The premium is arithmetic. The diagnosis is the work.
Quote the premium as (P - NAV) / NAV, where NAV is the fund's published net asset value per unit. That is the number every screener shows, and on its own it is close to useless, because a published net asset value is a photograph of prices at a moment that has already passed. For a domestic fund the moment is the previous close, a few hours ago. For a fund holding overseas securities the moment can be sixteen hours ago and one full trading session behind.
How do you split an ETF premium into two parts?
Split it in two. The stale-valuation component is (V - NAV) / NAV, the amount by which fair value has moved since the net asset value was struck. It is not a dislocation, nobody can arbitrage it, and it will vanish by itself when the next net asset value is published. The genuine dislocation is (P - V) / NAV, the amount by which the exchange price sits away from live fair value. It is the part that represents a real transfer between the buyer and the seller, and it is the only part an arbitrageur can attack. The two sum to the quoted premium by construction, which is the identity to check first.
Estimating V intraday is a judgement, and there are three routes. Many funds publish an indicative net asset value, computed every fifteen or thirty seconds from live or last-traded prices of the constituents. It is useful for domestic funds and close to meaningless for overseas ones, because it typically re-uses the underlying market's stale closing prices and only refreshes the exchange rate. Where the underlying market is closed, the honest estimate comes from index futures on the tracked index plus the currency move, which is exactly what the arbitrageur uses to hedge. Where neither is available, a basket of correlated listed proxies is the fallback, and you say so.
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How do you diagnose a premium, and what should you do?
The diagnostic question then becomes tractable. A large stale-valuation component and a small dislocation is a fund working correctly in a time zone that makes it look broken. A small stale component and a large dislocation is a fund whose arbitrage is impeded, and the next question is why: an expensive basket, a stressed market, or a halted creation. Worked example 2 runs both halves of that split on one afternoon and then computes the price at which the participant's arbitrage restarts, which turns out to be a long way from parity.
For a household the practical rule is short and worth taking literally. Never buy an exchange-traded fund with a market order at the open or the close. Never buy one whose quoted premium is above its usual level without knowing why. And treat any premium above the fund's own typical band as a fee you are volunteering to pay the person selling to you.
{
"skill": "Diagnosing an exchange-traded fund's premium or discount from live and published data",
"use": "Have an assistant assemble the four inputs a premium diagnosis needs - the fund's published net asset value and its strike time, the exchange price and time, the tracked index's futures move over the same window, and the currency move - into one table with every timestamp attached, then compute the stale-valuation and dislocation components and check that they sum to the quoted premium.",
"tools": ["A research or browsing assistant, grounded on the fund's own factsheet and the exchange's quote page", "The index provider's futures quote and the central bank's published reference rate", "A spreadsheet or a short Python script for the decomposition and the sum check"],
"prompt": "Here are five figures for one exchange-traded fund on one date: published net asset value per unit and the timestamp it was struck, the exchange closing price and its timestamp, the tracked index's futures move between those two timestamps, and the currency move over the same window. Compute (a) the quoted premium to published net asset value, (b) the live fair value per unit, (c) the stale-valuation component in percentage points of net asset value, (d) the genuine dislocation in percentage points of net asset value, and (e) an explicit assertion that (c) plus (d) equals (a) to within 1e-10. Do not round intermediate values. Then list every figure whose timestamp you could not confirm.",
"verify": "Trace every input to a primary source: the asset manager's own published net asset value with its strike date, the exchange's own quote and time, the index provider's futures settlement. Match the two timestamps before computing anything, because a fair value built from a futures move over the wrong window produces a decomposition that sums correctly and means nothing. Recompute the sum check by hand on one date. Date-check the creation status: a model will not know that the fund suspended creations, and that single fact changes the reading from 'wide band' to 'no band at all'. Cite the document and the pull date for each input.",
"diy": "You must be able to compute the premium, split it and check the sum with a calculator, and to say from the two timestamps alone whether a decomposition is even possible. Worked example 2 is the drill. A tool assembles the inputs; only you can decide that an indicative net asset value built from a closed market's stale prices is not a fair value and must not be used as one.",
"market": "IN"
}