What is the spread, and why isn’t it zero?
The chart below illustrates the spread on an order book with a best bid of 100 and a best ask of 102. Buy at once and you trade at the best ask of 102; sell at once and you trade at the best bid of 100. So buying 1 unit and immediately selling it again loses 2, exactly the spread. That money goes to those who are willing to leave resting orders: the spread is the price you pay to trade now instead of waiting. The spread also cannot be narrower than one tick, because bids and asks can sit only on the price steps the exchange allows.How far does a large order move the price?
Cont, Kukanov and Stoikov measured price impact, how far an order pushes the price, on data for 50 US stocks. Over short intervals the price changes mainly with the imbalance between supply and demand at the best bid and best ask, counted from new orders, trades and cancellations. The relation is linear, and its coefficient is inversely proportional to the depth of the book. So for the same excess of buy orders, a book half as thin moves the price twice as far. A large fund’s order is not sent all at once. According to Jean-Philippe Bouchaud, even a highly liquid market has very little volume that can be traded at once, so a large order has to be split and traded gradually over many hours, days, sometimes weeks. The whole series of small orders is called a metaorder. The price impact of a whole metaorder, from the first small order to the last, follows the square-root law that Tóth et al. summarize: is the average price change, as a percentage of the price. is the size of the metaorder, the trading volume of the whole day, the day’s price volatility and a constant of order 1. The law has been observed in stocks, futures and foreign exchange, for orders from about 0.01% to a few percent of daily volume, with a measured exponent between 0.4 and 0.7 rather than exactly 0.5. Take : a metaorder of 1% of daily volume moves the price by about a tenth of the day’s volatility, since . An order four times larger, 4% of daily volume, moves the price only twice as far, about two tenths of the day’s volatility. So how far does a large order move the price? For an order sent all at once, it depends on how large the order is against the size resting in the book. For an order split into pieces, it depends on what share of the day’s volume it is, and the price moves with the square root of that share. In the trading costs of a strategy, this move in the price is one source of slippage, the difference between the price you meant to trade at and the price you got.In short
Liquidity is the ability to buy or sell at once without pushing the price far, and the spread and depth are its two basic measures on an order book. The spread is the cost of a small order: buy and immediately sell and you lose exactly one spread. Depth decides how much more a large order costs, since the thinner the book, the further the price is pushed. A liquid asset has a narrow spread and many orders resting around the price.References
- Limit order books by Gould et al.: an overview of order books, including the explanation of the spread as the price of being filled at once.
- Measuring market liquidity: An introductory survey by Gabrielsen, Marzo and Zagaglia: definitions of liquidity and how it is measured.
Read next
Order book and order matching
What an order book holds, at what price orders trade and why the price moves.
Market participants
Who places the resting orders that make up liquidity, market makers among them.