Explanation of Bond Prices vs. Interest Rates

Introduction

• Bond prices and interest rates have an inverse relationship.
• A bond example: $1,000 bond with 2-year maturity and 10% coupon rate, paid semi-annually.

Understanding Bond Payments

• Semi-annual coupon payments:
  • Total annual coupon: 10% of $1,000 = $100
  • Semi-annual payment: $50 every six months
• At maturity (24 months), receive par value ($1,000) plus final coupon ($50).

Initial Bond Valuation

• At issuance, with interest rates at 10%, bond is worth $1,000.
• Matches the coupon rate with the current interest rate.

Impact of Rising Interest Rates

• If interest rates rise to 15%, new bonds offer better returns.
• Existing bond now less attractive:
  • Buyer demands a discount to achieve the new market rate (15%).
  • Existing bond’s value decreases.
• Example: Bond trades at a discount to par.

Impact of Falling Interest Rates

• If interest rates fall to 5%, existing bond offers superior returns.
• Buyer willing to pay a premium for better yield.
• Example: Bond trades at a premium to par.

Mathematical Explanation Using Zero-Coupon Bonds

• Zero-Coupon Bond: Pays no coupons, only the face value at maturity.
  • $1,000 face value at 2 years.

Initial Valuation

• Expected rate: 10%
• Present value (PV) calculation:
  • PV = $1,000 / (1.10)^2
  • PV = $826

Effect of Interest Rate Changes

• Interest Rate Increase to 15%:

  • New PV = $1,000 / (1.15)^2 = $756
  • Bond price decreases.

• Interest Rate Decrease to 5%:

  • New PV = $1,000 / (1.05)^2 = $907
  • Bond price increases.

Conclusion

• The bond price decreases with rising interest rates and increases with falling interest rates.
• Higher expected return equates to a lower bond price due to increased discounting.
• Intuitive understanding reinforced by mathematical examples.