# How to understand micro-price (aka, weighted mid-price)?

The definition of micro-price is

S = Pa * Vb / (Va + Vb) + Pb * Va / (Va + Vb)


where Pa is the ask price, Va is the ask volume, Pb is the bid price, and Vb is the bid volume.

The typical explanation for micro-price is that a larger quantity of shares on the bid than on the ask indicates greater buying pressure, and therefore the "true" price is closer to the ask than to the bid.

But my confusion is: The bid price should be hit by the aggressive sell orders, so the "true" price should still be closer to bid, opposite to the definition of micro-price.

Could anyone help to explain?

• You are right, but nobody knows if aggressive market sell or market buy orders are about to hit or not. If all we can observe is the limit order book, it makes sense to assume that the market buy/sell orders that will arrive are going to be roughly matched and use the quantities at the bid and ask to try to predict which way the price is going to go. It is only a heuristic; a big market sale can cause the price to go down even though the bid queue is much bigger than the ask queue. A comparison of the queues on both sides only tells you which side is more vulnerable, not who is going to win. Jan 11 '20 at 16:37
• @noob2 Thanks. So you both agree with and disagree with the definition of microprice. But then why do people still use such definition to build their trading algorithm? Jan 12 '20 at 2:35

## 2 Answers

The justification for that microprice is empirical, not theoretical. In most market I can think of, most of the time, if there are more orders and more size on the bid than the ask, then it's more likely that that BBO will tick up rather than down. And the greater the imbalance, the higher the probability of an uptick (and vice-versa for downticks). For your market, you can grab some tick data to verify this. If you work in HFT, then you'll likely spend a good amount of time looking at tick data and trying to come up with a better formula than the one you describe (there are lots of ways to improve it).

• can you please describe one? Jan 13 '20 at 9:56
• An obvious improvement is to include orders deeper in the book than just the BBO. Jan 14 '20 at 12:46
• It add a lot to the noise, makes the output very close to useless the way I have been using it. Is it possible for you to share some insights? Jan 14 '20 at 15:13
• what have you tried? Jan 15 '20 at 13:39
• I have used top 3, 5 levels, all level on both sides of the book, a lot of noise. Jan 16 '20 at 4:48

From my own experience, if there is significantly more size on the bid than the ask, then it is easier for market participants to clear the remaining asks than to clear the remaining bids.

This phenomenon is, of course, not absolute or automatic. But it happens more than half the time, which is the whole point of a weighted average like this. There is a greater than 50-50 chance that the price will rise, so we want a value that is higher than the standard mid.