Lesson 3: Interest Rates and Bond Prices

The Fundamental Relationship

The Golden Rule of Bonds:
Bond prices and interest rates move in opposite directions.

When interest rates rise, existing bond prices fall.
When interest rates fall, existing bond prices rise.

Why This Inverse Relationship Exists

Conceptual Explanation:
Imagine you own a bond paying 4% interest. If new bonds are issued paying 5%, your 4% bond becomes less attractive. To sell it, you must lower the price until its yield matches the new 5% bonds.

Mathematical Explanation:
Bond prices are the present value of future cash flows. When discount rates (interest rates) increase, the present value of those cash flows decreases.

Measuring Interest Rate Risk: Duration

What is Duration?

• Measures bond price sensitivity to interest rate changes
• Expressed in years
• Estimate of percentage price change for 1% rate change

Key Duration Concepts:

Modified Duration:

• Most commonly used measure
• Price change % ≈ -Duration × Interest Rate Change %

Example:

• Bond with 5-year duration
• Interest rates rise by 1%
• Expected price change: -5%

Effective Duration:

• For bonds with embedded options (callable, puttable)
• Accounts for changing cash flows

Types of Duration

1. Macaulay Duration

• Weighted average time to receive cash flows
• Theoretical measure

2. Modified Duration

• Practical trading measure
• Macaulay Duration ÷ (1 + Yield/Number of periods)

3. Dollar Duration

• Price change in dollars for 1% yield change

Factors Affecting Duration

1. Maturity

• Longer maturity = higher duration
• More sensitive to rate changes

2. Coupon Rate

• Higher coupon = lower duration
• More cash flows received earlier

3. Yield Level

• Higher yield = lower duration
• Present value of distant cash flows reduced more

Convexity: The Second-Order Effect

What is Convexity?

• Measures how duration changes with yield
• Accounts for curved price-yield relationship
• Positive convexity = price increases more when yields fall than decreases when yields rise

Why Convexity Matters:

• More accurate price change estimates
• Bonds with higher convexity are more desirable
• Callable bonds have negative convexity

The Yield Curve

What is the Yield Curve?

• Graph showing yields across different maturities
• Typically upward sloping (longer maturities = higher yields)

Yield Curve Shapes:

1. Normal/Upward Sloping

• Longer terms = higher yields
• Expectation of future rate increases
• Compensation for time and inflation risk

2. Flat

• Similar yields across maturities
• Transition period or uncertainty

3. Inverted/Downward Sloping

• Shorter terms = higher yields
• Expectation of future rate decreases
• Often precedes recessions

4. Steep

• Large difference between short and long yields
• Often during economic recovery

Factors Influencing Interest Rates

1. Central Bank Policy (Federal Reserve)

• Federal funds rate decisions
• Quantitative easing/tightening
• Forward guidance

2. Inflation Expectations

• Higher expected inflation = higher rates
• Real vs. nominal interest rates

3. Economic Growth

• Strong growth = potential inflationary pressure = higher rates
• Weak growth = potential rate cuts

4. Supply and Demand

• Government borrowing needs
• Foreign investment flows
• Investor risk appetite

5. Global Factors

• Foreign central bank policies
• Currency exchange rates
• International capital flows

Practical Implications for Investors

Managing Interest Rate Risk:

1. Bond Laddering

• Spread maturities across time
• Regular principal returns for reinvestment
• Smooths rate exposure

2. Barbell Strategy

• Concentrate in short and long maturities
• Avoid intermediate maturities
• Combines liquidity and yield

3. Bullet Strategy

• Concentrate in specific maturity range
• Match liabilities or expectations
• Targeted rate exposure

4. Active Duration Management

• Adjust portfolio duration based on rate outlook
• Requires market timing skill

Interest Rate Forecasting Tools

Economic Indicators to Watch:

1. Consumer Price Index (CPI): Inflation measure
2. Employment Reports: Labor market strength
3. GDP Growth: Economic expansion/contraction
4. Federal Reserve Statements: Policy indications
5. Bond Market Indicators: Yield curve, breakeven inflation rates

Market-Based Indicators:

• Fed Funds Futures: Market expectations for Fed policy
• Treasury Inflation-Protected Securities (TIPS): Market inflation expectations
• Yield Curve Spreads: Economic growth expectations

Special Considerations

Floating Rate Bonds:

• Coupon adjusts with reference rate (LIBOR, SOFR)
• Lower interest rate risk
• Spread remains fixed

Inflation-Linked Bonds:

• Principal adjusts with inflation (TIPS)
• Protects purchasing power
• Lower nominal yields

Zero-Coupon Bonds:

• No periodic interest payments
• Sold at deep discount
• Highest interest rate sensitivity

Practical Exercise

Analyze the current yield curve:

1. Plot Treasury yields for 1-month, 1-year, 5-year, 10-year, and 30-year maturities
2. Identify the curve shape (normal, flat, inverted, steep)
3. Calculate the spread between 10-year and 2-year Treasuries
4. Based on the curve, what does the market expect for future interest rates and economic conditions?