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.

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 ~5%

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Bond Price Relationships to Par

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Types of Yields

1. Nominal Yield (Coupon Rate)

Example: 5% coupon on $1,000 par = $50 annual interest (regardless of price)

2. Current Yield

Current Yield = Annual Interest Payment / Current Market Price

Example: $50 annual interest / $950 price = 5.26% current yield

3. Yield to Maturity (YTM)

YTM accounts for everything: coupon income, time value, and any premium/discount amortization.

4. Yield to Call (YTC)

Rule: For callable bonds at a premium, compare YTC to YTM—use the lower (yield to worst).

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Yield Relationships by Bond Price

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

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Duration: Measuring Price Sensitivity

Duration measures a bond's sensitivity to interest rate changes.

What Duration Tells You

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

Duration Examples

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Convexity

Convexity measures the curvature of the price/yield relationship.

Positive convexity is good for bondholders: You gain more when rates fall than you lose when rates rise.

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Bond Pricing Conventions

Treasury Notes and Bonds (32nds)

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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

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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

Expect 3-4 questions on bond pricing and yields. You need to know relationships but likely won't calculate complex YTM formulas.

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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 ≈ 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