Index replication: methodology

In depth6 min read · updated 3 November 2026 · 2 sources

This page describes how the index replication tool calculates: which index ETFs are available as targets and which building blocks can be chosen, how the weights come from the index ETF's composition and from returns, why the replication by composition runs as a buy-and-hold with backed-out start weights, and which metrics compare the replication with the original.

Targets and building blocks

The target is always an ETF on a well-known index: MSCI World, ACWI, Emerging Markets, Europe, EMU and Pacific ex Japan, FTSE All-World and FTSE Developed, S&P 500 and S&P Composite 1500, Russell 3000 and 1000, and two Solactive indexes. Each target has one or more sets of building blocks: ETFs on regions (MSCI USA, Europe, Japan …), on single countries, on the sectors of the S&P 500, on size segments (S&P 500, MidCap 400, SmallCap 600; Russell 1000 and 2000) or on styles (value and growth). Some sets mix index families, such as the S&P 500 for the US with MSCI for the rest of the world.

Where possible, the target's prices come from the same exchange as those of the building blocks. For the S&P 500, for example, the page uses the US ETF because the sector ETFs also trade in New York; the sector weights come from the holdings file of a European ETF on the same index. Everything is converted into the chosen currency, euros or US dollars, and calculated on month-ends of completed months.

Weights from composition

For sets of building blocks by country or sector, the page reads the holdings file of the index ETF, the same one the look-through uses, and adds up the weights per building block: the MSCI Europe block gets the shares of all 15 European countries, the technology block the share of information technology. Cash, futures and positions without a country do not count. Countries without a matching building block are listed as not covered in a note, and the covered weights are scaled up to 100%.

The MSCI EMU is exactly the euro area part of the MSCI Europe: both follow the same methodology and cover about 85% of free-float market capitalization per country (MSCI GIMI Methodology 2024). The page therefore takes the country weights of the MSCI Europe for the EMU and keeps only the euro area countries. Holdings files exist only for ETFs whose file can be retrieved; FTSE, Russell and Solactive targets get weights from returns only.

Buy-and-hold with backed-out start weights

A market-cap-weighted index behaves like buy-and-hold of its parts: if one country rises faster than the rest, its weight grows by itself without the index trading. Today's weights are therefore the end point of a buy-and-hold since the start of the comparison. The page backs out the start weights and runs the replication from there without rebalancing; at the end it has exactly today's weights.

Yearly or monthly resets to today's weights can also be chosen. These variants show the error that arises when today's shares are carried back into the past, because country and sector shares shift considerably over the years. Differences of the buy-and-hold replication then come only from additions and deletions, changes in free float, sector reclassifications, costs and data errors.

Weights from returns

The second route needs no holdings file: like the style analysis following Sharpe (1992), the page looks for the weights w_i ≥ 0 with Σ w_i = 100% that minimize the volatility of the monthly difference between the target and the weighted building blocks. This replication is reset to the estimated weights every month, as the regression assumes.

Because the weights come from exactly the months on which they are measured, the comparison flatters the replication. The rolling estimate is more honest: for each month, the weights are estimated only from the preceding 24, 36 or 60 months and applied to the following month. At least 24 common months are needed; with many building blocks and a short history, the page warns when there are fewer than three times as many months as building blocks.

Metrics

• Difference p.a.: annual return of the replication minus annual return of the index ETF; differences in costs between the ETFs are included.
• Tracking error: standard deviation of the monthly difference, annualized by multiplying by √12; more in the article tracking error.
• Correlation and R²: how closely replication and target move together month by month.
• Largest gap: the largest distance in performance, value of the replication divided by the value of the target minus 1, over the whole period.
• Calendar years: returns of target and replication per year and their difference.

Limitations

Calculations use ETF prices after fund costs with distributions reinvested. Target and building blocks sometimes close on different exchanges at different times; this raises the tracking error on monthly data without distorting the difference p.a. For US ETFs, withholding tax on distributions to European investors is not deducted. The first months of some ETFs contain data errors; the page then starts the comparison later and says so. Some countries no longer have an ETF (such as Portugal), and there is none with a long history for the MSCI Europe ex EMU: single country ETFs stand in.

This page describes how Portfolio Lab calculates; past results are not a forecast. All terms in the glossary.