Calculate full-cap and float-adjusted weights, see why prices change weights without trading, and identify when a cap-weighted portfolio needs maintenance.
Capitalization-weighted portfolio
A capitalization-weighted portfolio assigns each constituent a share of portfolio value proportional to its equity market capitalisation within a chosen universe. Larger equity values receive larger weights. This determines which companies drive portfolio returns—and explains why a rising stock can become a larger holding by value without the investor buying another share.
The universe matters: weighting a selected group of stocks by capitalisation does not turn that group into the entire market portfolio.
First choose what counts as capitalisation
For full equity capitalisation, let Pi be the price per share and Ni the shares outstanding of constituent i, using consistent share-class treatment. Its portfolio weight is
Ci=PiNi,wi=∑jCjCi.
All capitalisations must be measured in a common currency at consistent valuation times, and their sum must be positive. The denominator covers the chosen constituents, not every listed company. Equity capitalisation is not enterprise value: debt is not added to this weighting base.
A free-float-adjusted version instead uses eligible shares available to investors. If fi is the eligible fraction of shares outstanding, replace Ci with PiNifi. An index provider determines which holdings are excluded and how float factors are maintained. The full-cap and float-adjusted portfolios can therefore differ even with identical constituents and prices. S&P's methodology guide explains this distinction.
A rising weight, with no purchase
Consider a synthetic universe containing only A and B. Prices are in USD; there are no dividends, cash flows, costs or share-count changes during the period.
Constituent
Shares outstanding
Initial price per share
Initial capitalisation
Initial weight
A
50
USD 20
USD 1,000
2/3, or 66.67%
B
100
USD 5
USD 500
1/3, or 33.33%
Total
—
—
USD 1,500
100%
A then rises 10% to USD 22 while B stays at USD 5. Their capitalisations become USD 1,100 and USD 500, giving
wA,1=1,6001,100=68.75%,wB,1=31.25%.
Now take an investor who initially owns 5 A shares and 10 B shares: one tenth of each company's outstanding shares. The portfolio is worth USD 150 initially and USD 160 after the move. The investor still owns exactly 5 A and 10 B. Their new value weights already match the new capitalisation weights.
A and B capitalisations change from USD 1,000 and 500 to USD 1,100 and 500. Weights change from 66.67% and 33.33% to 68.75% and 31.25%; the investor holds 5 A and 10 B shares throughout.
Original synthetic USD ledger. Fixed shares outstanding and investor holdings; no distributions, external flows or costs. Initial weights are rounded; final weights are exact.
This is weight drift, not rebalancing. For an uncapped cap-weighted portfolio that initially matches the target, price changes alone require no trades when constituents, shares outstanding and float factors stay fixed. A portfolio starting at equal weights generally needs trades to restore those equal weights after unequal returns.
The period's portfolio return uses the initial weights:
Rp=32(10%)+31(0%)=150160−150≈6.67%.
Using the final weights would incorrectly give the winner extra influence over a period that has already passed. Here price return equals total return because the example excludes dividends. The Equities lesson develops the ownership and dividend distinction; its preview is public and the full lesson requires membership.
What still requires maintenance
The no-trade argument has limits. New issues, buybacks, changes to eligible float, constituent replacements and weight caps can change the target share holdings. An index fund may also need to invest subscriptions and dividends or meet redemptions. Cap weighting does not promise zero turnover or zero tracking costs.
A mechanical two-for-one split is different: A's original 50 shares at USD 20 become 100 at USD 10, leaving its USD 1,000 capitalisation unchanged. The investor's share count adjusts with the split without creating wealth. Index-level divisor adjustments and other corporate-action treatments follow the particular methodology; they are not portfolio gains. S&P's Index Mathematics Methodology distinguishes these calculation and maintenance rules.
Float adjustment can also change the starting result. If only half of A's original shares qualify while all of B's qualify, eligible capitalisations are USD 500 each: float-adjusted weights are 50% each, rather than two thirds and one third. “Cap-weighted” should therefore prompt a question about the capitalisation base and any caps.
Finally, larger companies receive larger capital allocations, not necessarily equal risk contributions or higher expected returns. A cap-weighted portfolio can be concentrated in a few names or sectors. Its weighting rule alone establishes neither broad diversification nor optimality for a particular investor.
Elton, Gruber, Brown and Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, Wiley, 2014, Chapter 24, printed p. 637 — portfolio weights proportional to shares outstanding times price.
