Indexes, ETFs and Creation/Redemption

An index is a rule, not something you can buy

An **index** is a published rule for choosing and weighting securities. The **S&P 500** is a committee-selected set of large U.S. companies, weighted by **float-adjusted market capitalisation** — shares actually available to trade, so a company with a large strategic holder is weighted by less than its full size. The **Dow Jones Industrial Average** holds thirty names and weights them by **share price**, not by company size, which is why a $500 stock with a modest market capitalisation moves it more than a $50 stock that is worth more. Equal-weighted versions of the same names exist too, and behave quite differently: they sell the winners back to their neutral weight every rebalance. Two consequences follow. First, a cap-weighted index is **self-rebalancing in the direction of its winners** — when a constituent triples, it becomes a larger share of the index without anyone deciding that it should, which is why a handful of names can dominate an index’s return. Second, an index’s holdings change even when its committee does nothing: weights **drift with price** day by day, and committees act on top of that with periodic **reconstitutions**, additions and deletions. You cannot buy an index. You buy a **fund** that is managed to track it, in one of two wrappers. A **mutual fund** is priced **once a day** at the closing net asset value — you buy and sell at that price, with no bid-ask spread to cross but no intraday control either. An **ETF** trades on an exchange all day like a stock, at a price the market sets. Everything interesting about an ETF flows from that one difference. The same 500 companies, three ways — Cap-weighted (the standard S&P 500): The largest few names drive the return · Equal-weighted (the same 500 names): The smallest name counts as much as the largest · Price-weighted (the Dow’s thirty): A high share price counts more than a big company ←

Why an ETF tracks its basket

An ETF has a market price and a **net asset value** — the value of the shares it actually holds, per ETF share. Nothing forces those two numbers to agree, and in a fund that cannot be exchanged the gap can persist for years: **closed-end funds** have traded at double-digit discounts to NAV for a decade, because the only way out is to sell to another investor. ETFs are different because of **creation and redemption**, a two-way door that only **authorised participants** — large dealers with agreements with the issuer — may use, and only in **creation units** (tens of thousands of shares). When the ETF trades **above** NAV, an AP buys the underlying basket, delivers it to the issuer, receives newly created ETF shares, and sells them at the higher market price, pocketing the gap. When the ETF trades **below** NAV, the AP buys the ETF, redeems it for the basket, and sells the basket. Creation increases supply, redemption decreases it, and both push the market price back toward NAV. That is the whole answer to "why does the ETF track its basket": not because anyone promises it, but because **someone is paid to close the gap**, and the competition among APs is what keeps the gap at a few basis points in liquid funds. It is also why the gap **widens exactly when the mechanism is least able to work** — when the underlying market is closed, as with a broad international ETF overnight, or when the basket itself stops trading. In March 2020 many bond ETFs traded at real discounts to NAV, because the bonds inside had not printed a price all day and nobody could hedge the arb. The fund was not broken; the underlying market was. One more structural point worth knowing. When an AP redeems in **kind**, the fund hands over the lowest-cost securities in its portfolio instead of selling them, so the ETF does not realise the gain and does not have to distribute it as a taxable capital gain — the structural reason ETFs are typically more tax-efficient than a mutual fund holding the same basket. The catch is that you pay for that efficiency elsewhere: the **spread** and any premium or discount when you trade, which is why the expense ratio is the *smallest* number in the comparison of two ETFs. The mid-point of the spread is not a promise. When you buy an ETF you cross the spread (M3), and a fund quoting at a 20 bp spread costs you more per round trip than a decade of its expense ratio.

Leveraged and inverse funds decay on purpose

Leveraged and inverse ETFs promise a multiple of the index’s **daily** return, and they rebalance at the close every day to keep that promise. That single design choice decides everything else. Because the fund resets on the new, latest base, its return over a period is the product of the daily multiples — and a product of returns is **path-dependent** while the underlying index itself is not. The arithmetic is the reason. A loss needs a bigger gain to repair: fall 27.27% and you need a 37.5% gain to get back to where you were. A 3× fund multiplies the day’s move, so it takes larger losses in dollars than the gains it earned reaching the same level. Over a choppy stretch, the index can end where it started while the fund is materially down — not through fees or mismanagement, but through compounding a volatile path. The practical rule follows from the label: these are instruments for a view over hours or days. Held for a month, a 3× fund is not "3× the index" — it is a different, path-dependent bet whose outcome depends on the order of the moves. Inverse funds add their own wrinkle: they are a way to be short without borrowing shares, and they decay the same way, which makes them a tool for a trade, not a position. The label is a daily promise. Reading "3×" as a holding-period return is the single most expensive misreading in retail fund investing — and the fund did nothing wrong.

Why your fund is not the index

A fund that tracks an index does not return the index, and the gap has two names. **Tracking difference** is the number — usually negative — left over when you subtract the index return from the fund return over a period. **Tracking error** is the volatility of that gap around its average. They answer different questions: tracking difference tells you what the fund cost you, and tracking error tells you how reliably it will keep costing that. A fund with a tracking difference of −0.20% and a tracking error of 0.02% is doing exactly its job; one with the same −0.20% difference and 1.5% of error is taking bets it does not disclose. The gap is built from a short list of causes, and the expense ratio is only the first. Fees are taken from the fund’s assets every day, so they come straight out of the return. **Transaction costs** come next: the index reconstitutes without paying a spread, while the fund has to buy the additions and sell the deletions and cross the market to do it — which is why a fund tracking a small-cap or emerging-market index trails by more than its fee. **Cash drag** is structural: a fund holds cash for pending creations and redemptions and for dividends waiting to be paid out, and that cash earns nothing while the index assumes it is fully invested. **Withholding tax** on foreign dividends is a further drag for an international fund, because the fund pays the treaty rate and cannot always reclaim the difference. Two causes run the other way, which is how a fund can beat its own index net of fees. **Securities lending** lets a fund lend the shares it holds to borrowers — short sellers, mostly — for a fee the fund keeps, and in a portfolio of hard-to-borrow names the revenue can exceed the whole expense ratio, turning the tracking difference positive. **Fair-value pricing** of a foreign fund’s holdings, applied while the home market is shut, makes the fund trade at an estimate rather than a stale price set hours earlier, which shrinks the arbitrage of stale NAV — an improvement that shows up as a smaller gap rather than as a gain. The use of all this is comparative, and it needs discipline. Compare two funds only on the same index and the same window, and read the gap over years rather than quarters, because tracking difference is small next to a fund’s own volatility and a single year of it is mostly noise. Then weight what the ratio never shows: the spread you cross to trade it (M3), the fund’s securities-lending policy and how much of the revenue it hands back, and whether it uses **full replication** or **sampling** — holding a representative subset rather than every name, which is normal in illiquid markets and is itself a source of tracking difference. The comparison is not a hunt for the smallest expense ratio; it is a hunt for the smallest total gap, and the ratio is merely its most visible term. • Fees, transaction costs, cash drag and foreign withholding tax push the fund behind its index. • Securities lending and fair-value pricing can push it back in front, which is how a fund beats the index it tracks. • Read the gap over years on the same index — and weigh replication and lending policy, not just the ratio. Expense ratio, transaction costs and cash drag push a fund behind its index; securities lending can push it back in front. Two funds with identical fees can have different gaps, which is why the fee is the beginning of the comparison rather than the whole of it.

Sources

• Index methodology and float-adjusted weightingS&P Dow Jones Indices — index methodology
• Creation and redemption, and how ETF shares reach the marketSEC — ETFs and the creation/redemption process
• Leveraged and inverse funds: daily reset and compoundingSEC — investor bulletin on leveraged and inverse ETFs
• Tracking difference, premiums and discountsETF.com / issuer disclosures on tracking