Stock Splits, Tick Size, and Trading Liquidity

Summary

The note explains why fractional shares offered by brokers do not fully replace stock splits as a way to adjust a share’s trading price. On exchanges, orders generally trade in whole shares, while brokers can aggregate customers’ fractional orders to execute full-share trades. The quoted market therefore reflects whole-share trading, with some venues also recognizing odd lots.

The explanation connects share price to tick size, the minimum price increment in a double auction. With a fixed tick, the increment represents a different fraction of the share price at different price levels, affecting how costly it is to improve an existing bid or offer. Very small relative increments can encourage frequent queue-jumping and noise, while large relative increments can make price improvement expensive. The note presents splits and reverse splits as ways to move a share price toward a more suitable tick-to-price relationship. Its numerical illustration is explicitly exaggerated, and it does not quantify an optimal tick or measure liquidity effects empirically.

Key ideas

• Broker fractional-share services can aggregate customer orders, while exchange trading generally takes place in whole shares.
• A tick size is the smallest permitted price increment and affects the cost of improving a bid or offer.
• The relative size of a fixed tick changes with the share price, influencing competition and trading noise.
• Stock splits and reverse splits can adjust the share price relative to the tick size.
• The explanation gives a conceptual illustration rather than an empirical estimate of the optimal tick size.

Tags

# Stock split and fractional shares


# Stock split and fractional shares












One of the main reasons for the stock split is liquidity. By increasing the number of shares, the new price will be half or one-third, depending on the split ratio. Wouldn't it be possible to achieve the same result by buying fractional shares? Why is stock split necessary if we can achieve the same results with fractional shares?

## Answer by lehalle (score 3, accepted)

https://quant.stackexchange.com/a/79420

It is not possible to buy a fraction of one share on exchanges (or on any trading facility). Brokers are offering this by (somehow) pulling all the fractional buy or sell to achieve one full buy or sell.

As a consequence, on exchange the best bid and offer are always for multiples of one share (putting aside the issue of "odd lots" on some exchanges).

Knowing that, you have to know that trading takes place as a double auction, and for a lot of reasons (historical, technical, and priority management), there is a smallest possible price increment, that is called the tick size.

Say that the tick is 1 dollar (this is an exaggerated example), then if the price of a share is 1,000 dollars, traders can "jump" in front of an existing seller or buyer for 1/1,000 of the price (that is very cheap, participants will move back and forth a lot, generating noise), whereas, if the price of a share is 2 dollars, the cost to jump is 1/2 of the price (that is very expensive).

Both are not very efficient, there is an optimal tick size. Splitting (and reverse splitting) shares is a way to maintain the ratio in the "best" sweetspot.

Have a look at L., and Sophie Laruelle. Market microstructure in practice. World Scientific, 2nd Edition 2018.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.