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Lecture 18: Bonds (Part 3)

Bonds and Interest Rate Sensitivity

  • Coupon Rates and Bond Pricing

  • Two bonds are compared:

    • Bond A: 5% coupon rate
    • Bond B: 10% coupon rate

  • Both bonds have a yield to maturity (YTM) of 8% and 5 years until maturity.

  • Price change is analyzed when YTM decreases from 8% to 7%.

  • Price Calculation Steps

  • Calculate price at YTM of 8% and 7% for both bonds.

  • Evaluate the percentage change in price between the two yield scenarios.

  • Semi-annual Cash Flows

  • For Bond A (5% coupon):

    • Cash flows per $100 face value:
    • $2.50 (every 6 months) + $100 (at maturity)

  • For Bond B (10% coupon):

    • Cash flows per $100 face value:
    • $5 (every 6 months) + $100 (at maturity)

  • Yield Adjustment

  • Yields are semi-annual rates:

    • Current rate: 8% → 4%; future rate: 7% → 3.5%

Price Change Results

  • Bond A (5% Coupon):
  • Price increased from $87.83 to $91.68 → 4.4% increase
  • Bond B (10% Coupon):
  • Price increased from $108.11 to $112.47 → 4.0% increase

Interest Rate Sensitivity Insights

  • Sensitivity to Interest Rate Changes
  • The bond with lower coupon payments (5%) is more sensitive to interest rate changes:
    • Smaller relative cash flows received earlier
    • Later cash flows significantly affected by interest rate fluctuations.

Bond Pricing Dynamics

  • Time Effects and Price Volatility
  • Bond prices converge to face value (par value) over time.
  • Unpredictable changes in yields can cause price fluctuations.

Corporate Bonds

  • Understanding Credit Risk

  • Government bonds seen as risk-free; corporate bonds inherit credit risk (default risk).

  • Higher default risk leads to higher coupon rates to entice buyers to invest.

  • Yield to Maturity (YTM)

  • Defaultable bond YTM does not equal the expected return.

  • Higher YTM does not guarantee higher expected returns.

  • Bond Ratings

  • Given by credit rating companies (e.g., DBRS, S&P, Moody's).

  • Ratings assess creditworthiness and risk of default.

  • Categories include investment-grade and speculative (junk) bonds.

  • Yield Curves

  • Constructed for corporate and provincial bonds, showing credit spread relative to risk-free government securities.

Example: Credit Spreads

  • Credit Spread Calculation

  • Firm guarantees a credit rating of AA; observe a 90 basis point spread for 5-year maturity.

  • Government bonds issuing at a 4.5% yield implies the firm's YTM is 5.4% (4.5% + 0.9%).

  • Price Calculation for Corporate Bonds

  • Cash flows are $5 per year ($2.50 semi-annually).

  • Using a 5.4% yield, compute price of bonds, which shows trade-offs with coupon vs. default risk leading to price gaps (e.g., $98.27 vs. $100 for government bonds).