DEFINITION of 'Interpolated Yield Curve - I Curve'

An interpolated yield curve (I curve) is a yield curve derived by using on-the-run Treasuries. Because on-the-run treasuries are limited to specific maturities, the yield of maturities that lies between the on-the-run treasuries must be interpolated. This can be accomplished by a number of methodologies, including bootstrapping and regressions.

BREAKING DOWN 'Interpolated Yield Curve - I Curve'

The yield curve is the curve that is formed on a graph when the yield and various maturities of Treasury securities are plotted. 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 the yield curve is plotted using data on the yield and maturities of on-the-run Treasuries, it is referred to as an interpolated yield curve, or I curve. Note that on-the-run Treasuries are the most recently issued U.S. Treasury bills, notes, or bonds, of a particular maturity. Conversely, off-the-run Treasuries are marketable Treasury debt consisting of more seasoned issues. The on-the-run Treasury will have a lower yield and higher price than a similar off-the-run issue, and they only make up a small percentage of the total issued Treasury securities.

Interpolation is simply a method used to determine the value of an unknown entity. Treasury securities issued by the U.S. government are not available for every period of time. For example, you will be able to find the yield for a 1-year bond, but not a 1.5-year bond. To determine the value of a missing yield or interest rate in order to derive a yield curve, the missing information can be interpolated using various method including bootstrapping or regression analysis. Once the interpolated yield curve has been derived, yield spreads can be calculated from it, as few of the bonds have maturities comparable to those of the on-the-run Treasuries.

The bootstrapping method uses interpolation to determine the yields for Treasury zero-coupon securities with various maturities. Using this method, a coupon-bearing bond is stripped of its future cash flows, that is, coupon payments, 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, inter-bank money market rates can be used.

To recap, first interpolate rates for each missing tenor. This can be done using a linear interpolation method. Once all the term structure rates have been determined, use the bootstrapping method to derive the zero curve from the par term structure. This is an iterative process that makes it possible to derive a zero coupon yield curve from the rates and prices of coupon bearing bonds.

Several different types of fixed-income securities trade at yield spreads to the interpolated yield curve, making it an important benchmark. For example, certain agency Collateralized Mortgage Obligations (CMOs) trade at a spread to the I curve at a spot on the curve equal to their weighted average lives. A CMO's weighted average life will most likely lie somewhere within the on-the-run treasuries, which makes the derivation of the interpolated yield curve necessary.

RELATED TERMS
  1. Interpolation

    Interpolation is a statistical method by which related known ...
  2. Off-The-Run Treasuries

    Off-the-run treasuries are all Treasury bonds and notes issued ...
  3. Term Structure Of Interest Rates

    The term structure of interest rates is the relationship between ...
  4. Spot Rate Treasury Curve

    The spot rate treasury curve is a yield curve constructed using ...
  5. Flat Yield Curve

    The flat yield curve is a yield curve in which there is little ...
  6. One-Year Constant Maturity Treasury ...

    The one-year constant maturity Treasury (CMT) is the interpolated ...
Related Articles
  1. Investing

    Interest Rates and Your Bond Investments

    By understanding the factors that influence interest rates, you can learn to anticipate their movement and profit from it.
  2. Investing

    The impact of an inverted yield curve

    Understand how the relationship between short- and long-term interest rates contributes to an inverted yield curve – a noteworthy economic event.
  3. Investing

    A Flattening Yield Curve Is Good For The Economy and Stocks

    Wall Street is concerned because the yield curve is flattening, but that doesn't mean a recession is near.
  4. Insights

    Is a Recession in the Works? Ask an Inverted Yield Curve

    An inverted yield curve has predicted the last seven recessions. Is number eight around the corner?
  5. Investing

    The Importance Of U.S. Treasury Rates

    U.S. Treasury bond interest rates affect more than just bondholders! It impacts the day to day lives of all consumers.
  6. Insights

    Four Scenarios: Fed Policy, the Yield Curve and Recessions

    If you were to compile a list of the most effective recession predictors, the term spread, or difference between short and long-term interest rates, would likely be at the top of that list.
  7. Investing

    How Rising Interest Rates and Inflation Affect Bonds

    Understand bonds better with these four basic factors.
  8. Investing

    TLT: Why Low Interest Rates Are Dangerous for Investors

    Explore how the rally in long-dated Treasury bonds has escalated the risks in ETFs such as the iShares iBoxx $ Investment Grade Corporate Bond ETF.
  9. Investing

    Understanding Bond Prices and Yields

    Understanding this relationship can help an investor in any market.
  10. Investing

    Understanding the Different Types of Bond Yields

    Any investor, private or institutional, should be aware of the diverse types and calculations of bond yields before an actual investment.
RELATED FAQS
  1. What is the current yield curve and why is it important?

    Understand what the current yield curve represents, and learn how market analysts commonly interpret various changes in the ... Read Answer >>
  2. Which economic factors impact treasury yields?

    Discover the economic factors that impact Treasury yields. Treasury yields are the benchmark yield for the rest of the world, ... Read Answer >>
  3. How is the interest rate on a treasury bond determined?

    Explore the difference between interest rates and bond coupons, what determines current yield on debt instruments, and why ... Read Answer >>
Hot Definitions
  1. Discount Rate

    Discount rate is the interest rate charged to commercial banks and other depository institutions for loans received from ...
  2. Economies of Scale

    Economies of scale refer to reduced costs per unit that arise from increased total output of a product. For example, a larger ...
  3. Quick Ratio

    The quick ratio measures a company’s ability to meet its short-term obligations with its most liquid assets.
  4. Leverage

    Leverage results from using borrowed capital as a source of funding when investing to expand the firm's asset base and generate ...
  5. Financial Risk

    Financial risk is the possibility that shareholders will lose money when investing in a company if its cash flow fails to ...
  6. Enterprise Value (EV)

    Enterprise Value (EV) is a measure of a company's total value, often used as a more comprehensive alternative to equity market ...
Trading Center