Index Construction, ETFs and the Mechanics of Passive and Active Equity

Learning objectives

You can:

1. Read an index rulebook as a binding constraint on a fund, identify the four provisions that drive a tracker's turnover, and compute what a buffer zone costs in index purity and saves in trading.
2. Describe the exchange-traded fund wrapper in terms of its four parties and two markets, and state precisely which party bears which risk in each market.
3. Walk a creation and a redemption through in creation units, using a portfolio composition file, an in-kind basket and cash in lieu, and compute the authorised participant's economics on both legs.
4. Derive the no-arbitrage band around an exchange-traded fund's price from stated transaction costs, and compute the price at which an authorised participant restarts creating.
5. Compute a premium or discount from live quotes and decompose it into a stale-valuation component and a genuine dislocation, and name the conditions under which the second one persists.
6. Distinguish tracking difference from tracking error, compute both on the same fund, and decompose a tracking difference into fees, cash drag, withholding tax, securities-lending revenue and rebalancing cost so the parts reconcile exactly.
7. Compare full replication, stratified sampling and optimisation on one universe, computing the ex-ante tracking error, the reconstitution turnover and the build cost of each, and state which method wins for which mandate.
8. Build a total-cost-of-ownership comparison across four routes to the same exposure and solve for the holding period at which the ranking changes.
9. Compute the compounding gap on a daily-rebalanced leveraged or inverse fund over a stated path, reconcile it against the variance-drag approximation, and explain why the gap is a property of volatility rather than of fees.
10. Classify an active equity approach by process, breadth and style, and state what a factor or smart-beta mandate is actually selling.
11. Compute active share, ex-ante tracking error and the ex-ante information ratio of a 30-name book, apply position and sector limits, and price what those limits cost in expected active return and information ratio.
12. Decompose the implementation shortfall of one rebalance into delay, execution, opportunity and explicit costs, and read the decomposition as evidence about the trading process rather than about the market.

The gated skill throughout is the by-hand arithmetic: a premium decomposed, a tracking difference that reconciles, an active share computed from a weight vector. A spreadsheet does all of it faster once you can do it slowly, and the two augmentation blocks below say exactly where a tool helps and what it can never check for you.

Prerequisites & connections

Builds on. M0.02 supplies the order book, price-time priority and the impact-cost calculation, all used here without re-deriving them. EC1.02 owns index construction proper: the four weighting schemes, free-float adjustment and the Investible Weight Factor, the Nifty 50 and S&P 500 methodologies as their providers publish them, and the turnover a weighting scheme forces. Read that treatment first, because what follows starts where it ends, at the point where a real fund has to hold the thing the rulebook describes.

AA1.01 supplies the policy portfolio, constrained mean-variance optimisation and the idea that a constraint has a price in forgone expected return. AA1.03 supplies tracking error, the seven benchmark-validity properties and the price-return-versus-total-return defect. QM1.01 and QM1.02 supply variance, covariance and the factor-model algebra behind every tracking-error computation below.

Feeds forward. QD2.01 owns execution and microstructure in code: order types, the limit order book dataset, time-weighted and volume-weighted schedules, the square-root impact law, and the full implementation-shortfall decomposition. Section 13 applies that decomposition to one index-fund rebalance and hands the machinery straight back. QD1.04 builds the portfolio optimiser that Section 8 and Section 12 describe by hand. M0.06 owns the retail decision between an index fund and an exchange-traded fund, including the costs and taxes a household actually pays, and cross-links here for the mechanics behind that decision. AL1.04 takes the wrapper into alternatives. ES1.02 owns the regulatory perimeter around fund distribution and disclosure.