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The same stocks can produce different index returns because each weighting rule assigns them a different share of the starting index. Price weighting follows the share prices, equal weighting gives each stock the same starting influence, and market-capitalisation weighting follows each company’s price multiplied by its shares. Work out the initial weights before combining the individual returns.
The weight is the decision
CFA Institute’s security market indexes reading makes weighting a central construction choice because it changes the index’s value and return. A high share price does not imply a large company: share count matters for market value. Equal weighting ignores both share price and company size when the weights are set.
For a price-weighted index, the constituent prices are summed and divided by an index divisor. With no split, replacement or other adjustment over a short measurement period, the percentage change in that sum gives the price return. A CFA Institute explanation of index construction also shows how the same stocks can give different returns under price, equal and capitalisation weights.
One illustrative pair, three returns
The following stocks and prices are invented. Assume no dividends, stock splits, share-count changes or rebalancing during this one period, so every calculation is a price return.
| A | 80 | 88 | 10 | +10% |
| B | 20 | 18 | 40 | -10% |
Price weighted: A starts at 80 out of the combined price of 100, so it has an 80% weight; B has 20%. A’s gain contributes 8 percentage points and B’s loss subtracts 2, leaving a 6% index return. Check it directly: the sum of prices rises from 100 to 106.
Equal weighted: Each stock starts at 50%. A’s 10% gain and B’s 10% loss cancel, giving a 0% return. The weights would drift after this period unless the index were rebalanced.
Market-capitalisation weighted: A begins at 80 times 10 shares, or 800; B begins at 20 times 40 shares, also 800. They therefore start at equal 50% weights and the return is 0%. The ending combined market value is 880 plus 720, or 1,600, matching the starting total of 1,600. Here equal and capitalisation weighting agree only because the two starting market values happen to match.
Where candidates go wrong
The common mistake is to use A’s higher share price as evidence that A must dominate every index. It dominates this price-weighted example, but share count erases that advantage under capitalisation weighting. Another mistake is to use ending weights to explain the return already earned. The weighted-return calculation uses the weights in place before the prices move.
The CFA programme page places index construction in the wider course. When practising this calculation under time pressure, the Level I pacing guide offers a way to allocate your time.
Sources
- Security Market Indexes | CFA Institute · cfainstitute.org · Retrieved
- Does It Matter How an Index is Put Together? - CFA Institute Daily Browse · blogs.cfainstitute.org · Retrieved
