4.6 Bond Pricing & Yields
Understanding bond pricing and yields is essential for evaluating fixed-income investments. This section covers the critical relationships that investment advisers must know.
The Fundamental Inverse Relationship
Bond prices and interest rates move in opposite directions.
When Interest Rates Rise: Bond Prices Fall
When Interest Rates Fall: Bond Prices Rise
Why This Happens
When new bonds are issued at higher rates, existing bonds with lower coupon rates become less attractive. Their prices must fall until their yields are competitive.
Example:
- You own a bond paying 4% coupon
- New bonds issued at 5%
- Your 4% bond's price must fall until its effective yield rises to about 5%
Bond Price Relationships to Par
At Par (100): Coupon rate = Market rate; Fair value
Premium (greater than 100): Coupon rate > Market rate; Higher coupon is valuable
Discount (less than 100): Coupon rate < Market rate; Lower coupon is less valuable
Types of Yields
1. Nominal Yield (Coupon Rate)
Definition: Stated interest rate on the bond
Fixed? Yes, never changes
Based On: Par value
Relevance: Annual interest payment
Example: 5% coupon on $1,000 par = $50 annual interest (regardless of price)
2. Current Yield
Current Yield = Annual Interest Payment / Current Market Price
Based On: Current market price
Shows: Income return relative to price paid
Limitation: Ignores capital gains/losses
Example: $50 annual interest / $950 price = 5.26% current yield
3. Yield to Maturity (YTM)
Definition: Total return if held to maturity
Includes: Coupon payments AND capital gain/loss
Most Important: Primary yield measure for bond analysis
Assumption: Coupons reinvested at YTM rate
YTM accounts for everything: coupon income, time value, and any premium/discount amortization.
4. Yield to Call (YTC)
Definition: Return if bond called at first call date
When Used: Callable bonds trading at premium
Important Because: Premium bonds likely to be called
Rule: For callable bonds at a premium, compare YTC to YTM, use the lower (yield to worst).
Yield Relationships by Bond Price
Premium: Nominal Yield > Current Yield > YTM
Par: All yields are equal
Discount: Nominal Yield < Current Yield < YTM
Memory Trick:
- For discount bonds: yields increase (N < CY < YTM) because you gain the discount
- For premium bonds: yields decrease (N > CY > YTM) because you lose the premium
Duration: Measuring Price Sensitivity
Duration measures a bond's sensitivity to interest rate changes.
What Duration Tells You
Higher duration: More price change for rate change
Lower duration: Less price change for rate change
Rule of Thumb: A bond with duration of 7 years will change approximately 7% in price for each 1% change in interest rates.
Factors Affecting Duration
Longer maturity: Higher duration
Lower coupon: Higher duration
Lower yield: Higher duration
Zero coupon: Duration = maturity (maximum)
Duration Examples
Duration 3 years: 1% Rate Rise, about -3% price; 1% Rate Fall, about +3% price
Duration 7 years: 1% Rate Rise, about -7% price; 1% Rate Fall, about +7% price
Duration 15 years: 1% Rate Rise, about -15% price; 1% Rate Fall, about +15% price
Convexity
Convexity measures the curvature of the price/yield relationship.
Duration Limitation: Assumes linear price change
Reality: Price changes are curved, not linear
Positive Convexity: Prices rise faster/fall slower than duration predicts
Negative Convexity: Prices rise slower/fall faster (callable bonds, MBS)
Positive convexity is good for bondholders: You gain more when rates fall than you lose when rates rise.
Bond Pricing Conventions
Treasury Notes and Bonds (32nds)
99-16: 99 + 16/32 = 99.5%; $995.00 per $1,000
101-08: 101 + 8/32 = 101.25%; $1,012.50 per $1,000
98-24: 98 + 24/32 = 98.75%; $987.50 per $1,000
In Practice: How Investment Advisers Apply This
Interest rate expectations:
- Expecting rates to rise? Shorten duration (less price decline)
- Expecting rates to fall? Extend duration (more price appreciation)
Client communication:
- YTM is the most comprehensive yield measure
- Duration quantifies interest rate risk
- Premium/discount affects realized return
Bond selection:
- Compare YTM across similar credits
- Consider YTC for callable premium bonds
- Match duration to client time horizon
On the Exam
The Series 65 exam tests your understanding of:
1. Inverse relationship: Rates up = prices down
2. Yield relationships: N vs. CY vs. YTM for premium/discount bonds
3. Duration: Measures price sensitivity; rule of thumb
4. Current yield formula: Annual interest / Price
5. Premium vs. discount: Which yields are higher/lower
You need to know relationships but likely won't calculate complex YTM formulas.
Key Takeaways
- Bond prices move inversely to interest rates
- Premium bonds: N > CY > YTM (yields decrease left to right)
- Discount bonds: N < CY < YTM (yields increase left to right)
- At par: All yields are equal
- Duration measures price sensitivity to rate changes
- Duration of 7 means about 7% price change per 1% rate change
- Longer maturity and lower coupon = higher duration
- Zero-coupon bonds: Duration equals maturity
- Convexity measures the curvature beyond what duration captures