Bond Yields and Pricing
Understanding different yield measures is essential for Series 7 representatives. The exam tests both yield calculations and the relationships between yields for bonds trading at premium, discount, and par.
Types of Bond Yields
Nominal Yield (Coupon Rate)
Nominal yield is simply the coupon rate stated on the bond. It never changes regardless of the bond's market price.
Nominal Yield = Annual Interest Payment ÷ Par Value
Example: A bond paying $70 annually on a $1,000 par value has a nominal yield of 7%.
Current Yield
Current yield measures the bond's annual return based on its current market price—not par value.
Current Yield = Annual Interest Payment ÷ Current Market Price
Example: A 7% bond ($70 annual interest) trading at $875: Current Yield = $70 ÷ $875 = 8.0%
Key insight: Current yield is higher than nominal yield when a bond trades at a discount, and lower when it trades at a premium.
Yield to Maturity (YTM)
Yield to maturity (YTM) is the total return an investor receives if they hold the bond until maturity. YTM accounts for:
- Annual interest payments
- The gain or loss from the difference between purchase price and par value
- Time remaining until maturity
YTM is considered the most comprehensive yield measure for comparing bonds.
Approximate YTM Formula:
YTM ≈ [Annual Interest + ((Par Value − Market Price) ÷ Years to Maturity)] ÷ [(Par Value + Market Price) ÷ 2]
Example: A 6% bond trading at $950 with 10 years to maturity:
- Annual interest: $60
- Annual gain: ($1,000 − $950) ÷ 10 = $5
- Average price: ($1,000 + $950) ÷ 2 = $975
- YTM ≈ ($60 + $5) ÷ $975 = 6.67%
Yield to Call (YTC)
Yield to call (YTC) applies to callable bonds and calculates the yield if the bond is called before maturity. Use the call date and call price instead of maturity date and par value.
YTC ≈ [Annual Interest + ((Call Price − Market Price) ÷ Years to Call)] ÷ [(Call Price + Market Price) ÷ 2]
Important: YTC is most relevant for premium bonds because issuers are more likely to call bonds when interest rates fall.
Yield to Worst (YTW)
Yield to worst (YTW) is the lower of YTM or YTC. This represents the minimum yield an investor can expect and is the most conservative yield measure.
The Bond See-Saw: Yield Relationships
Understanding how yields compare is crucial for the Series 7 exam. The relationship depends on whether the bond trades at premium, discount, or par.
Discount Bond (Price < Par)
When a bond trades at a discount:
Coupon < Current Yield < YTM < YTC
Memory tip: Everything is higher than the coupon because the investor gets a gain at maturity/call.
Premium Bond (Price > Par)
When a bond trades at a premium:
YTC < YTM < Current Yield < Coupon
Memory tip: Everything is lower than the coupon because the investor takes a loss at maturity/call.
Par Bond (Price = Par)
When a bond trades at par:
Coupon = Current Yield = YTM = YTC
All yields are equal when the bond trades at par value.
Yield Comparison Summary
| Bond Price | Yield Order (Low to High) |
|---|---|
| Premium | YTC → YTM → Current Yield → Coupon |
| Par | All yields equal |
| Discount | Coupon → Current Yield → YTM → YTC |
The Yield Curve
The yield curve shows the relationship between bond yields and time to maturity for bonds of similar credit quality.
Types of Yield Curves
| Curve Type | Shape | Interpretation |
|---|---|---|
| Normal (Positive) | Upward sloping | Longer maturities = higher yields; economy expected to grow |
| Inverted (Negative) | Downward sloping | Shorter maturities = higher yields; potential recession indicator |
| Flat | Horizontal | Yields similar across maturities; economic uncertainty |
Why the Yield Curve Matters
- Normal curve: Investors demand higher yields for longer-term bonds due to greater risk
- Inverted curve: Often precedes recessions; investors expect rates to fall
- The spread between short-term and long-term rates provides economic signals
On the Exam
The Series 7 exam frequently tests:
- Calculating current yield (most common calculation)
- Understanding yield relationships for premium, discount, and par bonds
- Recognizing that YTC is most relevant for premium callable bonds
- Interpreting different yield curve shapes
A bond with a 6% coupon is trading at $1,100. The current yield is:
For a bond trading at a discount, which yield is the highest?
An inverted yield curve indicates:
2.3 Corporate Bonds
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