Answer: a premium.

## Explanation **Correct Answer: C (a premium)** **Key Concept:** Macaulay duration and its relationship with bond pricing **Detailed Explanation:** 1. **Duration Basics:** Duration measures a bond's price sensitivity to interest rate changes. Macaulay duration is the weighted average time to receive cash flows. 2. **Relationship with Bond Pricing:** - **Premium bonds** (priced above par): Have coupon rates > market rates - **Discount bonds** (priced below par): Have coupon rates < market rates - **Par bonds** (priced at par): Have coupon rates = market rates 3. **Duration vs. Time to Maturity:** - For **premium bonds**, as time to maturity increases, duration initially increases but eventually **decreases** toward the duration of a perpetuity - For **discount bonds**, duration generally increases with time to maturity - For **par bonds**, duration increases with time to maturity but at a decreasing rate 4. **Why Premium Bonds Show Duration Reduction:** - Premium bonds have higher coupon payments relative to market rates - As maturity extends, the present value of distant cash flows becomes less significant - The weighted average time to receive cash flows (duration) actually decreases for very long maturities - This creates a "humped" duration curve where duration peaks and then declines 5. **Mathematical Reason:** The duration formula shows that for bonds priced at premium, the duration approaches (1 + y)/y as maturity approaches infinity, which is less than the duration of some finite-maturity premium bonds. **Example:** A premium bond with 10% coupon when market rates are 5% will have its duration decrease as maturity extends beyond a certain point because the higher coupon payments are received sooner, reducing the weighted average time. **In summary:** Premium bonds are most likely to exhibit duration reduction with increasing maturity due to their higher coupon payments being received earlier in the bond's life, which reduces the weighted average time to cash flows as maturity extends.

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