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At this link: http://www.investopedia.com/articles/trading/06/daytradingretail.asp they mention:

Liquidity allows you to enter and exit a stock at a good price (i.e. tight spreads and low slippage)

I know the definitions of liquidity (how much volume is traded),spread (low difference between bid and ask) and low slippage(trades get executed at the price at which you order (for market order). But I am not able to see for myself how more volume means low spread and tight slippage. More volume just means more people are interested in the stock...i.e supply and demand are matched well.

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Consider the case where a stock has low volume. If the stock normally has a few hundred shares trade each minute and you want to buy 10,000 shares then chances are you'll move the market by driving up the price to find enough sellers so that you can get all those shares. Similarly, if you sell way more than the typical volume, this can be an issue.

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You have just answered your question in the last sentence of your question:

More volume just means more people are interested in the stock...i.e supply and demand are matched well.

If the stock is illiquid there is more chance of the spread and slippage being larger. Even if the spread is small to start with, once a trade has been transacted, if no new buyers and sellers enter the market near the last transacted price, then you could get a large spread occurring between the bid and ask prices.

Here is an example, MDG has a 50 day moving average volume of only 1200 share traded per day (obviously it does not trade every day).

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As you can see there is already an 86% spread from the bid price. If a new bid price is entered to match and take out the offer price at $0.039, then this spread would instantly increase to 614% from the bid price.

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Theoretically, it's a question of rate of return.

If a desired or acceptable rate of return for market makers' capital is X, and X is determined by the product of margin & turnover then higher turnover means lower margin for a constant X. Margin, in the case of trading, is the bid/ask spread, and turnover, in the case of trading, is volume.

Empirically, it has been noted in the last markets still offering such wide-varying evidence, equity options: http://faculty.baruch.cuny.edu/lwu/890/mayhew_jf2002.pdf

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