Yield Curve Explained: Normal, Flat and Inverted Curves
Jude Wallis
Founder of EconLearn · 2nd place internationally at the Economics Olympiad (econolympiad.org)
The yield curve is a graph of the interest rates, or yields, on bonds of the same credit quality plotted against their time to maturity, usually drawn with U.S. Treasury securities. Maturity runs along the horizontal axis and yield runs up the vertical axis. A normal curve slopes upward, a flat curve shows similar yields at every maturity, and an inverted curve slopes downward because short-term yields sit above long-term yields.
What a yield curve shows
Each point on the curve is one bond. The horizontal position is how long until the bond repays its face value. The vertical position is its yield to maturity, the annual return a buyer earns by paying today's price and holding to maturity. The yield to maturity calculator finds it from a bond's price, coupon and years left.
The bonds must share the same credit quality, so only maturity changes along the curve. Plot a risky company's bond next to a government bill and the gap mixes pay for lending longer with pay for default risk. Textbook models treat Treasury securities as free of default risk, which is why the Treasury yield curve is the standard one. A yield curve is the picture of this pattern, and its formal name is the term structure of interest rates.
Yields and bond prices move in opposite directions. When buyers bid up the price of a ten-year note, its yield falls and that point on the curve drops. The bonds explainer shows why.
How to read a yield curve
The table below uses made-up numbers for illustration only. None of them are real Treasury yields from any date.
| Maturity | Normal curve (hypothetical) | Flat curve (hypothetical) | Inverted curve (hypothetical) |
|---|---|---|---|
| 3-month | 3.0% | 4.1% | 5.2% |
| 2-year | 3.4% | 4.0% | 4.7% |
| 5-year | 3.8% | 4.0% | 4.4% |
| 10-year | 4.2% | 4.0% | 4.2% |
| 30-year | 4.6% | 4.1% | 4.1% |
Read any curve in four steps.
1. Find the short end. The 3-month yield sits closest to the central bank's policy rate.
2. Find the long end. The 10-year and 30-year yields reflect expected rates over many years plus extra pay for waiting.
3. Compute a spread. Common choices are the 10-year minus the 2-year, or the 10-year minus the 3-month.
4. Name the shape. Positive means upward sloping, near zero means flat, negative means inverted.
The 10-year minus 3-month spreads:
- Normal: 4.2% - 3.0% = +1.2 percentage points, or 120 basis points.
- Flat: 4.0% - 4.1% = -0.1 percentage point, close enough to zero to call flat.
- Inverted: 4.2% - 5.2% = -1.0 percentage point, or negative 100 basis points.
A basis point is one hundredth of a percentage point.
Normal, flat and inverted yield curves
Normal. The curve slopes upward: the longer the loan, the higher the yield. Markets expect short-term rates to stay steady or rise, often because they expect growth, and lenders want extra pay for tying up money longer.
Flat. Yields are about the same at every maturity. A flat curve can appear when short-term rates rise toward long-term rates, and buyers expect short rates to hold near current levels.
Inverted. The curve slopes downward. In the hypothetical inverted curve, a three-month bill pays 5.2% while a ten-year note pays 4.2%. Investors accept the lower long-term yield only when they expect short-term rates to fall well below 5.2% in the coming years.
Why long-term yields depend on expected short-term rates
Expectations theory: a worked example
The expectations theory says a long-term yield is about the average of the short-term rates investors expect over the same period.
Suppose you have $10,000 to invest for two years. Use hypothetical rates: the 1-year rate today is 5%, and investors expect the 1-year rate next year to be 3%.
Option A: roll over two 1-year bonds.
- After year 1: $10,000 x 1.05 = $10,500
- After year 2: $10,500 x 1.03 = $10,815
Option B: buy one 2-year bond. For buyers to be indifferent, the 2-year bond must also turn $10,000 into about $10,815.
- Two-year growth factor: 1.05 x 1.03 = 1.0815
- Annual yield: square root of 1.0815, minus 1 = 1.03995 - 1 = about 4.0%
- Check: $10,000 x 1.04 x 1.04 = $10,816, within a dollar of Option A.
The 2-year yield (4.0%) is below the 1-year yield (5%). The curve is inverted, and nothing caused it except the expectation that short rates will fall from 5% to 3%.
Flip the expectation. If investors expect next year's 1-year rate to be 7% instead, the growth factor is 1.05 x 1.07 = 1.1235. The square root is 1.05995, so the 2-year yield is about 6.0%, above today's 5%. The curve slopes upward. The term structure calculator runs this geometric average for any list of expected rates.
The term premium
Expectations do not explain everything. Long bonds carry more risk when rates change, so lenders demand a term premium on top of the average expected rate. This is interest rate risk, and the arithmetic shows its size.
Take two hypothetical bonds that each pay $1,000 at maturity and nothing before. Suppose market rates rise from 5% to 6%.
| Bond | Price at 5% | Price at 6% | Price change |
|---|---|---|---|
| Pays $1,000 in 1 year | $1,000 / 1.05 = $952.38 | $1,000 / 1.06 = $943.40 | -0.9% |
| Pays $1,000 in 10 years | $1,000 / 1.05^10 = $613.91 | $1,000 / 1.06^10 = $558.39 | -9.0% |
The same one-point rise cuts the ten-year bond's price about ten times as much, so buyers want a higher yield to hold it. That is why the curve normally slopes upward even when no one expects short rates to change.
Why an inverted yield curve is watched as a recession signal
An inverted curve is read as a forecast built into bond prices. The chain of reasoning goes like this:
1. Long yields sit below short yields, so investors must expect short-term rates to fall.
2. Short-term rates fall mainly when the central bank cuts its policy rate.
3. A central bank usually cuts when the economy weakens and unemployment rises.
4. So an inversion suggests bond buyers expect a slowdown ahead.
A second channel runs through banks, which borrow short and lend long, a business called maturity transformation. When short rates rise above long rates, the margin on new lending shrinks, and some banks may lend less.
That is why the curve counts among the leading economic indicators, data that tend to turn before the economy does. The leading indicators vs yield curve comparison shows how the two fit together. See the business cycle guide, and the recession vs depression guide for the downturn being forecast.
The inversion reports what investors expect; it does not cause a recession by itself. Expectations can be wrong, and the time between an inversion and any downturn is not fixed, so analysts read the curve alongside other indicators.
The yield curve and monetary policy
Through its target for the federal funds rate, the overnight rate between banks, the Federal Reserve directly steers the short end. Long-term yields are mostly set by traders weighing expected short rates and the term premium, unless the Fed buys long-term bonds itself (last row of the table). That split explains how policy moves the shape:
| Policy move | Short end | Long end | Typical effect on the shape |
|---|---|---|---|
| Contractionary (raise the policy rate) | Rises with the policy rate | Rises less, or falls if markets expect future cuts | Flattens or inverts |
| Expansionary (cut the policy rate) | Falls with the policy rate | Falls less | Steepens |
| Large purchases of long-term bonds | Little change | Prices rise, yields fall | Flattens from the long end |
The last row is quantitative easing, used when the short rate has little room left to fall. For the full toolkit, see the monetary policy guide and the monetary policy module.
The yield curve and the loanable funds market
The AP loanable funds graph shows one rate: the real interest rate on the vertical axis, the quantity of loanable funds on the horizontal axis, an upward-sloping supply from saving and a downward-sloping demand from borrowers. Try shifting the curves in the loanable funds sandbox.
The loanable funds market: saving and investment set the real interest rate. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.
The yield curve adds time to that single rate: there is a market rate for every length of loan. Firms building factories borrow long term, so long-term rates matter most for investment. If the Fed raises short rates but long yields barely move, investment paid for with long-term loans may change little in practice. On the AP exam, use the course model: a higher policy rate raises the interest rate firms pay, investment falls, and aggregate demand shifts left. The loanable funds explainer covers the shifts.
Treasury yields are nominal. To turn a point into a real rate, subtract expected inflation, as in the Fisher equation guide.
Is the yield curve on the AP Macro exam?
The yield curve itself goes beyond the AP Macroeconomics course. It rests on three ideas the course does test:
- Topic 4.1, Financial Assets: bond prices and interest rates move inversely.
- Topic 4.6, Monetary Policy: the central bank moves short-term rates to shift aggregate demand. See AP Macro 4.6.
- Topic 4.7, The Loanable Funds Market: the real interest rate is set by saving and borrowing.
Common mistakes when reading a curve:
- Assuming an inversion means long rates collapsed. An inversion can also come from short rates rising while long rates hold still.
- Treating the inversion as the cause of a recession. The curve shows what bond buyers expect; any slowdown comes from the conditions they are reacting to.
- Forgetting that price and yield move opposite. Strong demand for long bonds lowers their yields.
Frequently asked questions
What is a yield curve?
A yield curve is a graph of bond yields plotted against time to maturity for bonds of the same credit quality, usually U.S. Treasury securities. Maturity sits on the horizontal axis and yield on the vertical axis. The shape of the yield curve, whether upward sloping, flat or inverted, reflects what investors expect short-term interest rates to do in the future plus the extra pay, or term premium, they demand for lending longer.
What does an inverted yield curve mean?
An inverted yield curve means short-term bonds pay higher yields than long-term bonds of the same credit quality. Investors accept a lower long-term yield only when they expect short-term rates to fall, and short rates usually fall when a central bank cuts in response to a weakening economy. That is why an inverted yield curve is read as a forecast of slower growth.
Why is an inverted yield curve a recession signal?
An inverted yield curve is watched as a recession signal because it shows that bond buyers expect short-term interest rates to fall, which usually happens when a central bank cuts rates in a slowdown. Inversion also squeezes bank lending margins. An inverted yield curve is a market forecast rather than a cause, and the time between an inversion and any downturn is not fixed.
What is the Treasury yield curve?
The Treasury yield curve plots the yields on U.S. government securities, from short-term bills to long-term bonds, against their maturities. Treasuries are used because textbook models treat them as free of default risk, so differences in their yields reflect maturity alone. The Treasury yield curve is the benchmark analysts usually mean when they talk about the yield curve.
Why does the yield curve usually slope upward?
The yield curve usually slopes upward because lenders want a term premium for tying up money longer, and long bonds lose more value when interest rates rise. Markets may also expect short-term rates to rise as the economy grows. Together, the term premium and those expectations keep long-term yields above short-term yields on a normal yield curve.
Is the yield curve on the AP Macro exam?
The yield curve itself goes beyond the AP Macroeconomics course, but the yield curve rests on tested ideas: topic 4.1, Financial Assets, where bond prices and interest rates move inversely; topic 4.6, Monetary Policy, where the central bank moves short-term rates; and topic 4.7, The Loanable Funds Market, where saving and borrowing set the real interest rate.
More on yield curve
- DefinitionYield Curve, AP Economics
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