yield for a 1-year bond, but not necessarily for a 1.5-year one.
To fill in those missing yields or interest rates for the yield curve, you interpolate using techniques like bootstrapping or regression analysis. Once you've got the interpolated yield curve, you can calculate yield spreads from it, since few bonds match the exact maturities of on-the-run Treasuries.
Remember, yield curves reflect the bond market's views on future inflation, interest rates, and economic growth. That's why you, as an investor, can use them to inform your decisions.
Bootstrapping
The bootstrapping method applies interpolation to find yields for Treasury zero-coupon securities across different maturities. You start by stripping a coupon-bearing bond of its future cash flows—those coupon payments—and turn it into multiple zero-coupon bonds. Often, some short-end rates are known, but for unknowns due to low liquidity, you might use inter-bank money market rates.
To sum it up, first interpolate rates for each missing maturity using something like linear interpolation. Once all term structure rates are set, apply bootstrapping to derive the zero curve from the par term structure. It's an iterative process that lets you build a zero-coupon yield curve from the rates and prices of coupon-bearing bonds.
Special Considerations
Various fixed-income securities trade at yield spreads to the interpolated yield curve, which makes it a crucial benchmark. For example, some agency collateralized mortgage obligations (CMOs) trade at a spread to the I curve at a point matching their weighted average lives. Since a CMO's weighted average life usually falls between on-the-run Treasury maturities, deriving the interpolated yield curve becomes essential.
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