Bond Yield Curve Simulator & Term Structure

simulator intermediate ~8 min
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Slope = 0 bps — flat curve

The default curve is approximately flat with 3M at 4.5% and 10Y at 4.5%. Adjust rates to see normal, inverted, and humped curve shapes.

Formula

Slope = Y(10Y) − Y(3M)
Butterfly = 2 × Y(2Y) − Y(3M) − Y(10Y)
Nelson-Siegel: y(τ) = β0 + β1·(1−e^(−τ/λ))/(τ/λ) + β2·[(1−e^(−τ/λ))/(τ/λ) − e^(−τ/λ)]

The Economy's Crystal Ball

The yield curve is arguably the most important chart in finance. By plotting interest rates across maturities from 3 months to 30 years, it reveals the market's collective expectations about future growth, inflation, and monetary policy. When the curve inverts — short-term rates exceeding long-term rates — it has predicted every US recession since 1970, typically 12–18 months in advance. No other indicator has such a consistent track record.

Curve Shapes and Their Meanings

A normal (upward-sloping) curve reflects healthy economic expectations: investors demand higher yields for longer maturities to compensate for duration risk and inflation uncertainty. A flat curve suggests economic uncertainty or a transition period. An inverted curve signals that investors expect rate cuts ahead — typically because they anticipate economic weakness. A humped curve, where medium-term rates peak above both short and long rates, can indicate a transition between regimes.

Term Structure Models

The Nelson-Siegel model decomposes the yield curve into three factors: level (the overall interest rate environment), slope (the difference between short and long rates), and curvature (the shape of the belly). These three factors explain over 99% of yield curve movements across global bond markets. More complex models like Svensson add a second curvature factor, while affine term structure models derive curve dynamics from no-arbitrage conditions.

Trading the Curve

Bond traders express views on curve shape through spread trades. A steepener profits when the curve steepens (buying short, selling long bonds). A flattener profits from curve flattening. Butterfly trades exploit curvature — going long the wings and short the belly, or vice versa. These relative-value strategies allow traders to express opinions about monetary policy and economic trajectory without taking outright interest rate directional risk.

FAQ

What is a yield curve?

A yield curve plots bond yields (interest rates) against their maturities. In a normal yield curve, longer-term bonds have higher yields to compensate for duration risk. The shape of the curve — normal, flat, or inverted — is one of the most watched indicators in financial markets.

Why does an inverted yield curve predict recession?

An inverted curve means short-term rates exceed long-term rates, signaling that investors expect future rate cuts due to economic weakness. Every US recession since 1970 was preceded by yield curve inversion. The 2Y-10Y spread and 3M-10Y spread are the most tracked indicators.

What is the term premium?

The term premium is the extra yield investors demand for holding longer-maturity bonds instead of rolling over short-term bonds. It compensates for interest rate risk, inflation uncertainty, and liquidity differences. Negative term premiums occur when demand for long bonds drives yields below expected short rates.

How do central banks influence the yield curve?

Central banks directly control the short end of the curve through policy rates. They influence the long end through forward guidance, quantitative easing (buying long bonds to push yields down), and quantitative tightening. Yield curve control, used by the Bank of Japan, explicitly targets specific maturities.

Sources

Embed

<iframe src="https://homo-deus.com/lab/finance/bond-yield-curve/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub