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Indices, interlisting, and why markets matter

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Price-weighted versus cap-weighted — move a three-stock index both ways — then a stock listed in two countries, and the four things a securities market does for an economy.

Two ways to weight an index

An index is a portfolio of stocks reduced to one number so a market can be described by a single move. The question is how much each stock counts.

A price-weighted index adds the prices and divides by a divisor. Each stock's weight is its price over the sum of prices — an expensive stock counts more, whatever the size of the company. The Dow Jones Industrial Average is the famous example.

A capitalisation-weighted index weights each stock by its market capitalisation — price × shares outstanding — so a large company counts more, whatever its share price. The S&P 500 and the S&P/TSX Composite are cap-weighted; in practice both use the float-adjusted capitalisation, counting only the shares available to public investors.

Worked example — a three-stock index

PriceSharesMarket cap
Tamarack Foods300,000,000
Prairie Grid Energy300,000,000
Lakehead Robotics180,000,000

Total capitalisation $780,000,000. Price-weighted index level: =AVERAGE(30,60,90) = 60 (divisor 3). Weights: price-weighted 16.7 % / 33.3 % / 50 %; cap-weighted 38.5 % / 38.5 % / 23.1 %. Notice Lakehead: the smallest company, but half of the price-weighted index because its share price is the highest.

Now Lakehead rises 10 % to $99. Nothing else moves.

  • Price-weighted: =AVERAGE(30,60,99) = 63, a move of .
  • Cap-weighted: new total million; =SUMPRODUCT(prices1,shares)/SUMPRODUCT(prices0,shares)-1 = .

Same company, same news, and the price-weighted index moved more than twice as far — because the expensive stock is half of it. Run it the other way: if Tamarack (the $30 stock, and the joint-largest company) rises 10 %, the price-weighted index goes to =AVERAGE(33,60,90) = 61, only +1.67 %, while the cap-weighted index rises +3.85 %. The scheme decides which company's news matters.

Interlisting

A Canadian company can be listed on the TSX and on a US exchange at the same time — interlisted. Its share then has two prices in two currencies, and arbitrage keeps them aligned: if the NYSE price, converted at the current exchange rate, sits above the TSX price, traders buy in Toronto and sell in New York until the gap closes to the cost of doing so. The exchange rate is part of the price; a stock that is flat in US dollars has moved in Canadian dollars whenever the dollar has.

Why markets matter — four functions

  1. Price discovery — the continuous auction produces a price that reflects everything traders know, and that price is used far beyond the market itself.
  2. Liquidity — an investor can turn a security into cash quickly and at low cost, which is what makes people willing to buy long-lived securities in the first place.
  3. Capital allocation — capital flows toward the companies the market prices most highly, and away from those it does not.
  4. Risk transfer — securities and derivatives let those who do not want a risk pass it to those who will bear it for a price.

Recompute, cold

Prairie Grid (the $60 stock) rises 10 % to $66: price-weighted =AVERAGE(30,66,90) = 62, +3.33 %; cap-weighted 30/780 = +3.85 % — the same cap-weighted move as Tamarack's, because the two companies are the same size.

StockPriceSharesPriceweightCap weightNew priceTamarackFoods$3010,000,00016.7 %38.5 %$30PrairieGrid Energy$605,000,00033.3 %38.5 %$60LakeheadRobotics$902,000,00050.0 %23.1 %$99Index move+5.00 %+2.31 %Price-weighted: sum of prices ÷ divisor. Cap-weighted: Σ price × shares, before and after.
Lakehead is the smallest company and half of the price-weighted index. Its 10 % rise moves that index +5 % but the cap-weighted index only +2.31 %.
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