Duration Matching in Liability-Driven Investment

In a liability-driven investment (LDI) framework, portfolio managers are required to align their fixed income investments with specific liabilities to ensure that funds are available when needed. One of the basic techniques used in LDI is duration matching. This involves selecting assets whose duration matches the duration of the liabilities.

Assume a pension fund has liabilities totaling $10 million due in 10 years, and the duration of these liabilities is 8 years. Describe the concept of duration matching in the context of this pension fund and explain the steps to achieve effective duration matching. Include any assumptions you consider necessary for your analysis.