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, $Q_i$. The aggregate reference value is the total market value, and the index return is simply the change in the total value of the companies.

$$w_i = \frac{Q_i P_i}{\sum_j Q_j P_j}$$

The index value divides the total market value by a divisor:

$$V_{MCI} = \frac{\sum_i Q_i P_i}{D}$$

And the return of the index is:

$$r = \frac{\sum_i Q_i P_{i,1} + Div}{\sum_i Q_i P_{i,0}} - 1$$

Here $Div$ is the total dividends paid by the constituents during the period.

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

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

The main advantage: as prices move, each holding’s share of the total moves with them, so the index never needs rebalancing for price changes and is cheap to replicate. It still needs a divisor change for corporate actions and constituent changes. The main drawback: it tends to become a large-company momentum index, putting the most weight on the shares that have risen most, so the biggest firms can dominate.

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?

The 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. Float-adjusted market-capitalization weighting multiplies each market value by the float fraction $f_i$ before weighting.

$$w_i = \frac{f_i Q_i P_i}{\sum_j f_j Q_j P_j}$$

Dividends count on the float too: X 2.00 × 50 = 100, Y 0.50 × 200 × 0.60 = 60, Z none, so 160 in total. The total return is (9,440 + 160) ÷ 8,800 − 1 = 9.09%.

A free float-adjusted index goes one step further and also leaves out shares that foreign investors are not allowed to buy, so it shows what an international investor can actually hold. Most cap-weighted share and bond indexes are float adjusted.

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.

An index return is a weighted average of constituent returns

Use it

Using the float-adjusted start weights: 45.45% × 10% + 34.09% × (−4%) + 20.45% × 20% = 4.55 − 1.36 + 4.09 = 7.27%, the same answer as the change in total value. Each product is that constituent’s contribution to index return : Y took 1.36 points off. With total returns (X 12.5%, Y −2%, Z 20%) the same weights give 9.09%.

$$\text{contribution}_i = w_i \times r_i, \qquad r_{index} = \sum_i w_i r_i$$

How does fundamental weighting work?

Fundamental factor weighting sets weights by a measure of company size that does not depend on the share price: assets, book value, cash flow, revenue, earnings, dividends or even the number of employees. An index built this way is a fundamental factor-weighted index. Some indexes use a single metric (for example total dividends); others blend several metrics into a composite score.

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

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.

Weighting by earnings leaves out companies with no earnings and favors those with high earnings relative to price, which is why fundamental indexes lean toward value shares and away from growth shares. They are also the fair benchmark for a manager who weights holdings by such factors.

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%. At each periodic rebalancing the index sells what has risen relative to its fundamentals and buys what has fallen.

With total returns the earnings-weighted index returns 0.375 × 12.5% + 0.50 × (−2%) + 0.125 × 20% = 4.6875 − 1.00 + 2.50 = 6.19%.

How do the four methods compare?

Method	Aggregate reference value	Pros	Cons	Suits	Examples
Market cap (float-adjusted)	Total market value (of the float)	Reflects relative size, low turnover, rebalances itself, favored by institutions	Concentrates in the largest firms, follows price run-ups	Broad passive investing	S&P 500, S&P BSE SENSEX
Equal	Number of constituents	Every constituent counts the same, less large-company concentration	Needs frequent rebalancing, overweights small companies	Spreading influence evenly	S&P 500 Equal Weight Index, MSCI USA Equal Weighted
Fundamental factor	Total of the chosen fundamental	Weights by economic size rather than price, potential for better risk-adjusted returns	Sector tilts, leaves out companies without earnings or dividends	Value-minded investors	FTSE RAFI US 1000
Price	Sum of one share of each	Simple to calculate and understand	Ignores market values, skewed by high prices	Illustrations, long price histories	Dow Jones Industrial Average, Nikkei 225

Index weighting methodsthe same shares, a different rule

• Price weighting Memorize weight follows share price
  • Aggregate sum of one share of each
  • Favors high-priced shares; splits shift weights
• Equal weighting Memorize weight 1 ÷ N
  • Aggregate number of constituents
  • Favors small companies; needs frequent rebalancing
• Market-cap weighting Memorize weight follows market value
  • Aggregate total market value (of the float)
  • Float-adjusted version counts only shares the public can buy
  • Favors large, recently risen shares (momentum)
• Fundamental factor weighting Memorize weight follows earnings, sales, book value, cash flow, dividends
  • Aggregate total of the chosen fundamental
  • 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). The total returns are 12.33%, 10.17%, 7.04%, 9.09% and 6.19%. 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

The capital asset pricing model (CAPM) 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 Learning Module 8 of this topic and in the Portfolio Construction 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.