17 Chapter 6 Bond

Conceptual Questions

1. Bond Terminology

• • Face Value: The principal amount of the bond to be repaid at maturity. It determines the size of coupon payments.
  • Coupon Rate: The annual interest rate paid on the face value. Determines periodic interest payments.
  • Yield to Maturity (YTM): The annualized return expected if the bond is held to maturity, considering both coupon payments and capital gains or losses.
  • Maturity Date: The date when the bond issuer repays the face value. Bonds with longer maturities are more sensitive to interest rate changes.

2. Zero-Coupon Bond vs. Coupon Bond

• • Zero-Coupon Bonds: No periodic interest payments; sold at a discount and mature at face value. Advantages: simpler structure, higher return potential in certain markets. Disadvantages: no regular income.
  • Coupon Bonds: Provide periodic interest payments. Advantages: regular income, predictable cash flow. Disadvantages: lower return if market rates rise.

3. Credit Risk and Bond Ratings

Higher credit ratings indicate lower risk of default, resulting in lower yields. Investors may prefer higher-rated bonds for stability despite lower returns. Lower-rated bonds (high-yield or junk bonds) offer higher returns to compensate for increased risk.

4. Interest Rate Changes and Bond Prices

Bond prices and interest rates are inversely related. When interest rates rise, existing bonds with lower coupon payments become less attractive, reducing their market price. Conversely, when rates fall, bond prices rise as they offer higher returns relative to new bonds.

Short Calculations

1. Pricing a Zero-Coupon Bond

[latex]\text{Price} = \frac{\text{Face Value}}{(1 + r)^n} = \frac{1000}{(1 + 0.06)^5} \approx 747.26[/latex]

2. Yield to Maturity of a Zero-Coupon Bond

[latex]r = \left(\frac{\text{Face Value}}{\text{Price}}\right)^{\frac{1}{n}} - 1 = \left(\frac{1000}{750}\right)^{\frac{1}{10}} - 1 \approx 0.0284 \text{ or } 2.84%[/latex]

3. Pricing a Coupon Bond

[latex]\text{Price} = \sum_{t=1}^{10} \frac{50}{(1 + 0.04)^t} + \frac{1000}{(1 + 0.04)^{10}} \approx 1081.11[/latex]

4. Current Yield of a Bond

[latex]\text{Current Yield} = \frac{\text{Coupon Payment}}{\text{Bond Price}} = \frac{60}{950} \approx 6.32%[/latex]

Scenario-Based Problems

1. Bond Price Sensitivity to Interest Rate Changes

•a) At 6%:

[latex]\text{Price} = \sum_{t=1}^{20} \frac{70}{(1 + 0.06)^t} + \frac{1000}{(1 + 0.06)^{20}} \approx 1158.12[/latex]

•b) At 8%:

[latex]\text{Price} = \sum_{t=1}^{20} \frac{70}{(1 + 0.08)^t} + \frac{1000}{(1 + 0.08)^{20}} \approx 882.28[/latex]

•c) Bonds with longer durations exhibit more significant price changes for the same interest rate shift due to their greater sensitivity.

2. Comparing Corporate Bonds with Different Ratings

•a) Annual income:

• • • Bond A: $10,000 × 4% = $400
    • Bond B: $10,000 × 6% = $600

•b) Risks:

Bond B offers higher returns but comes with greater default risk. Bond A is safer but has a lower yield.

3. Credit Spreads in a Crisis

•a) Credit Spread:

[latex]5% - 3% = 2%[/latex]

•b) During a crisis, credit spreads typically widen as default risks increase. For example, spreads might rise to 4-5%, leading to higher corporate bond yields and lower prices.

Case Study: Corporate Bond Analysis During Economic Uncertainty

1. Bond Price Calculation

• • At issuance (4% market rate):

[latex]\text{Price} = \sum_{t=1}^{10} \frac{50}{(1 + 0.04)^t} + \frac{1000}{(1 + 0.04)^{10}} \approx 1079.85[/latex]

• • After downgrade (6% market rate):

[latex]\text{Price} = \sum_{t=1}^{10} \frac{50}{(1 + 0.06)^t} + \frac{1000}{(1 + 0.06)^{10}} \approx 926.40[/latex]

2. Impact of Downgrade

The downgrade increases yield expectations, reducing bond prices and making it less liquid. Bondholders face potential capital losses if they sell before maturity.

3. Bondholder’s Options

• • Hold to maturity and earn the original YTM.
  • Sell now and reinvest in safer or higher-yielding assets.
  • Monitor further downgrades and market conditions.