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Stocks with smaller market capitalisation sometimes have the potential for greater price growth. But when trying to invest the same amount of money as you would do with a mainstream share, your act of buying or selling pushes up or pushes down the share price, and in addition often it is not possible to buy or sell immediately and you have to wait to do so for an unknown price at an unknown time. This can make the price growth just an illusion.

Are there any rules of thumb or other ways of calculating the maximum amount that can be invested in a stock without affecting its price, using readily available data such as market capitalisation and trading volume?

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The first metric I would look at would be the average daily volume. I would only look to trade stocks with an average daily volume of at least 10x the volume I was looking to trade.

For example, if you were looking to trade 10,000 shares, you would only look for shares with an average daily volume of at least 100,000.

As a second metric I would also only trade stocks with a tight spread.

Using these 2 metrics you shouldn't move the market more than a couple of cents with your trades.

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I think you're looking for the bid-ask spread. When you trade a stock, that is the price of the stock until another trade is executed, so any trade can move the "price" depending on where the trade is executed relative to the most recent trade. However, if you buy a stock, the bid-ask spread determines how much you would "lose" if you sell the stock back immediately. It also indicates how much the bid must rise in order for you to break even. So one metric might be the bid-ask spread as a percentage of the market price (you use the ask or the bid or the midpoint, so long as you're consistent).

Also note that it's always possible to buy or sell immediately if you're willing to take the current ask or bid, respectively.

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