Understand the inverse price-yield relationship, distinguish par, premium, and discount bonds, and interpret yield measures in WME bond-pricing cases.
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Bond pricing is built on one simple principle: the market price of a bond reflects the present value of its promised cash flows at current required yields. For WME purposes, students usually do not need deep institutional pricing methods. They do need to understand what happens to a bond when yields change and what it means when a bond trades at par, at a premium, or at a discount.
The Inverse Relationship Between Price and Yield
Bond prices and yields move in opposite directions.
when market yields rise, existing bond prices usually fall
when market yields fall, existing bond prices usually rise
This happens because the bond’s coupon is fixed by its terms, but the market’s required return changes over time. If new bonds offer higher yields, older lower-coupon bonds become less attractive and must trade at lower prices. If new bonds offer lower yields, older higher-coupon bonds become more attractive and can trade at higher prices.
Basic Pricing Logic
At a high level, a bond’s value is the present value of:
future coupon payments
principal repaid at maturity
$$
\[
P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}
\]
$$
Where:
P is the bond price
C is the coupon payment each period
F is the face value repaid at maturity
r is the market discount rate per period
n is the number of remaining periods
Students do not need to solve every bond price from scratch in WME. The formula matters because it explains why changing the discount rate changes the bond price.
Par, Premium, and Discount Bonds
A bond trades:
at par when its coupon rate is roughly equal to the required market yield
at a premium when its coupon rate is above the required market yield
at a discount when its coupon rate is below the required market yield
This is a core exam distinction. If the bond’s coupon looks better than what the market now requires, investors will pay more than face value. If it looks worse, they will pay less.
Pricing status
Usual cause
WME interpretation
Par
Coupon broadly matches the required market yield
Pricing is aligned with current yield conditions
Premium
Coupon is above current required yield, or demand is strong
Not automatically bad; assess total return and role
Discount
Coupon is below current required yield, or risk concerns increased
Not automatically cheap; assess credit, maturity, and yield-to-maturity context
Yield and Price Comparison
Students may see light calculation or comparison questions using information already provided in the stem. The exam often tests interpretation rather than long arithmetic.
For example, current yield is often shown conceptually as:
This measure is useful, but it is not the same as total return or yield to maturity. It ignores capital gain or loss at maturity.
Why Coupon Rate Matters
Coupon rate affects both pricing and volatility.
higher-coupon bonds distribute more cash earlier
lower-coupon bonds leave more value tied to distant cash flows
That is why lower-coupon bonds are usually more sensitive to yield changes than otherwise similar higher-coupon bonds.
Example
Assume two otherwise similar bonds each have face value of $1,000. Bond A pays a 6% coupon and Bond B pays a 3% coupon. If market yields rise above those coupon rates, both prices will fall, but Bond B will generally fall more because more of its value depends on cash flows that arrive further in the future.
Sample Exam Question
A bond trades below par. The client assumes that means it is automatically a bargain. What is the strongest response?
A. Agree, because every discount bond is underpriced.
B. Explain that a discount can reflect a lower coupon, higher required yield, or greater risk, so the price must be interpreted in context.
C. Recommend avoiding all discount bonds because they never pay interest.
D. Treat the discount as irrelevant because bond prices do not respond to market yields.
Correct answer:B
Explanation: A discount price is a signal, not a conclusion. It may reflect ordinary coupon-yield mechanics or a more serious credit or marketability concern.
Common Pitfalls
confusing coupon rate with current market yield
assuming a premium bond is automatically a bad investment
assuming a discount bond is automatically cheap
forgetting that current yield is not the same as yield to maturity
focusing only on coupon size instead of total pricing context
Key Takeaways
Bond prices and yields move in opposite directions.
A bond trades at par when coupon and required yield are aligned.
A bond trades at a premium when its coupon is above market rates.
A bond trades at a discount when its coupon is below market rates.
WME pricing questions usually test interpretation of these relationships rather than heavy bond math.
Quiz
### What is the core relationship between bond prices and market yields?
- [x] They generally move in opposite directions.
- [ ] They always move in the same direction.
- [ ] They are unrelated unless the bond is callable.
- [ ] They move together only for government bonds.
> **Explanation:** When market yields rise, existing bond prices usually fall, and when market yields fall, existing bond prices usually rise.
### What does it mean if a bond trades at a premium?
- [x] The bond's coupon is above the market yield for similar bonds.
- [ ] The bond has no default risk.
- [ ] The bond must be redeemed early.
- [ ] The bond pays no coupons.
> **Explanation:** Investors pay above face value when the coupon is more attractive than current market rates.
### What does it mean if a bond trades at a discount?
- [x] The bond's coupon is below the market yield for similar bonds.
- [ ] The issuer has already defaulted.
- [ ] The bond is more liquid than all other bonds.
- [ ] The coupon automatically rises over time.
> **Explanation:** Investors pay below face value when the coupon is less attractive than current market rates.
### Why is current yield not the same as yield to maturity?
- [x] It ignores capital gain or loss between price and maturity value.
- [ ] It includes every future reinvestment assumption perfectly.
- [ ] It is used only for zero-coupon bonds.
- [ ] It applies only to stocks.
> **Explanation:** Current yield looks only at coupon income relative to price and does not capture the bond's full maturity outcome.
### Which bond is usually more price-sensitive, all else equal?
- [x] A lower-coupon bond
- [ ] A higher-coupon bond
- [ ] A bond trading at par
- [ ] A bond with annual coupons instead of semi-annual coupons
> **Explanation:** Lower-coupon bonds have more value tied to later cash flows and are typically more sensitive to yield changes.
### In a WME case, which conclusion about a premium bond is strongest?
- [x] It may still be suitable if its role and price characteristics fit the client's objective.
- [ ] It should always be avoided because it costs more than par.
- [ ] It guarantees higher total return than a discount bond.
- [ ] It has no reinvestment risk.
> **Explanation:** Premium versus discount status does not decide suitability by itself.