Passive Equity Index Fund Construction

Consider a large investment management firm that employs a passive equity investment strategy. The firm aims to construct a new index fund that tracks the performance of the U.S. equity market. As the portfolio manager, you must design a broad market index that best represents the underlying market. In your response, discuss the main considerations and methodologies involved in the index construction process. Address the advantages and disadvantages of different weighting schemes (e.g., market capitalization, equal weighting, fundamental weighting) and how they affect the fund's performance, tracking error, and exposure to various sectors.

Additionally, consider how factors such as liquidity, turnover, and potential market anomalies might impact the index's construction and rebalancing strategies. Finally, evaluate how the choice of index may influence the investment strategy, the role of benchmarking in passive investing, and the implications of using a custom-built index versus a standard index.