Setting Market-Making Order Sizes Through Inventory Limits

# Determine the right order size with market making strategy


# Determine the right order size with market making strategy












In a market market strategy https://web.stanford.edu/class/msande448/2017/Final/Reports/gr4.pdf, how can we determine the right order size? Assuming I use a market making strategy and on a specific stock at a time t, I place a limit buy order at price p_1 with volume v_1 and limit sell order at price p_2 with volume v_2. In taking into account that v_1 = v_2, how can we determine the right order size?

The author of that paper told me : "That's a question I don't fully address. But the goal is typically to manage inventory, so you will never fall outside +/- x around a neutral position. Therefore if you are long x, then you will typically place an order to sell x and return to a neutral position (sometimes market orders are placed to do this more aggressively). "

I did not fully understand what he meant.

Be aware that I possess the full market depth.

## Answer by Alexey Golyshev (score 6, accepted)

https://quant.stackexchange.com/a/41264

> "I need to get an algo or a formula to determine to right quantity to trade each time I place the pair (limit_buy_order, limit_sell_order)."

Actually, you need a formula for determination of the optimal prices, not quantities.

For example, if the market goes down and you have long positions in inventory, you should reduce ask price to attract more buy orders and close long positions. And the optimal price reduction step depends on how many orders you want to attract.

http://www.cmap.polytechnique.fr/IMG/pdf/stoikov.pdf https://www.math.nyu.edu/faculty/avellane/HighFrequencyTrading.pdf

## Answer by Attack68 (score 2)

https://quant.stackexchange.com/a/41147

He meant the following:

Market makers (MMs) seek to make money by simultaneously selling high and buying low. The risk they run is that those trades are not simultaneous, instead there is an intermittent period between buy and sell when the market may move adversely for the MM, impacting overall profits.

If the mid market price of some marketable instrument is 0, and the MM has bid -1 and offered +1 and been hit so that he is now long at -1 he has greater inclination to sell and reduce risk rather than buy more and increase risk exposure so that his marketable prices might now be -1.5 +0.5, even if the mid-price is still believed to be 0. This is called skew.

The author is suggesting that the size of (skewed) positions is such that they offset the current risk position of the portfolio after aggregating trades.

## Answer by LazyCat (score 2)

https://quant.stackexchange.com/a/41148

Given your data, you have absolutely no way of determining the right order size. Just assume, that you place 100 shares on each side (or 1 share if it makes your calculations simpler). If you want to compare different market-making strategies, just assume, the same risk/position for each strategy.

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/41268

As the author suggested you need an upper limit $X$ on the dollar value of the inventory you are willing to hold. This depends on the amount of capital that you are willing to employ in the market-making business. (If the limit is reached market-makers take strong action, even market orders, to reduce the inventory. This could cause significant loss).

The order size you display at any time can be a fraction $p$ of that limit. The arrival of $\frac{1}{p}$ orders on the same side (consecutive buys or consecutive sells) would bring your inventory to the limit. You want this to be fairly unlikely in a random situation and you can set $p$ small enough accordingly.

Let's say you have 1 million dollars and you think $p=0.1$ is safe enough, then you can post limit orders for 100,000 dollars worth of stock.