You bought a safe bond. Why is it worth less today?
The story so far To steady your portfolio (Lesson 14.1), you buy a bond from a big bike maker. It costs $1,000, pays $50 a year for 3 years, then gives your $1,000 back. A week later, interest rates jump, and new bonds just like yours pay 7%. You check your account: your "safe" bond is now worth $947.51. Nobody defaulted. Nothing went wrong with the company. This lesson shows exactly where the $52.49 went.
A bond is a loan you make to a company or government. It pays you interest on a schedule and returns your money on a set date.
The bond market is bigger than the stock market. Bonds fund governments and companies, steady portfolios, and set the interest rates on mortgages and car loans.
A bond's price is the present value of all its future payments. When market rates change, that present value, and the price, change too.
Bond traders buy and sell bonds all day. Fixed income analysts judge which issuers will pay. Credit rating agencies grade them. Debt capital markets bankers help companies sell new bonds.
What you're looking at: the most important rule in bonds, drawn as a seesaw. When interest rates rise (orange), the prices of existing bonds fall (blue). Your 3-year bond's price fell from $1,000 to $947.51 when rates went from 5% to 7%.
A bond is a stream of payments.
You met bonds in Lesson 13.1 as a way for companies to borrow. Now you're on the other side: the lender. And you'll price one with the present value math from Lessons 10.2 and 13.2.
The three parts of a bond
Every bond has a face value (also called par), the amount paid back at the end. It has a coupon, the fixed interest it pays each year. And it has a maturity, the date it ends.
- Face value
- $1,000, paid back in year 3.
- Coupon
- 5% of $1,000 = $50 a year.
- Maturity
- 3 years. Total payments: $50 + $50 + $1,050.
A bond's price is a present value
What is that stream of payments worth today? Bring each one back to today at the rate new bonds pay, just like the van in Lesson 13.2, and add them up. That's the bond's price.
- At 5%, the day you buy
- The payments are worth exactly $1,000, because the bond pays the market rate.
- At 7%, a week later
- $501.07 + $501.072 + $1,0501.073 = $46.73 + $43.67 + $857.11 = $947.51.
Why rates up means prices down
Think like a buyer. New bonds now pay $70 a year. Yours pays only $50, locked in. Nobody will pay $1,000 for it; it has to go on sale until its total return matches 7%. When rates fall, the opposite happens. A bond selling below face value trades at a discount; above face value, at a premium.
- Rates rise to 7%
- Price $947.51: a discount.
- Rates fall to 3%
- $501.03 + $501.032 + $1,0501.033 = $48.54 + $47.13 + $960.90 = $1,056.57: a premium.
Yield to maturity and current yield
The yield to maturity (YTM) is the yearly return you'd earn buying at today's price and holding to the end. It's the bond's IRR (Lesson 13.2). A quicker number is the current yield: the coupon divided by the price.
- Buy at $947.51
- YTM: 7%, the rate that makes the payments worth $947.51.
- Current yield
- $50$947.51 = about 5.3%. The rest of the 7% comes from getting $1,000 back for a bond you paid $947.51 for.
Interest rate risk: long bonds swing more
The risk that rate changes move a bond's price is interest rate risk. Longer bonds have more, because more of their payments are far in the future, where discounting hits hardest. Professionals measure this sensitivity with duration. Slide the rate to compare.
- Rates 5% → 7%
- 3-year bond: $1,000 → $947.51, about −5%. A 10-year bond with the same 5% coupon: $1,000 → $859.53, about −14%.
What you're looking at: the price of two bonds that each pay a 5% coupon on $1,000, at market rates from 1% to 9%. Blue is a 3-year bond; green is a 10-year bond. The dashed line is the $1,000 face value. The steeper the curve, the more interest rate risk.
Credit risk, ratings and spreads
The other risk is that the issuer can't pay: credit risk. Agencies like S&P, Moody's and Fitch give credit ratings from AAA down. BBB− and above is investment grade; below that is high-yield, or "junk." Riskier issuers must pay more. The extra yield over a U.S. Treasury of the same maturity is the credit spread.
- The bike maker
- If 3-year Treasuries yield 4% and the bike maker's bond yields 5%, the credit spread is 5% − 4% = 1%, the pay for the chance the company can't pay.
Two minutes. Just listen.
Tap any line to jump to it.
Bond desk.
Eight questions a junior bond trader should answer fast. Each one gives you the numbers. One try each.
What you're looking at: made-up bonds. Each lists the details, then asks one question.
The logic, step by step.
Pricing any bond takes four steps.
Step 1: List the payments
- The bike maker's bond
- $50, $50, $1,050.
Step 2: Find the market rate
- A week later
- 7%.
Step 3: Bring each payment back to today
- At 7%
- $46.73 + $43.67 + $857.11 = $947.51.
Step 4: Compare with face value
- 5% coupon, 7% market
- Discount: $947.51 < $1,000.
Worked example: did you really lose money?
Your bond is now priced at $947.51. Here are the facts:
- You paid: $1,000.
- The issuer: still healthy, still paying.
- Your plan: hold it all 3 years.
- If you sell today. You get $947.51, a real loss of $1,000 − $947.51 = $52.49.
- If you hold. You still collect $50 + $50 + $50 = $150 of coupons and get your $1,000 back. Total $1,150, exactly what you were promised.
- The catch. New buyers earn 7% while you earn 5%. That's the real cost: $20 a year of missed interest for 3 years.
- Check it. The $52.49 drop is about what those three missed $20 payments are worth today at 7%: $201.07 + $201.072 + $201.073 = $52.49.
- The answer. Holding avoids a loss on paper, but you can't escape the lower return. And if you're forced to sell, the loss becomes real. That's what sank Silicon Valley Bank in 2023: it held long bonds, rates jumped, and it had to sell at a loss when customers pulled their money.
Tall trees sway more.
In a gust of wind, the top of a tall tree swings much farther than the top of a shrub. The same push travels up a longer trunk, and the far end moves the most. Forest scientists measure this sway with motion sensors to study which trees snap in storms.
What you're looking at: an illustration, not data. A shrub and a tall tree in the same wind. The dashed orange line shows how far the tall tree's top swings.
Why this sticks. A change in interest rates is the gust. A short bond is the shrub; a long bond is the tall tree. Same push, much bigger swing at the far end.
The page you'd copy down.
- Face value $1,000, coupon 5% = $50 a year, maturity 3 years.
- Price = present value of every payment. At 7%: $46.73 + $43.67 + $857.11 = $947.51.
- Rates up, prices down. At 3%: $1,056.57 (premium). At 7%: $947.51 (discount).
- Yield to maturity: the bond's IRR from today's price. Current yield = couponprice: $50$947.51 = about 5.3%.
- Interest rate risk: longer bonds swing more (higher duration). 5% → 7%: 3-year −5%, 10-year −14%.
- Credit risk: ratings from AAA down; BBB− and up is investment grade. Credit spread = bond yield − Treasury yield.
Fill in the blanks
Grab a friend or a study group.
Bond auction
One person holds a "bond" paying $50 a year. Another announces the new market rate. Everyone bids what it's worth. Who got closest?
Check today's rates
Look up today's yields on 2-year and 10-year U.S. Treasuries. Which is higher? Discuss what that might say about where rates are headed.
Rate the issuers
List five organizations, from the U.S. government to a new startup. Agree on a rating for each and how big a credit spread they should pay.
Just you and your money.
These stay on this device. Nobody else sees them.
Exam-style questions.
Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.
On the job: you're a fixed income analyst
You work for a pension fund. Here's the situation:
- The holding: 10,000 bonds, each with a $1,000 face value: $10 million in total.
- Each bond: a 4% coupon ($40 a year), 10 years left, bought at $1,000.
- The news: market rates for similar bonds jump from 4% to 6%.
- At 6%, each bond's payments are worth: $852.80 today.
Your task: what's the holding worth now, and how much did it drop? What's the new current yield? If the fund holds every bond to maturity, what does it get back? What would you tell the fund's board?
See a model answer
New value: 10,000 × $852.80 = $8,528,000, down $10,000,000 − $8,528,000 = $1,472,000, about 14.7%.
Current yield: $40$852.80 = about 4.7%. A new buyer at $852.80 earns a 6% yield to maturity.
Held to maturity: the fund still collects $40 a year per bond and gets $1,000 back per bond, $10,000,000 in total, as long as the issuer pays.
To the board: the drop is a paper loss unless we sell, but it reflects a real cost: we're earning 4% while new bonds pay 6%. As long as we never need to sell early, we can hold. To limit this risk in the future, we could mix in shorter bonds, which swing less when rates move.
Every loan has a price tag.
What you're looking at: a map of where this lesson fits in the course. Read it left to right: the lessons it builds on, this lesson in the middle, and the lesson that comes next.
- Back · Unit 10The time value of money
- Back · Unit 13Picking projects with NPV
- Back · Unit 9Interest rates and the Fed
- You are hereHow bonds work
- Next · Unit 15Valuing a company with DCF