Duration Matching in Liability-Driven Strategies

Consider a pension fund that is tasked with ensuring its future obligations to retirees. The fund currently holds a portfolio of fixed income securities and is engaged in a liability-driven investment strategy. The fund's liabilities are forecasted to be approximately $50 million, with expected cash outflows of $10 million annually for the next five years and a balloon payment of $20 million due at the end of year five.

The current modified duration of the fund's liability stream is 4.5 years. In response, the fund manager is considering adjusting the duration of the fixed income portfolio to align with the duration of its liabilities. The manager has a choice between purchasing bonds with a modified duration of 4.0 years and bonds with a modified duration of 5.0 years.

Discuss the implications of duration matching as a strategy for managing the interest rate risk of the pension fund’s liabilities. Additionally, assess the risks associated with over-matching or under-matching the duration of the liabilities to the duration of the portfolio. Use quantitative analysis to justify your recommendations on the selection of bonds for optimal duration matching.