Yield curves explained: maturities and shapes

Read maturity and understand how curves are made

A bond's maturity describes the time until its principal is due. A yield curve places maturity on the horizontal axis and yield on the vertical axis. Each curve represents one source date. It is different from a time-series chart that follows one maturity across many dates.

Public institutions estimate curves using market prices and a published method. The US Treasury derives its nominal par curve from market quotations for Treasury securities. It then reads yields at constant maturities from that fitted curve. A constant-maturity point need not equal the yield on a particular bond with exactly that time remaining.

The Bank of England estimates nominal zero-coupon yields from gilt prices and related short-term market information. A zero-coupon yield represents the rate for a single payment at maturity. It can be estimated from securities that themselves pay coupons.

These curves summarise market pricing. A central bank policy target is a separate measure. Market yields can move between policy decisions as prices and expectations change.

Compare shapes with illustrative numbers

All yields in this example are illustrative and use the same curve measure and source date. Suppose the two-year yield is 4.25% and the ten-year yield is 3.75%. The ten-year minus two-year spread is 3.75 - 4.25 = -0.50 percentage points, or -50 basis points. That part of the curve is inverted.

An illustrative upward-sloping, often called normal, curve might have a two-year yield of 3.50% and a ten-year yield of 4.50%. The spread is positive at 1 percentage point. A flat comparison might show 4.25% at both maturities, giving a zero spread.

Two points describe one segment. Intermediate maturities can reveal a hump or another change in slope, so inspect the available curve before giving the whole curve one label. Always state which maturities you used for a spread.

The shape reflects market conditions and expectations, but it does not establish a future policy decision or a certain economic outcome. A negative spread describes the relative yields on the selected date.

Keep zero-coupon and par yields separate

A par yield is the coupon rate at which a hypothetical coupon-paying bond would trade at its face value. A zero-coupon yield applies to one payment at maturity. They weight cash flows differently, so a ten-year par yield and a ten-year zero-coupon yield can differ even within the same market.

Narwhal returns Bank of England continuously compounded nominal zero-coupon yields for GBR, with history from 2 January 1979. For USA, it returns US Treasury nominal par yields at constant maturities, with history from 2 January 1990.

Compounding conventions also matter. Continuous compounding expresses interest using a different convention from Treasury par yields. Relabelling a rate does not convert it. Keep the source's curve measure visible when comparing the two countries, and use an explicit method for any analytical conversion.

Match the source date and maturity as well as the measure. Different market calendars can leave observations on different dates. Both documented curves are nominal; do not describe them as inflation-adjusted yields.

Request a curve from Narwhal

Use GET /v1/economics/{country}/yield-curve for a curve and GET /v1/economics/{country}/yield-curve/history for history. The requests below select the documented USA and GBR series. Send the API key as a Bearer token in the Authorization header.

Choose the series based on the measure your application needs. For a country comparison, retain separate labels for US nominal par yields and UK continuously compounded nominal zero-coupon yields. A shared vertical axis in percent does not remove their methodological differences.

curl --request GET \
  --url "https://api.narwhalapi.com/v1/economics/USA/yield-curve" \
  --header "Authorization: Bearer $NARWHAL_API_KEY"

curl --request GET \
  --url "https://api.narwhalapi.com/v1/economics/GBR/yield-curve" \
  --header "Authorization: Bearer $NARWHAL_API_KEY"

Read decimal values and preserve missing maturities

Yield values are decimal strings in percent. The illustrative value below represents 4.25%, rather than a fractional rate of 4.25. It shows the documented value format only, not a complete response body. Divide a percentage by 100 if a calculation requires a fractional rate.

Narwhal returns only the maturities published for each source date. Missing maturities are omitted and never filled. Do not replace an absent maturity with zero or assume every date has the same set of points.

When calculating a spread, require both maturities on the same source date. If either is absent, leave the spread unavailable. A plotted line between published points is a display choice; it should not be stored or presented as an additional published observation.

"4.25"

Explore the US and UK yield curve pages

Open United States yield curve and United Kingdom yield curve below to examine the two measures. Keep the source date, maturity, and curve definition with the yields you display. Use the Economics API reference for response structure and history request details.

“Central bank policy rates explained” covers official targets, target ranges, and effective dates. Read it alongside the curve data when comparing a central bank setting with market yields.