Market-cap, float-adjusted and fundamental weighting

How does market-cap weighting work?

In market-capitalization weighting (also called value weighting) each constituent’s weight is its market value divided by the total market value of all constituents. Market value is share price times shares outstanding. The index return is simply the change in the total value of the companies.

$$w_i = \frac{P_i N_i}{\sum_j P_j N_j}$$

$$R = \frac{\sum P_1 N + Div}{\sum P_0 N} - 1$$

Back to the three-stock table from the last lesson.

Stock	Start price	End price	Shares (m)	Dividend
X	80	88	50	2.00
Y	25	24	200	0.50
Z	45	54	40	0.00

The advantage of market-cap weighting is that securities are held in proportion to their value in the target market. A second advantage is that it rebalances itself: when a price moves, the weight moves with it, and no trading is needed. The drawback is that shares that have risen most get the biggest weights, so the index leans toward large companies that may be overvalued. This is a momentum effect.

Exam tip A cap-weighted return is never an average of returns. If you are averaging, you are doing equal weighting.

What does float adjustment change?

market float is the part of a company’s shares available to the investing public. Shares held by controlling shareholders, and often by governments or in strategic cross-holdings, are left out. Many indexes also exclude shares that foreign investors are not allowed to own. float-adjusted market-capitalization weighting multiplies each market value by the float fraction f before weighting. Most cap-weighted indexes are float adjusted.

$$w_i = \frac{f_i P_i N_i}{\sum_j f_j P_j N_j}$$

Why bother? An index that holds only shares investors can buy is one they can actually replicate. An unadjusted index would include shares nobody can purchase.

How does fundamental weighting work?

fundamental weighting sets weights by a measure of company size that does not depend on the share price: book value, cash flow, revenue, earnings, dividends or the number of employees. Some indexes use one measure and others blend several.

$$w_i = \frac{F_i}{\sum_j F_j}$$

Compare with cap weights of 37.0%, 46.3% and 16.7%. Earnings yields (earnings ÷ market value) are X 7.5%, Y 8.0% and Z 5.6%, against 7.4% for the three together. Shares whose yield is above the overall yield, X and Y, get more weight than under cap weighting. Z, with the lowest yield, gets less.

That is the value tilt: a fundamentally weighted index holds more of the shares that are cheap relative to their earnings, book value or dividends. It is also contrarian. If Y’s price drops 30% with no change in earnings, its cap weight shrinks (from 46.3% to 37.6% at the start of the example), while its fundamental weight stays at 50%. Rebalancing moves weight away from shares that have risen and toward shares that have fallen.

How do the four methods compare?

Method	Weight driven by	Tilt or bias	Rebalancing need
Price	share price	high-priced shares; changed by splits	none for price moves; divisor after splits
Equal	1 ÷ N	small companies	high
Market cap (float-adjusted)	market value of the float	large companies, momentum, possibly overvalued	low, it rebalances itself
Fundamental	earnings, sales, book value	value; contrarian	periodic

Index weighting methodsthe same shares, a different rule

• Price weighting Memorize weight follows share price
  • Favors high-priced shares; splits shift weights
• Equal weighting Memorize weight 1 ÷ N
  • Favors small companies; needs frequent rebalancing
• Market-cap weighting Memorize weight follows market value
  • Float-adjusted version counts only shares the public can buy
  • Favors large, recently risen shares (momentum)
• Fundamental weighting Memorize weight follows earnings, sales, book value, cash flow, dividends
  • Favors value; contrarian when rebalanced

On the three-stock table the price returns are 10.67% (price-weighted), 8.67% (equal-weighted), 5.19% (cap-weighted), 7.27% (float-adjusted, Y at 60%) and 4.25% (fundamental). Exam options are built from these. Work out the one asked for, then check that it does not match the trap.

Go deeper Why cap weighting matches the market portfolio in CAPM

The capital asset pricing model says every investor should hold the market portfolio: all risky assets in proportion to their market values. A broad cap-weighted index does exactly that, which is why it is the usual stand-in for “the market” when estimating beta. It is also why holding a cap-weighted index fund needs almost no trading. You will use this link again in the Portfolio Management topic.

Go deeper Bubbles and cap weighting

Because cap weights rise with prices, a sector that has soared for years becomes a larger and larger share of the index. If that sector was overvalued, the index is most exposed to it just before a fall. Fundamental weighting avoids this by looking at earnings or sales rather than price. It trades that for a different risk: it can sit in cheap shares that are cheap for good reason.