Bond Risk Measures and Immunization › Key Parameters

The key parameters for bond risk measures and immunization are:

• Face Value: The contractual principal due at maturity. The examples use $1,000 per bond; denominations depend on the instrument.
• Coupon Rate: Annual coupon payment as a percentage of face value. At fixed maturity, yield and payment frequency, higher coupons shorten Macaulay duration when there is a coupon date strictly before maturity. If all remaining payments arrive at maturity, duration is unchanged.
• Years to Maturity: Time until principal is due. Moving cash flows later changes duration and convexity; compare the complete cash-flow schedules and yield conventions rather than relying on maturity alone.
• Yield to Maturity (y): The discount rate that equates the bond's price to the present value of its cash flows. For fixed nonnegative cash flows with at least one positive future payment and a positive discount base, higher yields reduce modified duration. Macaulay duration does not increase; it falls strictly when positive cash flows occur at more than one date.
• Frequency: Number of coupon payments per year. These examples use two, so both pricing and reinvestment use the corresponding semiannual periodic yield.
• Modified Duration: Measures percentage price sensitivity to yield changes. Used for hedging and risk management.
• Convexity: Measures the curvature of the price-yield relationship. Positive convexity benefits bondholders as it creates asymmetric price responses.
• Target Duration: For the single-liability flat-yield example, the horizon matched by portfolio Macaulay duration to remove first-order terminal-value yield exposure.