Explanation

In bond portfolio management, there's a relationship between Macaulay duration, investment horizon, and interest rate risk:

Key Concepts:

1. Macaulay Duration: The weighted average time until a bond's cash flows are received, measured in years.
2. Interest Rate Risk Components:
   • Price Risk: The risk that bond prices will fall when interest rates rise.
   • Reinvestment Risk: The risk that coupon payments will be reinvested at lower rates when interest rates fall.

The Relationship:

• When Macaulay duration > Investment horizon: Price risk dominates reinvestment risk in a rising rate environment.
• When Macaulay duration < Investment horizon: Reinvestment risk dominates price risk.
• When Macaulay duration = Investment horizon: Price risk and reinvestment risk offset each other (immunization).

Why Option C is Correct: In a rising interest rate environment:

1. If duration > horizon, you'll sell the bond before maturity at a potentially lower price (price risk dominates).
2. If duration < horizon, you'll hold the bond longer and benefit from higher reinvestment rates on coupons (reinvestment risk dominates).
3. If duration = horizon, the two effects offset - price decline is compensated by higher reinvestment returns.

Example:

• Bond with 10-year duration, 5-year horizon: Rising rates → price falls significantly, you sell at loss before maturity.
• Bond with 5-year duration, 10-year horizon: Rising rates → price falls less, you hold longer and reinvest coupons at higher rates.

This concept is fundamental to bond immunization strategies where duration is matched to investment horizon to eliminate interest rate risk.