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Premium experiment • rates across different maturities

ECONOMICS • FINANCE

Yield Curve, Term Structure & Interest Rate Expectations

Explore the yield curve and term structure of interest rates. Change expected future short rates and the term premium to create upward, flat or inverted curves.

● YIELD CURVEexpectations + term premium
Short yield
Long yield
Curve slope
Curve shape

Reasoning inspector

live model state
Short yield—
Long yield—
Slope—
Shape—
Term premium—
Long expected short rate—

Experiment with the mechanism

A yield curve compares interest rates across maturities. One way to understand its shape is to combine expectations of future short-term rates with a maturity-related term premium. Changing either component can steepen, flatten or invert the curve.

LEARN WITH THE SIMULATION

Understand Yield Curve, Term Structure & Interest Rate Expectations by experimenting.

START HERE

A yield curve plots interest rates for otherwise comparable debt across different maturities. Its shape reflects more than today's short-term rate. Expected future short rates matter, and investors may also require a term premium for holding longer maturities. Combining those forces can create upward-sloping, flat or inverted yield curves.

BUILD THE IDEA

What you should understand first

  • Read a yield curve as a relationship between maturity and interest rate.
  • Explain how expectations of future short-term rates can change the curve's slope.
  • Separate expectations effects from the maturity-related term premium in the simplified model.

TRY IT YOURSELF

How can falling expected future short rates create an inverted yield curve?

  1. Start with future short-rate expectations above today's short rate and record the curve shape.
  2. Lower the expected future rates step by step.
  3. Replay the maturities as the curve is drawn.
  4. Compare the long yield with the short yield and identify when the slope becomes negative.
Read the visual:

When expected future short rates are sufficiently below today's rate, their average can pull longer yields below the current short yield. A positive term premium works in the opposite direction, so stronger downward expectations are needed to produce inversion.

WHY IT WORKS 01

Why longer yields depend on expected future short rates

A long-term investor could buy one long bond or repeatedly reinvest in shorter bonds. If markets expect short-term rates to be higher in the future, investors generally require a higher long-term yield today to remain competitive with that expected sequence. The simplified expectations component therefore averages expected short rates across the maturity horizon.

WHY IT WORKS 02

Why the term premium can steepen the curve

Longer bonds expose investors to more interest-rate risk because their prices move more when yields change. Investors may demand extra compensation for holding that risk. The simulation adds a maturity-related term premium on top of expected short rates, so even unchanged expectations can produce an upward-sloping curve when the premium is positive.

WHY IT WORKS 03

Why inversion is informative but not deterministic

An inverted curve often appears when markets expect future policy rates to fall, which can happen when investors anticipate weaker growth or lower inflation. But the observed curve also reflects term premiums and other market forces. That is why inversion can contain useful information about expectations without functioning as a guaranteed recession clock.

DO NOT MIX THESE UP

Common misconception

An inverted yield curve does not mechanically cause a recession or guarantee one. It summarizes market pricing under expectations, risk and term-premium assumptions. Different securities also carry credit, liquidity, tax and option differences, so a real-world yield curve must compare instruments carefully.

PRACTICE CHALLENGE

Can the curve stay upward sloping even when future short rates are expected to fall?

  • Set future expected short rates modestly below today's short rate.
  • Increase the term-premium scale.
  • Replay the maturities.
  • Explain why the positive premium can offset some or all of the downward expectations effect.
Reveal the reasoning

Yes. Longer yields in the simulation combine the average expected short rates with a maturity-related term premium. If future rates are expected to fall only slightly, a sufficiently positive term premium can keep long yields above the short yield. The observed slope therefore does not reveal expectations by itself; the premium embedded in longer maturities matters too.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Longer yields are approximated by averages of expected short rates plus a maturity-related term premium.
  • Five representative maturities are shown.
  • Expected future rates and the term-premium scale are user-controlled assumptions.

Model limitations

  • Real term premiums vary through time and by maturity, and bonds may differ in credit, liquidity, tax and option features.
  • The model is explanatory rather than a forecasting model for actual bond yields.

CONNECT IT

Where this matters

  • Bond markets
  • Monetary policy expectations
  • Recession indicators
  • Fixed-income strategy

WORDS THAT MATTER

Key vocabulary

Yield curve
A plot of interest rates against maturities for comparable debt instruments.
Term structure
The relationship between interest rates and time to maturity.
Term premium
Extra yield investors may require for bearing risks associated with longer maturities.
Inverted curve
A yield curve where longer-maturity yields are below shorter-maturity yields over the compared range.