Debt Securities: Bonds Fundamentals
About This Lesson
Bond fundamentals are the math and vocabulary that the entire debt side of the SIE rests on. Get the inverse relationship between prices and rates firmly in mind here, and the rest of the bond material, premium and discount pricing, the yield measures, and duration, follows naturally. This chapter builds that foundation.
What you'll cover
- what a bond is and the core terms: par, coupon, maturity, current yield, and YTM
- the inverse relationship between bond prices and interest rates
- premium, discount, and par pricing, and how the yield measures rank
- duration and why long, low-coupon bonds carry the most rate risk
This is the third chapter of the products module.
Bond Basics & the Inverse Relationship
A bond is a debt security. When you buy one, you are lending money to the issuer, a corporation, a municipality, or the government, and in return the issuer promises two things: periodic interest payments along the way, and repayment of the principal when the bond matures. A bondholder is a creditor, not an owner. A handful of terms anchor everything else in this chapter:
- Par value (face value): the amount repaid at maturity, almost always $1,000 per bond.
- Coupon rate: the annual interest rate paid on par. A 5% coupon on a $1,000 bond pays $50 a year, and that dollar amount never changes once the bond is issued.
- Maturity date: the day the issuer repays the par value.
- Current yield: the annual coupon divided by the bond's current market price, the income you earn relative to what you actually paid.
- Yield to maturity (YTM): the total return if you hold the bond to maturity, folding in the coupons, the price you paid, and the time remaining.
See how bond prices, coupon rates, and yields interact in real time. Adjust inputs and watch the numbers change.
When market interest rates rise, what happens to existing bond prices?
Pricing: Premium, Discount & Yields
Where a bond trades relative to its $1,000 par value tells you how its coupon rate compares to current market interest rates. There are three cases:
| Trading At | Price vs Par | Coupon vs Market Rate | Yield Relationship |
|---|---|---|---|
| Premium | Above $1,000 | Coupon > Market rate | Coupon > CY > YTM |
| Par | $1,000 | Coupon = Market rate | Coupon = CY = YTM |
| Discount | Below $1,000 | Coupon < Market rate | Coupon < CY < YTM |
This is just the inverse relationship at work. A bond whose coupon is higher than current market rates is more attractive, so buyers bid its price above par and it trades at a premium. A bond whose coupon lags the market has to be marked below par to attract a buyer, so it trades at a discount. When the coupon matches the market rate, the bond sits right at par.
Basis points
Yields are usually quoted in basis points. One basis point is 0.01%, a hundredth of a percent, so 100 basis points equal 1%. A yield moving from 4.50% to 4.75% has risen 25 basis points.
For a bond trading at a discount (price below par): yields go in alphabetical order from smallest to largest:
Coupon < Current Yield < YTM
For a bond trading at a premium (price above par): reverse alphabetical:
Coupon > Current Yield > YTM
At par: Coupon = Current Yield = YTM
Why? A discount bond's investor earns extra return from the price appreciation to par at maturity, pushing YTM above current yield above the coupon. A premium bond pays back less at maturity than paid, reducing YTM below coupon.
A bond with a 6% coupon is currently trading at a premium. Which of the following correctly ranks this bond's yields?
An investor pays $950 for a bond with a $1,000 par value and a $60 annual coupon. What is the bond's current yield?
Duration & Interest-Rate Risk
Duration measures how sensitive a bond's price is to a change in interest rates. The detailed math is Series 7 material, but the SIE expects the concept and the direction: a higher duration means the price swings more when rates move, while a lower duration means it holds steadier.
Three things push duration up or down:
- Maturity: longer maturity raises duration. A 30-year bond reacts far more to a rate change than a 2-year note.
- Coupon: a lower coupon raises duration. A zero-coupon bond has the highest duration of all, because every dollar of its cash flow arrives at maturity.
- Yield: a lower yield raises duration.
As a rough rule of thumb, a bond with a duration of 7 would lose roughly 7% of its price if rates rose by 1%. Treat that as an approximation rather than an exact figure, but it captures why long-term, low-coupon bonds are the most exposed when rates climb, which is exactly what the exam wants you to recognize.
Which bond would experience the GREATEST price decline if interest rates rise by 1%?
Chapter Essentials
The one idea everything in this chapter hangs on: bond prices and interest rates move in opposite directions. When rates rise, existing bonds fall in price, and when rates fall, prices rise. That single relationship explains premium and discount pricing and why duration matters.
On pricing, a bond trades at a premium when its coupon beats market rates (yields run Coupon > Current Yield > YTM) and at a discount when its coupon lags (Coupon < Current Yield < YTM); at par, all three are equal. Current yield is simply the annual coupon over the current price. And duration measures rate sensitivity, longest for long-maturity, low-coupon, and zero-coupon bonds, which is why those fall hardest when rates rise.
The reliable gotchas in this chapter:
• Rates up, prices down. The inverse relationship is the single most tested bond fact. If rates rise, every existing bond's price falls.
• Coupon is fixed; yield moves. The coupon rate is locked at issuance and never changes. Yield shifts with the market price, so buying at a discount gives you a yield above the coupon.
• Premium reverses the yield order. At a discount the order is Coupon < Current Yield < YTM; at a premium it flips to Coupon > Current Yield > YTM. A premium bond's YTM is the lowest of the three because you paid more than the $1,000 you get back.
• Current yield ignores maturity. It is just annual coupon divided by price, so $60 on a $950 bond is 6.32% no matter when the bond matures.
• Longest duration falls hardest. When a question asks which bond drops most as rates rise, look for the longest maturity and the lowest coupon; a zero-coupon bond has the highest duration of all.
• One basis point is 0.01%. A move of 100 basis points is a full 1%, so a yield going from 4.50% to 4.75% rose 25 basis points.
Why bond prices and interest rates always move in opposite directions, explained with examples.
Test yourself with exam-style questions on this topic.