If you follow markets, you hear about yields every day: “the 10-year yield jumped”, “the curve inverted”, “bonds sold off”. When I started my portfolio management class, I realized I could repeat these phrases without really understanding what was moving underneath them. This two-part primer is my attempt to fix that.
Part 1 covers the basics: what a bond is, what a yield is, and why bond prices and yields always move in opposite directions. Part 2 covers how the Federal Reserve sets interest rates, what the yield curve is, and how all of this moves through the business cycle.
What is a bond?
A bond is a loan that you can buy and sell. When you buy a bond, you are lending money to the issuer, which could be the US government, a company or a city. In return, the issuer promises you two things:
- Coupon payments: a fixed amount of interest, paid on a schedule (usually twice a year).
- Face value (or par): the original loan amount, paid back when the bond matures.
Take a simple example: a 10-year US Treasury bond with a face value of $1,000 and a 4% coupon. The government pays you $40 a year for 10 years, then hands back your $1,000 at the end. (Real Treasuries pay half the coupon every six months; I’m using annual payments to keep the math simple.)
The important thing is that these cash flows are fixed. The $40 never changes, no matter what happens in the economy. That one fact explains almost everything else in this post.
What is a yield?
The coupon is the interest rate printed on the bond when it was issued. The yield is the return you actually earn if you buy the bond today at today’s price.
These two are only equal when the bond trades at exactly its face value. Once the bond starts trading, its price moves, and the yield moves with it.
There are two common ways to measure yield:
- Current yield = annual coupon ÷ current price. If you pay $922.78 for a bond paying $40 a year, your current yield is 40 ÷ 922.78 = 4.33%.
- Yield to maturity (YTM) is the single discount rate that makes the present value of all future payments (every coupon plus the final $1,000) equal to today’s price. It is the bond’s internal rate of return, assuming you hold it to maturity. For that same bond, the YTM is 5%, because you also collect the $77.22 gap between the $922.78 you paid and the $1,000 you get back.
When people say “the 10-year yield is 4.5%”, they mean yield to maturity.
Why do bond prices and yields move in opposite directions?
This is the most important idea in fixed income, and it follows directly from the fact that a bond’s cash flows are fixed.
Imagine you own the 4% bond above. A year later, interest rates in the economy have risen, and the government is now issuing new 10-year bonds paying 5%. Nobody will pay you $1,000 for your bond paying $40 a year when they can get a brand new one paying $50 a year for the same price.
To sell your bond, you have to cut the price until the buyer earns 5% too. That price is about $922.78. Now the buyer gets $40 a year plus a $77.22 gain at maturity, which works out to the same 5% as a new bond.
The opposite also works. If rates fall to 3%, your 4% bond suddenly looks generous, and buyers will pay about $1,085.30 for it.
| Market yield | Price of a 10-year, 4% coupon bond |
|---|---|
| 3% | $1,085.30 |
| 4% | $1,000.00 |
| 5% | $922.78 |
So:
- Yields up → prices down
- Yields down → prices up
Mathematically, a bond’s price is the present value of its cash flows. The yield is the discount rate. A higher discount rate makes every future dollar worth less today, so the price falls.
Why do long bonds move more than short bonds?
Run the same experiment on bonds with different maturities, all with a 4% coupon:
| Maturity | Price at 3% | Price at 4% | Price at 5% |
|---|---|---|---|
| 2 years | $1,019.13 | $1,000.00 | $981.41 |
| 10 years | $1,085.30 | $1,000.00 | $922.78 |
| 30 years | $1,196.00 | $1,000.00 | $846.28 |
A one-point rise in yields knocks less than 2% off the 2-year bond, almost 8% off the 10-year, and more than 15% off the 30-year.
The reason is time. The further away a cash flow is, the more a change in the discount rate shrinks its present value. A 30-year bond is locked into its old coupon for three decades, so a rise in market rates hurts it for much longer.
This sensitivity has a name: duration. Roughly speaking, duration tells you how much a bond’s price changes, in percent, for a one-percentage-point change in its yield.
- The 2-year bond above has a duration of about 1.9, so a 1-point rise in yields cuts its price by about 1.9%.
- The 10-year bond has a duration of about 8.1, so the same move cuts its price by about 8%.
- The 30-year bond has a duration of about 17.3.
(The real price changes in the table are slightly smaller on the way down and larger on the way up than duration predicts. That curvature is called convexity, and it works in the bondholder’s favor.)
Rule of thumb: the longer the duration, the bigger the price swing when yields move.
Duration applies to stocks, too
This was one of the ideas from class that clicked for me. A stock is also a claim on future cash flows, so it also has a duration.
- A mature, profitable company that pays out large dividends today (a utility or a consumer staples company) gets most of its value from near-term cash flows. It is a short-duration stock.
- A fast-growing tech company, or an unprofitable small cap, gets most of its value from profits expected many years from now. It is a long-duration stock.
So when yields rise, long-duration growth stocks tend to fall the most, just like 30-year bonds. When yields fall, they tend to rally the most. This is a big reason why the “growth vs value” debate is really a debate about interest rates and inflation.
What actually makes yields go up or down?
Since a yield is the return lenders demand, it rises whenever lenders want more compensation. Three things drive that:
- Expected short-term interest rates. If the Fed is expected to keep its policy rate high, lenders will not accept less on a longer bond. (More on this in Part 2.)
- Expected inflation. Inflation eats into the real value of fixed coupon payments, so lenders demand higher yields when they expect more inflation. A simple way to see it: nominal yield ≈ real yield + expected inflation. In the US, you can compare regular Treasuries with inflation-protected Treasuries (TIPS) to estimate the inflation the market expects, called the “breakeven” rate.
- The term premium. Tying up your money for 10 or 30 years is riskier than lending for 3 months. A lot can go wrong over a long period, so investors usually want a little extra yield for holding long bonds.
Growth matters through all three. A strong economy tends to raise expected inflation, raise expected Fed rates, and increase demand for borrowing. That pushes yields up. A weakening economy does the reverse.
Key takeaways from Part 1
- A bond pays fixed cash flows: coupons plus face value at maturity.
- The yield is the return you earn at today’s price. Yield to maturity is the bond’s internal rate of return.
- Prices and yields move in opposite directions, because fixed cash flows are worth less when the discount rate rises.
- Longer bonds have higher duration, so their prices move more when yields change.
- Stocks have duration too. Long-duration growth stocks behave like long bonds.
- Yields reflect expected short rates, expected inflation and a term premium.
In Part 2, I’ll look at the rate everyone watches most closely, the federal funds rate, and how the shape of the yield curve changes through the business cycle.