Immunization Strategies in Managing Pension Fund Liabilities

You are a fixed income portfolio manager for a pension fund with a large liability due in 10 years, amounting to $10 million. The current interest rate environment is volatile, with rates expected to fluctuate significantly over the upcoming decade. Your goal is to implement an immunization strategy that shields the pension fund's assets from interest rate risk while ensuring that the fund can meet its liabilities when they come due.

Discuss the principles of immunization and the specific steps you would take to construct a bond portfolio that effectively immunizes this liability. Include considerations for convexity, duration matching, and how you would adjust your portfolio as interest rates change over time. Additionally, address the challenges and limitations of an immunization strategy in a volatile interest rate environment.