In which type of ETF does the portfolio manager select securities and their weighting to best match the performance of an index?

The technique described is sampling, also known as an optimization strategy. In this method, the portfolio manager does not purchase every security in the target index. Instead, they select a representative sample of securities that, in aggregate, mirrors the key characteristics and is expected to match the performance of the overall index. This approach is common for ETFs tracking very broad or illiquid indices where full replication would be impractical or too costly.

A. Rules-based (or smart beta) ETFs track a custom index constructed based on specific factors (e.g., value, momentum), not a standard market-cap-weighted index.
B. A synthetic ETF does not hold the underlying securities at all; it uses derivatives, such as swaps, to gain exposure to the index's return.
D. In full replication, the manager holds all securities from the index in their respective weights. There is no "selection" of a subset to match performance.

1. Canadian Securities Institute. (2023). Canadian Securities Course (CSC) Volume 2. Chapter 23, "Exchange-Traded Funds," Section 2, "Types of ETFs," explicitly defines sampling: "the portfolio manager selects a smaller sample of securities and their weighting to best match the performance of the underlying index."

2. Gastineau, G. L. (2010). The Exchange-Traded Funds Manual (2nd ed.). John Wiley & Sons. Chapter 4, "Index-Based ETFs," pp. 61-62, describes sampling (or optimization) as a method where the fund owns a subset of index stocks selected to track the index closely.

3. Rompotis, G. G. (2013). The Performance of Exchange Traded Funds: A Pan-European Analysis. The Journal of Trading, 8(1), 67–84. https://doi.org/10.3905/jot.2013.8.1.067 (The article discusses ETF replication methods, distinguishing between full replication and representative sampling on p. 68).