Indices and Benchmarks
9 min read
An index compresses a market into one number: a rule-based portfolio whose level tracks a defined universe of securities. Indices began as barometers and became infrastructure, the benchmarks performance is judged against and the underlyings for futures, options, and the fund products of module 4, so their construction rules have real consequences.
Weighting schemes
Each constituent weighted by market value (usually float-adjusted): the index holds the market in proportion to its size. Self-rebalancing under price moves, since weights drift WITH prices, and the scheme underlying most major benchmarks.
Two alternatives illuminate by contrast. Price weighting adds share PRICES and divides by a divisor, so a high-priced share moves the index more regardless of company size, an artefact of history surviving in some famous averages. Equal weighting gives every constituent the same share, tilting toward smaller names and requiring constant rebalancing as prices drift. Same universe, different weights, materially different behaviour: the weighting rule IS an investment strategy, stated or not.
Two companies: A at price 100 with 10 million shares (cap 1,000m), B at price 20 with 200 million shares (cap 4,000m). B rises 5 percent, A is unchanged.
The cap-weighted index reads B as four fifths of the market; the price-weighted one reads it as one sixth, because its PRICE is small. Neither is wrong; each answers its own definition, and knowing which definition a quoted index uses is prerequisite to reading it.
Maintenance: divisors and membership
Index levels must stay continuous through events that change the sum being computed, constituent changes, splits, buybacks, and the divisor is the device: it is adjusted so the level is identical the instant before and after the event, with only genuine price movement flowing through. Membership itself is rule-governed (size, liquidity, listing criteria) and periodically rebalanced, and because vast assets track the major indices, membership changes move real money: additions meet index-fund buying and deletions index-fund selling, measurable flows on announcement and effective dates, the index effect, a standing example of the uninformed-but-price-moving flow the markets course classified.
The divisor mechanism
Structural events change the numerator; the divisor is reset so the level does not jump. The published level is thus a chained series of price returns, not a raw sum.
The benchmark role completes the picture: a portfolio's performance is conventionally quoted RELATIVE to an index, active return over benchmark, and the tracking error statistics of module 4 measure the gap's variability. Total return variants of each index reinvest dividends, price return variants do not, and comparing a dividend-reinvesting portfolio against a price-return index flatters the portfolio by the yield every year, a base-discipline error from the statistics course in benchmark clothing.
Quick check
Stocks A (cap 1,000m) and B (cap 4,000m) form a cap-weighted index. What is B's weight as a decimal?
Quick check
In the two-stock example, B rises 5 percent and A is flat. What is the cap-weighted index return in percent? Answer as a decimal.
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