Japan Fell 2.16% and 0.95% on the Same Day. Both Are True

The same market can fall twice in one session, by different amounts, and neither number is wrong. On Monday, after US forces struck two Iranian rocket launchers at Larak Island in the Strait of Hormuz, Japan opened into the news and the Nikkei 225 fell 2.16%. The Topix, running through the same hours on the same exchange and covering a superset of those companies, fell 0.95%. Nothing about Japan differs between the two figures. The gap is the difference between a price weighted and a market cap weighted index, arithmetic that was settled long before anyone had heard of Larak Island.

This one runs as a conversation. Eunha lives between structure and emotion, and she gets at things by asking. Across from her is Nina, twenty-three, eleven months into her first brokerage account. Nina holds a Japan tracker she picked because the name sounded like the country. She has read both numbers and decided they disagree about Japan.

Eunha does not answer that question. She takes it apart first.

Two numbers, one session

"One of them has to be closer to what actually happened," Nina says. "A market fell. There is a real amount it fell by."

Eunha asks her which market she means. Not which country: which market. The 225 companies whose share prices the Nikkei adds together, or the 1,638 companies whose free-float value the Topix adds together. Both sets traded in Tokyo on Monday, both ended the session lower, and the two indices were never measuring the same object. There was no single true number for them to disagree about.

Nina pushes back, because that sounds like a dodge. Her tracker does not say "225 share prices added together." It says Japan.

That is the problem, and it is not a labelling accident. An index move is not a fact about a country. It is the output of a formula applied to a list, and both were chosen by people who published their reasoning and were never asked about it again. CNBC carried both Japanese numbers in the same paragraph on Monday. There was no contradiction to resolve.

What does a price-weighted index actually count?

Eunha starts with the arithmetic, because the arithmetic is short. Nikkei Inc. publishes it in its own index guidebook. Each constituent's share price is multiplied by a price adjustment factor. Those adjusted prices are added together, then divided by a number called the divisor. That is the index. A company's pull on it comes from where its share price sits inside that sum.

Nina works it through out loud and stops halfway. A company trading at 40,000 yen a share contributes ten times what a company trading at 4,000 yen contributes, even if the second company is worth five times more.

"Say that back to yourself," Eunha says. "A share price is a company's value divided by however many pieces it decided to cut itself into."

That decision is administrative. A board can double the share count and halve the price on a Tuesday, and nothing about the business changes. Under price weighting, that Tuesday changes how loudly the company speaks in a national benchmark.

The Topix takes the other route. JPX calculates it as a free-float adjusted market capitalisation weighted index. Influence follows what a company is worth in shares that can actually be traded, and how the shares were sliced is irrelevant. One formula weighs the business. The other weighs the sticker on a single share.

What a market cap weighted index does to the same company

"Give me the worst case," Nina says. "How far apart do these two get for one company?"

One name carrying better than a ninth of a 225-company index is a long way from the intuition that a benchmark spreads risk. Spread the same market across 1,638 names weighted by value and nothing comes close to that. The published figures for the largest Topix member disagree in the decimal depending on whose data you read. Every version of them sits in low single digits.

So Monday was not two opinions about Japan. It was two exposures. The one Nina holds concentrates a tenth of its fate in a single clothing retailer.

Why the Nikkei has two patches bolted onto its own formula

Nina assumes nobody at the index provider has noticed. They noticed a long time ago, and wrote two mechanisms to hold it back.

The first is the price adjustment factor. A stock joining the Nikkei gets a factor of 1, but the guidebook allows values from 0.1 to 0.9 when the stock's price is high enough to swamp the sum. When that dial was not enough, a blunter one followed. From the periodic review of October 2022, Nikkei introduced a weight cap threshold of 12%, scheduled to fall to 11% at the October 2023 review and 10% at the October 2024 review. Breach it and a capping ratio of 0.9 is applied on top of the existing factor, and each further breach knocks that ratio down another 0.1.

An index provider does not build a brake for a distortion it believes is imaginary.

Fast Retailing, the owner of Uniqlo, was the first company to trigger it. Once the threshold had stepped down to 10%, its weight reached 10.4% at a July review base date. The cap engaged, and its factor was cut from 3 to 2.7 with effect from 1 October, as Nikkei Asia reported. The brake worked exactly as designed and did not hold. By the base date of 31 January 2025 the weight had reached 11.4%, above where it started, and the factor came down again to 2.4 from 1 April.

Nina catches the shape of it before Eunha spells it out. The company was pushed down twice and ended up higher both times, because the thing being capped is a percentage of a sum that the same share price also inflates.

The cap is applied to the symptom.

A brake is an admission written into a rulebook. Somebody agreed in public that one company's share price could distort a national benchmark. They built a mechanism to restrain it, published the schedule, and then watched the distortion outlive the mechanism. That is roughly the honest position of every rule written to contain something nobody is willing to remove.

A stock split halves the weight and changes nothing else

The cleanest version of this lives on the other side of the world, in the index nobody thinks of as exotic. The Dow Jones Industrial Average has no adjustment factor sitting between a share price and its weight, which makes it the pure case.

Split a Dow constituent two for one and its share price halves overnight. Its contribution to the sum of prices halves with it, so its influence over the index halves, and the divisor is reset so the index level itself does not jump. Same revenue the next morning, same assets, same owners, twice as many shares at half the price, and half the say in what the Dow does tomorrow.

Nina asks whether that works the same way on the Nikkei. Not cleanly, Eunha says, because the adjustment factor sits in the way. A large split can move a constituent's factor, and the interaction gets settled at the next base date rather than on the day. The mechanic belongs to price weighting in general.

The Nikkei is the version with paperwork.

Under free-float weighting a split is invisible. Twice as many shares at half the price is the same market value, so the weight does not move and the index needs no rule for it at all.

Which means a price-weighted index weight is partly a record of corporate-action history. A company that split three times over twenty years and one that never split will sit at different influence levels even if they are worth the same today. The formula is not measuring the companies. It is measuring the companies plus everything that has been done to their share counts since they joined.

Who decides which 225 companies are in the index?

Cap weighting does not need anyone to pick the members. Set a threshold on free-float value and the list writes itself, which is how the Topix carries 1,638 names without a committee reading through them one at a time. That number is itself in motion. It was around 2,200 before the first stage of the exchange's index revisions and about 1,700 when that stage completed in January 2025. A second stage in October 2026 is projected to take it just past 960.

Price weighting has no such threshold, because share price ranks companies by nothing. So a rule has to do the choosing, and someone has to write the rule.

Nina expects an exchange. It is a newspaper company.

The Nikkei 225 is calculated and published by Nikkei Inc., which took the index over from the Tokyo Stock Exchange in 1970 and also publishes the Nihon Keizai Shimbun. Constituents are reviewed twice a year under the guidebook, with base dates at the end of January and July and effect from early April and October. Liquidity is assessed on trading value and on the ratio of a stock's high-low range to that trading value. The top 450 names on the Prime Market form a high liquidity group, constituents that fall out of it are deleted, and non-constituents inside the top 75 are added.

Then comes the step that decides the shape of the thing. Nikkei sorts companies into 36 industries and folds those into six sectors. Names are then added and deleted to balance the number of constituents across those sectors until the total lands on exactly 225. Sector representation is counted in company names, not in company value. Four enormous firms and four small ones arrive with equal footing in that count, and price weighting decides afterwards what each is worth inside it.

None of that is illegitimate. It is a stated editorial method, published in English and applied on a fixed schedule. It is simply not what the word benchmark suggests to someone buying a tracker.

Every rule is disclosed. Disclosure has never been the same thing as attention, and the index business has always been comfortable with the difference. Being added or dropped moves real money by itself, which is why the rules that decide index membership matter. Weighting decides something else. Not who is in the index, but how much each member counts once they are.

You already know this error in its crypto form

Nina already distrusts one version of this number, and has not noticed the connection yet.

Ask her about a token with a large market cap and she will ask what fraction of the supply is actually circulating. She has watched a headline valuation sit on coins that could not be sold. That instinct is correct, and it is why what a market cap number actually counts matters more than the figure printed beside it. Locked, vested, held by a treasury: what is actually in play is always smaller than the number on the page.

The benchmark is the same error, one level up. She checked what was inside the token and never checked what was inside the index that told her Japan fell. An index also hides less than a token does, which somehow makes it worse. The guidebook is a public PDF, the cap has a published schedule, the review dates are set a year ahead.

"So I should have asked which Japan," Nina says.

Not quite, Eunha tells her, and the correction is narrower and more useful than that. Before treating an index move as information, establish what the formula counts, because that is also what you own the moment you buy the tracker. A cap-weighted Japan fund and a price-weighted Japan fund are not two views on one country. They are two different exposures wearing one word.

That question travels well beyond Tokyo. It decides which index a contract settles against when a futures position expires. It sits under every product that promises you a market and hands you a formula.

Monday's two numbers will be stale by the weekend. The gap between them will not, because it was never about Larak Island or oil or Japan. A figure can be published, accurate, widely quoted, and still answer a question nobody said out loud.

Nina's question works on anything with an index in its name. The simulator's 34 tokenized stocks include S&P 500 and Nasdaq products, sitting alongside the individual companies they hold. Open one, then go and read what it is built to count before you decide a move in it means anything. The $5,000 balance is simulated, which makes it the cheapest place there is to build a habit that gets expensive to skip.

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