Government bonds: yield curves, spreads and history

Yield curves by country, spreads between maturities and countries, multi-country comparisons, the history of a single bond and how yields move together — read the curve, see the context.

Understanding Yield Curves

What the chart shows

A yield curve plots the yield (the annual interest rate the market currently demands) of one country's government bonds against their time to maturity. The chart shows every maturity the data source carries for the selected country, all read on one common date — the most recent date on which each maturity has a value — so the points describe one moment; the list under "Current Yields" prints the same numbers.

Key maturities

2-Year (2Y): short maturity; moves mostly with expectations for the central bank's policy rate.
5-Year (5Y): intermediate maturity, between policy expectations and longer-run growth and inflation expectations.
10-Year (10Y): the maturity most often used as a reference rate (mortgages, corporate borrowing, valuation models).
30-Year (30Y): the longest maturity; the most sensitive to long-run inflation expectations.

The 10Y-2Y term spread and the curve-shape label

The term spread is the slope of the curve measured between two points:

term spread = 10Y yield − 2Y yield (in percentage points)

Example: 10Y = 4.20%, 2Y = 3.60% → spread = +0.60 percentage points.

The "Curve Shape" label on this tab is set from that spread:

Inverted: spread below 0 (the 2Y yield is above the 10Y yield). The caption changes wording when the spread is below −0.5.
Flat: spread from 0 up to 0.5.
Normal: spread from 0.5 up to 1.0.
Steep: spread of 1.0 or more; the caption reads "Very steep" from 2.0 upward.

In the example above (+0.60) the label is "Normal". An upward-sloping curve means the market demands more yield to lend for longer; a downward-sloping (inverted) curve means short rates are above long rates. Inversions have preceded some past contractions, but the timing has varied widely and the label is a description of the current slope, not a forecast.

Historical curve comparison

The second chart overlays the curve as it stood 1, 5 and/or 10 years ago (tick the periods to compare) on top of the current curve. Each past curve is read on the last trading date on or before that anniversary; a maturity with no reading within the ten days before it is left out of that curve. A curve that has shifted up at every maturity means yields rose across the board; a change in slope means the short and long ends moved by different amounts.

Why curves differ between countries

Central bank policy rates and their expected path
Inflation expectations and growth expectations
Sovereign credit quality and fiscal position
Yields are quoted in each country's own currency, so two curves are not directly comparable as returns for an investor based elsewhere

Limitations

The set of maturities differs by country; a curve with few points is a coarse picture of the slope.
Data timing differs by market, so "current" can be one trading day older for some countries.
The shape label uses fixed spread bands; a spread sitting exactly on a boundary can flip label from one day to the next.

Educational tool only, not financial, economic, or policy advice. This data and content might be wrong and explains displayed metrics and model outputs and does not provide recommendations. Past patterns do not guarantee future results. Verify all information independently before relying on it.

Understanding Bond Spreads

What a spread is

A spread is the difference between two yields, measured in percentage points:

spread = yield A − yield B

Example: Italy 10Y = 3.80%, Germany 10Y = 2.50% → IT-DE spread = +1.30 percentage points (130 basis points; one basis point is 0.01 percentage point). This tab plots three charts over the selected time range: the US term spread, the euro-zone spreads against Germany, and the term spread of any countries picked in the third chart's dropdown.

US term spread (10Y − 2Y)

The first chart is the US 10-year yield minus the US 2-year yield on every trading day — the slope of the US curve through time. A reading below zero means the curve is inverted (short rates above long rates). The four statistics under the chart are computed over the selected time range:

Current: the latest spread value.
Average: the arithmetic mean of the daily spread readings in the range.
Inverted Days: the number of trading days in the range on which the spread was below zero.
Percentile: the share of the readings in the range that are at or below the current value. Example: readings of 0.2, 0.5, 0.8, 1.1 and 1.4 and a current spread of 0.8 → 3 of 5 readings are at or below it → 60th percentile. A 20th percentile means 80% of the readings in the range were higher than today.

Euro zone spreads vs Germany

The second chart plots, for Italy, Spain, France and Greece, the country's 10-year yield minus the German 10-year yield (Germany is the usual reference for the euro area because its bonds are the most traded). Each line is labelled by its pair in the legend (IT-DE, ES-DE, FR-DE, GR-DE). Because all these bonds are in the same currency, the spread isolates the difference the market charges for one issuer versus another. Its main drivers:

Credit risk: the perceived difference in ability and willingness to repay.
Liquidity: how easily large amounts can be traded.
Political and fiscal news: budgets, elections, policy uncertainty.
Central bank policy: in particular purchase programmes that target specific bond markets.

Term spread by country (10Y − 2Y)

The third chart plots the 10Y − 2Y spread of each country chosen in its own dropdown (United States and Germany by default), one line per country labelled in the legend, so curve slopes can be compared across countries: a line above zero is an upward-sloping curve, below zero an inverted one, and two lines converging mean the two curves have a similar slope even if their yield levels differ.

Recession shading

Shaded bands mark periods the National Bureau of Economic Research (NBER) has designated as US recessions. They appear on the US term-spread chart, on the euro-zone spreads chart, and on the by-country chart when the United States is among the selected countries. These designations are made after the fact, sometimes with a long delay; the lead time between an inversion and a recession has varied widely and some inversions were not followed by one.

Limitations

The statistics depend on the time range selected: the same current value can be a low percentile over 3 years and a high one over 25.
Daily data for some countries starts later than for others, so the euro-zone lines may not cover the whole range.
A spread compares yields, not returns; it says nothing about how either bond's price will move.

Multi-Country Rates Comparison

What this tab shows

Government bonds of different countries trade at different yields because each country has its own central bank policy, inflation, credit standing and currency. This tab lines up the yields of the selected countries at one maturity, in three views: a history chart, a change table and a spread matrix, plus a spread chart against a reference country.

Reference markets

US Treasury: its yield is widely used as a reference rate in pricing and valuation.
German Bund: the reference for the euro area (see the Spreads tab).
Other countries: each is priced off its own central bank and inflation, so its yield can move independently of both references.

The comparison table

Current: the latest available yield for each country at the selected maturity, in %.
1D / 1W / 1M: the change in yield, computed as the current yield minus the yield 1, 5 and 22 trading days earlier. The number is a difference in percentage points and is printed with a % sign: "+0.05%" means the yield rose by 0.05 percentage points, i.e. 5 basis points (from 4.00% to 4.05%), not by 5% of its level.

Cross-country spread matrix (heatmap)

Each cell is the yield of the row country minus the yield of the column ("reference") country at the selected maturity:

cell = row-country yield − column-country yield

The colour scale in the legend is labelled "Spread (%)" and is centred on zero, so cells on one side of the scale are countries yielding more than the column country and cells on the other side are countries yielding less; the diagonal is always zero (a country against itself). Example: a cell of +1.50 in the US row and Germany column means US bonds yield 1.50 percentage points more than German bonds at that maturity, and the mirror cell (Germany row, US column) reads −1.50.

Yield spread comparison

The lower chart picks one reference country and plots, for each other selected country, its yield minus the reference yield over the selected time range; each pair's current spread is listed under the chart. A positive line means the country yields more than the reference; a line moving toward zero means the two yields are converging. NBER recession shading appears when the reference country is the US.

What drives yield differences between countries

Monetary policy: the level and expected path of each central bank's rate.
Inflation: current inflation and what the market expects.
Credit quality: sovereign ratings and fiscal positions.
Currency: expected exchange-rate moves and the cost of hedging them.
Supply and demand: issuance volumes and investor flows.

Limitations

Yields are quoted in each country's own currency. A yield difference is not the return an investor based in another currency would earn; the exchange rate and hedging cost sit on top.
Data timing differs by market (time zones, holidays), so the "current" values in the table and the last points of the history chart are not always from the same day. The spread matrix avoids this by reading every country on one common date.
Liquidity and market structure differ across countries, which is part of the yield gap itself.

Historical Yield Analysis

What this tab shows

The chart plots the daily yield of one selected bond (country + maturity) over the chosen time range: 3, 5, 10 or 25 years, or the full available history. The cards under the chart summarise that same window.

The statistics cards

Current: the most recent yield.
Average: the arithmetic mean of the daily yields in the selected range.
Minimum / Maximum: the lowest and highest daily yield in the range, each with the date it occurred.
Percentile: the share of the daily readings in the range that are at or below the current yield. Example: with readings 2.0, 3.0, 3.5, 4.0 and 5.0 and a current yield of 3.5, three of five readings are at or below it → 60th percentile. A 75th percentile means the current yield is above three quarters of the readings in the window; a 10th percentile means it is near the bottom of the window.
52W Range: the lowest and highest yield over the last 252 trading days (about one year). This card is replaced by the Real Yield card (the current real yield, with the inflation rate used printed under it) when the real-yield toggle is on.

Average, Minimum, Maximum and Percentile depend on the selected time range — the same current yield can be at a high percentile over 3 years and a low one over 25 years — while Current and the 52W Range do not.

Recession shading

For US bonds the chart shades the periods designated as recessions by the National Bureau of Economic Research (NBER). The designations are made after the fact, and yields have behaved differently in each episode.

Real yield ("Show Real Yield" toggle)

With the toggle on, the chart shows two lines: "Nominal Yield" (the quoted yield) and "Real Yield" (the yield after removing inflation), plus a reference line at zero. The real yield uses the exact Fisher relation, not the shortcut "nominal minus inflation":

real yield = (1 + nominal) / (1 + inflation) − 1

Example: nominal 4.5%, inflation 3.0% → 1.045 / 1.030 − 1 = 1.46% (the shortcut 4.5 − 3.0 = 1.5% is close but not exact; the gap grows when inflation is high). A positive real yield means the quoted yield exceeds the inflation rate used; a negative one means it falls short of it.

The inflation input is the annual consumer-price inflation of the bond's country, taken from the macroeconomic data; each year's value is applied to every trading day of that calendar year. The real-yield line is therefore a historical approximation built on realised annual inflation, not the market's forward-looking real rate, and it does not reflect the return over any particular holding period.

Reading the history

Shorter maturities (for example the 2Y) track the central bank's policy rate more closely and tend to swing more than the 10Y over a cycle.
The longest maturity (30Y) moves most with long-run inflation expectations.
A long window mixes very different policy eras and market structures, so an average over 25 years is a description of the sample, not a level yields return to.

Limitations

Older data can be sparser or of lower quality; some country and maturity series start late, so "Full History" is not the same length for every bond.
The percentile and the min/max are sensitive to a handful of extreme days.
The real-yield line stops where annual inflation data is not yet available.

Understanding Bond Yield Correlations

What correlation measures

Correlation (the Pearson coefficient, r) measures how closely two series move together, on a scale from −1 to +1: +1 means they always move in the same direction in proportion, −1 means always in opposite directions, 0 means no straight-line relationship. It measures direction and consistency, not size: two yields can be highly correlated while one moves twice as much as the other.

r = covariance(ΔA, ΔB) / (std(ΔA) × std(ΔB))

Everything on this tab is computed on daily changes of the series (today's value minus yesterday's, in percentage points), not on levels, over the selected time range. Levels drift for years, so two unrelated yields that both trended down would show a high level correlation; daily changes remove that.

Series types (up to 5 series)

Single Yield: one country's yield at one maturity (e.g. US 10Y).
Country Spread: one country's yield minus a reference country's yield at the same maturity (e.g. IT-DE 10Y = Italy 10Y − Germany 10Y).
Term Spread: one country's long-maturity yield minus its short-maturity yield (e.g. US 10Y-2Y, the curve slope).
Term Spread Difference: the term spread of one country minus the term spread of a reference country (e.g. (US−DE) 10Y-2Y compares the two curve slopes).

Correlation matrix

One cell per pair of selected series, the coefficient printed in the cell: green cells are positive, red cells negative, and the deeper the colour the stronger the link (−1 to +1). The diagonal (a series against itself) is left blank and the matrix is symmetric.

Scatter matrix

Diagonal: a histogram of each series' daily changes, drawn on a random sample of up to 500 days; a wider histogram means larger day-to-day moves.
Below the diagonal: a scatter of one series' daily changes against another's, on the same sample. A cloud stretched along a rising diagonal is a positive correlation, along a falling diagonal a negative one, a round cloud no correlation.
Above the diagonal: the correlation coefficient of that pair.

Rolling correlation

A rolling correlation recomputes r inside a window that slides one day at a time, so the chart shows how the relationship of each pair changed over the range. Windows on offer: 20 trading days (about a month), 60 (a quarter), 120 (half a year) and 252 (a year). A short window reacts fast but is noisy; a long window is smooth but slow to register a change. When the short-window line departs from the long-window line, the recent relationship differs from the longer-run one.

Two-series scatter

Pick two series to see every day's pair of changes as one point. With "Show Regression" on, the chart adds the least-squares line (its slope is the change in the Y series that goes with a one-percentage-point change in the X series) and a box reporting:

Correlation (r): the coefficient defined above for that pair.
R²: the share of the Y series' day-to-day variation explained by the X series; it equals the correlation squared. Example: r = 0.80 → R² = 0.64, so 64% of Y's variation is accounted for by X and 36% is not.

Limitations

Currency: yields are local-currency rates, and the correlation of yield changes contains no currency-return component. It therefore says nothing about how hedged or unhedged bond returns across countries relate.
Time variation: correlations shift, often abruptly, in stress periods; a full-range coefficient is an average over regimes.
Trading calendars: different market hours and holidays across countries add noise to same-day comparisons, which lowers measured correlations slightly.
Data coverage: some country and maturity series start late; a pair is only correlated over the days both series have data.
Causation: a high correlation does not show that one series drives the other; both may respond to a common factor such as global rate expectations.

Understanding Cross-Module Correlation Analysis

### What this tab does It correlates government-bond series (yields, country spreads, term spreads) with macroeconomic indicators (GDP growth, inflation, unemployment, real interest rate, government debt, budget balance, exports, trade balance) for the selected countries and year range. Bond data is daily and macro data is annual, so everything is first brought to one observation per year. ### How the series are prepared 1. **Annual averages.** Each daily bond series is replaced by its average over each calendar year. 2. **Transform.** Each series is turned into the form that is correlated: - **Bond yields and spreads:** the change from one year's average to the next, in percentage points. - **Macro rates** (GDP growth, inflation, unemployment, real interest rate): used as they are. These are already yearly rates of change; differencing them again would measure the change of a change. - **Macro ratios in % of GDP** (government debt, budget balance, exports): the year-on-year change in percentage points. - **Trade balance (in US dollars):** the year-on-year change in dollars. 3. **Alignment.** Only years where every selected series has a value are kept. Correlating levels instead of changes is avoided because two series that both trend for a decade look correlated even if their yearly moves are unrelated. Example: debt/GDP 95% → 98% is a +3 percentage-point change; a 10-year yield averaging 3.1% one year and 2.6% the next is a −0.5 change. ### What is displayed - **Correlation matrix:** one cell per pair of series; the colour scale in the legend is labelled "Correlation" and runs from −1 (the two move in opposite directions year after year) through 0 (no straight-line relationship) to +1 (they move together in proportion). The diagonal is 1. - **Rolling correlation:** the coefficient recomputed inside a window that moves one year at a time, for 3-, 5- and 10-year windows. It shows whether a relationship held throughout the range or only in part of it. A 3-year window contains only three points, so its line is very noisy. - **Top & Bottom Correlations:** a table of the pairs with the highest and the lowest coefficients, with their p-values. - **Scatter plot:** one point per year for the pair chosen in the First Series / Second Series dropdowns, with the year as label and a least-squares line. - **Time series comparison:** the same two series overlaid on one chart (one axis each), so the years in which they moved together can be seen directly. - **Lagged correlation:** the same pair correlated after shifting the first series by −2, −1, 0, +1 or +2 years. At a positive lag the first series' value from *lag* years earlier is paired with the second series' current value, so a high bar at +1 or +2 means the **first** series leads (moves first); at a negative lag it is the second series' earlier value that is paired, so a high bar at −1 or −2 means the second series leads. The bar with the largest absolute value shows at which offset the two line up best. ### Formulas - `r = covariance(x, y) / (std(x) × std(y))`, with x and y the transformed yearly series. - The **p-value** is the probability of seeing a correlation at least this large if the true correlation were zero, given the number of years. With 20 years of data a correlation of about ±0.44 or larger has a p-value below 0.05; with 10 years the bar is about ±0.63. ### Limitations - **Few observations.** A 20-year range gives 20 points per series, and the rolling and lagged views use even fewer. Small samples produce large correlations by chance; the p-value helps but does not remove this. - **Correlation is not causation.** Both series may respond to a third factor, or one may respond to the other with a delay the annual data cannot resolve. - **Structural breaks.** Policy regimes, crises and changes in how a statistic is compiled alter relationships mid-sample. - **Timing.** Bond markets react to expectations and often move before a change shows up in annual macro data; the lag view is a coarse check of this. - **Data revisions.** Macro indicators (international statistical databases, national statistics) are revised after first publication; the bond data comes from financial data providers.

Disclaimer

Slowio is an educational and analytical tool. Nothing on this page is investment advice, a recommendation or an offer to buy or sell any security. Figures come from public statistics and market data that may contain errors or delays; always verify against primary sources and do your own research before taking any decision.