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Portfolio Management Pathway · Index-Based Equity Strategies

Equity Indexes and Weighting Schemes for CFA Level 3

Updated 8 October 2026 · Fact-checked

An equity index is a rule-based basket of securities, and its weighting scheme decides how much each stock counts. Common schemes are market-cap, price, equal, fundamental and factor weighting. To answer exam questions, compute the weights, then link each scheme to its tilts, turnover and risks.

Understand Equity Indexes and Weighting Schemes

An equity index measures the performance of a defined group of stocks. Building one needs four decisions: the target market (for example, large-cap developed markets), which securities qualify, how to weight them, and when to rebalance and reconstitute. The weighting choice drives most of the index's return and risk behaviour.

Market-cap weighting sets each weight equal to the security's market value divided by the total market value. Use free-float market cap (shares available to public investors) in most modern indexes. Weights drift with prices, so the index needs little trading. It is the closest match to the market portfolio and has low turnover and high capacity. The cost is that it holds more of stocks that have risen and are possibly overvalued, and it can become concentrated in a few large stocks or sectors.

Price weighting sets weight by share price. A stock with a price of 200 counts twice as much as one priced at 100, whatever the company's size. Stock splits change weights and need a divisor adjustment. Price weighting has no economic logic, and it is biased toward high-priced shares.

Equal weighting gives every constituent the same weight. It tilts toward smaller stocks and, relative to cap weighting, toward value. It has higher turnover because you must rebalance back to equal weights, and it has lower capacity and liquidity because small stocks make up a large share.

Fundamental weighting sets weights by company size measures such as sales, earnings, cash flow, book value or dividends, or a blend. It breaks the link between weight and price. It tends to tilt toward value, because it holds more of stocks whose price is low relative to fundamentals. Factor-based weighting (smart beta) builds weights from exposure to factors such as value, momentum, quality, size or low volatility. It can use tilting, screening or optimization. Both are rule-based but active in effect, with higher turnover and tracking error versus a cap-weighted benchmark. Factor tilts can underperform for long periods and may become crowded.

Key rules to remember

Market-cap weight
wᵢ = (Pᵢ × Sᵢ) ÷ Σ(Pⱼ × Sⱼ)
Use free-float shares (Sᵢ) for a free-float-adjusted index.
Price weight
wᵢ = Pᵢ ÷ ΣPⱼ
Index value = ΣP ÷ divisor. Adjust the divisor after a split so the index value does not change.
Equal weight
wᵢ = 1 ÷ N
Weights drift as prices move, so rebalance to restore 1/N.
Fundamental weight
wᵢ = Fᵢ ÷ ΣFⱼ
F is the chosen fundamental (sales, earnings, cash flow, book value or dividends). A composite averages several measures.
Index return
R = Σ(wᵢ × Rᵢ)
Use start-of-period weights.
New divisor after a split
New divisor = (sum of prices after split) ÷ (old index value)
This keeps the index value unchanged on the split date.

How to solve Equity Indexes and Weighting Schemes questions

Use this approach for any question on index construction or weighting, whether it asks for a calculation or a recommendation.

  1. 1Read the command word and what the question asks for: a weight, a return, a divisor, or a comparison.
  2. 2Identify the weighting scheme and the data given (price, shares, free float, fundamentals).
  3. 3Compute each security's raw measure, then divide by the total to get weights. Check that weights sum to 100%.
  4. 4For returns, multiply start-of-period weights by each security's return and add them.
  5. 5For a split or constituent change, recompute the divisor so the index value is unchanged.
  6. 6State the consequence: size or value tilt, concentration, turnover, capacity, and tracking error versus the cap-weighted benchmark.
  7. 7Tie the answer to the client's objective (cost, capacity, benchmark fit, factor exposure) and give a one-line justification.

Quickest way: Weights first, tilt second

When to use it: Use it when time is short and the question gives a small table of prices, shares or fundamentals.

  1. Write the one-line raw measure for each stock: price × shares, price, 1, or fundamental.
  2. Add the column and divide each by the total.
  3. Do not compute what is not asked; for a comparison, jump straight to the tilt.
  4. Recall the quick tilts: cap weight tracks the market; equal weight leans small and value; fundamental leans value; price weight has no economic meaning.
  5. Write the answer with the number and a short reason.

Common mistakes in Equity Indexes and Weighting Schemes

  • Using total shares instead of free-float shares when the question gives float.

    Students default to the simple market-cap formula.

    Fix: If free-float data is provided, use it. Weight = price × float shares ÷ total of that column.

  • Saying price-weighted indexes reflect company size.

    A high price feels like a big company.

    Fix: Price depends on the number of shares outstanding and on split history, so it says nothing about total company value. Two firms of equal value can have very different prices and weights.

  • Forgetting to adjust the divisor after a split.

    Students recompute the sum of prices but keep the old divisor.

    Fix: Set the new divisor so that new price sum ÷ new divisor equals the old index value.

  • Claiming equal weighting has low turnover because it is simple.

    Confusing simplicity with trading needs.

    Fix: Equal weights drift, so you must sell winners and buy losers at each rebalance. Turnover is higher than for cap weighting.

  • Describing fundamental weighting as passive market-cap exposure.

    Both are rule-based and transparent.

    Fix: Fundamental and factor weights depart from the market portfolio, so they carry tracking error and tilts versus a cap-weighted benchmark.

  • Giving a vague answer such as 'it is diversified' without a reason.

    Students avoid committing to a specific effect.

    Fix: Name the tilt, the concentration point or the cost, and tie it to the client need.

Worked examples

Example 1

An index holds three stocks. A: price 50, 200 free-float shares. B: price 20, 1,000 free-float shares. C: price 100, 100 free-float shares. Compute the market-cap weight and the price weight of stock B.

Show the solution
  1. Market caps: A = 50 × 200 = 10,000. B = 20 × 1,000 = 20,000. C = 100 × 100 = 10,000.
  2. Total market cap = 40,000. Weight of B = 20,000 ÷ 40,000 = 50%.
  3. Prices: 50 + 20 + 100 = 170.
  4. Price weight of B = 20 ÷ 170 = 11.76%.

Answer: B is 50% of the market-cap-weighted index and about 11.8% of the price-weighted index. B is the largest company but has the lowest price, so price weighting understates it.

Example 2

A price-weighted index has three stocks priced 30, 40 and 50, with a divisor of 3. The index value is therefore 40. Stock C (price 50) splits 2-for-1 to a price of 25. Find the new divisor, and state the index value on the next day if A rises to 33, B to 44 and C stays at 25.

Show the solution
  1. Prices after the split: 30 + 40 + 25 = 95.
  2. New divisor = 95 ÷ 40 = 2.375.
  3. Next day prices: 33 + 44 + 25 = 102.
  4. Index value = 102 ÷ 2.375 = 42.95.

Answer: The new divisor is 2.375 and the next-day index value is about 42.95. Without the divisor adjustment, the split would have pushed the index down with no change in value.

Exam tips

  • Show the weight calculation line by line. A correct number typed alone earns credit, but the working protects you if an input is wrong in your head.
  • For a comparison, name the tilt, one risk and one cost. Equal weight: small and value tilt, high turnover, low capacity.
  • Answer only the number of points asked for, in the order given.
  • Link the scheme to the client. A large, low-cost mandate fits cap weighting; a client seeking a value or small-cap tilt may prefer equal or fundamental weights.
  • Do not call factor or fundamental indexes passive in the same sense as a cap-weighted index. They have tracking error versus the market.

Equity Indexes and Weighting Schemes in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Equity Indexes and Weighting Schemes: frequently asked questions

What is the difference between market-cap and equal weighted indexes?

A market-cap index weights each stock by its size, so large companies dominate and turnover is low. An equal weighted index gives every stock the same weight. It tilts to smaller stocks and needs more trading to rebalance.

Why does fundamental weighting tend to tilt toward value?

Weights depend on measures like sales or earnings, not price. A stock with a low price relative to those measures gets a larger weight than in a cap-weighted index. That is a value tilt.

Why does a price-weighted index need a divisor?

The divisor converts the sum of prices into an index value. After a split or a constituent change, you adjust it so the index level does not jump when nothing has changed economically.

What is free-float weighting?

It counts only the shares available to public investors, excluding holdings that are locked in, such as by governments or founders. It gives a better picture of the investable market and improves tradability.