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From this article:

The fund manager mirrors the investments within an index using a very similar weighting. For example, a FTSE 100 tracker fund using this method would invest in all 100 companies, using their weighting within the FTSE 100 to determine representation.

What is this weigthing? What does the fund manager actually do to replicate the index?

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From How are indexes weighted?:

Market-capitalization weighted indexes (or market cap- or cap-weighted indexes) weight their securities by market value as measured by capitalization: that is, current security price * outstanding shares. The vast majority of equity indexes today are cap-weighted, including the S&P 500 and the FTSE 100. In a cap-weighted index, changes in the market value of larger securities move the index’s overall trajectory more than those of smaller ones.

If the fund you are referencing is an ETF then there may be some work to do to figure out what underlying securities to use when handling Creation and Redemption units as an ETF will generally have shares created in 50,000 shares at a time through Authorized Participants.

If the fund you are referencing is an open-end fund then there is still cash flows to manage in the fund as the fund has create and redeem shares in on a daily basis.

Note in both cases that there can be updates to an index such as quarterly rebalancing of outstanding share counts, changes in members because of mergers, acquisitions or spin-offs and possibly a few other factors.

How to Beat the Benchmark has a piece that may also be useful here for those indices with many members from 1998:

As you can see, its TE is also persistently positive, but if anything seems to be declining over time. In fact, the average net TE for the whole period is +0.155% per month, or an astounding +1.88% pa net after expenses. The fund expense ratio is 0.61% annually, for a whopping before expense TE of +2.5% annually. This is once again highly statistically significant, with p values of 0.015 after expenses and 0.0022 before expenses. (The SD of the TE is higher for DFSCX than for NAESX, lowering its degree of statistical significance.) It is remarkable enough for any fund to beat its benchmark by 2.5% annually over 17 years, but it is downright eerie to see this done by an index fund.

To complete the picture, since 1992 the Vanguard Extended Index Fund has beaten its benchmark (the Wilshire 4500) by 0.56% per year after expenses (0.81% net of expenses), and even the Vanguard Index Trust 500 has beaten its benchmark by a razor thin 0.08% annually before (but not after) expenses in the same period.

So what is going on here? A hint is found in DFA's 1996 Reference Guide:

The 9-10 Portfolio captures the return behavior of U.S. small company stocks as identified by Rolf Banz and other academic researchers. Dimensional employs a "patient buyer" discount block trading strategy which has resulted in negative total trading costs, despite the poor liquidity of small company stocks. Beginning in 1982, Ibbotson Associates of Chicago has used the 9-10 Portfolio results to calculate the performance of small company stocks for their Stocks, Bonds, Bills, and Inflation yearbook.

A small cap index fund cannot possibly own all of the thousands of stocks in its benchmark; instead it owns a "representative sample." Further, these stocks are usually thinly traded, with wide bid/ask spreads. In essence what the folks at DFA learned was that they could tell the market makers in these stocks, "Look old chaps, we don't have to own your stock, and unless you let us inside your spread, we'll pitch our tents elsewhere. Further, we're prepared to wait until a motivated seller wishes to unload a large block." In a sense, this gives the fund the luxury of picking and choosing stocks at prices more favorable than generally available. Hence, higher long term returns. It appears that Vanguard did not tumble onto this until a decade later, but tumble they did.

To complete the picture, this strategy works best in the thinnest markets, so the excess returns are greatest in the smallest stocks, which is why the positive TE is greatest for the DFA 9-10 Fund, less in the Vanguard Small Cap Fund, less still in the Vanguard Index Extended Fund, and minuscule with the S&P500.

There are some who say the biggest joke in the world of finance is the idea of value added active management. If so, then the punch line seems to be this: If you really want to beat the indexes, then you gotta buy an index fund.

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