10.a Bond Pricing Rule #1

Introduction to Bond Pricing Rules

  • Focus on bond pricing in relation to interest rates.

  • Transition from yield to maturity and yield curve to bond pricing rules.

  • Emphasis on the inverse relationship between interest rates and bond prices.

Bond Pricing Rule Number One: Inverse Relationship

  • Statement: Interest rates and bond prices are inversely related.

    • Higher interest rates lead to lower bond prices (present value concept).

    • Lower interest rates lead to higher bond prices.

Practical Example

  • Assumption: Face value bond of $1,000 lasting 10 years with annual payments.

  • Parameters:

    • Interest rate: 10%

    • Coupon rate: 10% (annual payment of $100).

Calculation Steps

  • Use financial calculator for present value: input face value, periods, interest rate, and payment amount.

  • Special case: Coupon rate equals yield to maturity (required return).

  • Result: Bond price remains at par value of $1,000.

Effects of Changing Interest Rates

  • If interest rates drop to 8%:

    • Bond price rises to $1,134.

    • Coupon rate (10%) is greater than yield to maturity (8%), so bond trades at a premium.

  • If interest rates rise to 12%:

    • Bond price falls to $887.

    • Coupon rate (10%) is less than yield to maturity (12%), so bond trades at a discount.

Time Value Considerations

  • Impact of Time on Bond Pricing:

    • Bond prices adjusted over time as maturity approaches.

    • Premium bonds (initially priced above par) decline in price over time, approaching par value at maturity.

    • Discount bonds (initially priced below par) increase in price over time, approaching par value at maturity.

Examples of Premium and Discount Bonds

  • Premium Bond:

    • Example: Priced at $1,134 (interest rates remain at 10%).

    • Price declines to $1,000 over time, indicating capital loss.

  • Discount Bond:

    • Example: Priced at $887 (interest rates higher than coupon).

    • Price increases to $1,000 at maturity, indicating capital gain.

Total Return Breakdown

  • Total return consists of:

    • Cash flow component (coupon payments).

    • Capital gain component (price change).

  • Current Yield: Annual coupon divided by current price of the bond.

Comparing Bonds A and B

  • Bond A:

    • Face value: $1,000, coupon: $100, price: $1,134, cash flow component = 8.82%.

    • Total yield = 8%, capital gain must yield -0.82% due to price drop approaching maturity.

  • Bond B:

    • Face value: $1,000, coupon: $80, price: $1,000, cash flow component = 8%.

    • No capital gains; price remains flat over time.

Conclusion

  • Reinforcement of rule number one: interest rates and bond prices inversely related.

  • Discussed implications of cash flow and capital gain components in determining total returns.

  • Future videos will cover rules two and three.