Suppose in a stock market we can access the information of buying/selling density per trader/account. For example during a trading session, V number of shares (i.e. volume) is traded by B number of accounts/traders are at the buyer side and S number of accounts/traders are at the seller side. Now if we define the densities as follow:

• buying density = V / B
• selling density = V / S

and then Buyer Seller Ratio (BSR) as "buying density" / "selling density", What relation could be between BSR and price? (if any).

If BSR < 1 (which means B > S) then the existing shares are held by more shareholders and vice versa for BSR > 1. Regarding this fact, my question is: when is the price likely to move higher? when number of shareholders is increasing (BSR > 1) or when number of shareholders is decreasing (BSR < 1).

If the current quote for XYZ is \$100.00 x \$100.10 with a size of 200 x 1000, it will take 1,000 shares of buying to move price up, assuming that no other sellers come in at \$100.10 (hidden orders or new sellers).

Let's say that the next ask on the order book is \$100.20 so the quote then becomes \$100.00 x \$100.20 (assuming that the bid does not move up.

Would it have made a difference if one person bought all 1,000 shares or if 10 people bought 100 shares each? In either case, all of the 1,000 shares had to be purchased in order to move the ask price.

Apropos to your question regarding the dispersion of shares among the participants at a given price, it has no bearing on subsequent price change.

You could possibly make a case for the price stability (volatility) of the entire float across individual versus institutional hands but that's not relevant to your question.

• Thank you for your answer. I think in theory you're right but in reality and from psychological view, it makes difference. If one person buys all the shares sold by 10 people, it's unlikely that he places sell orders until the price moves up enough for him to take a profit. So I think the dispersion of shares could affect the supply and demand mechanism. Feb 10 '19 at 21:44
• There is no "in theory" or a "psychological view" in play with this. Dispersion of ownership is meaningless when buying or selling share and it has no effect whatsoever on supply and demand. Dispersion of price and volume on the order book (buyers and sellers willing to transact now) determines whether one can get a fill or not. If you're not willing to accept this, collect Time and Sales data and collate buys at the ask and sells at the bid as well as the number of trades involved and do your calculations. Get back to us if you find a sustainable pattern. Trust me, you won't. Feb 10 '19 at 22:46
• I don't think it's completely meaningless. As an extreme point suppose someone has enough money to buy all shares of a company which makes him the only supplier. So there could be only one sell order and only one ask price. That's the effect on supply and demand. I think as the number of shareholders decreases, the price could move more easily. Is it right? Feb 11 '19 at 13:17
• How many companies are you aware of where someone had enough money to buy all of the shares of a company, making him the only supplier? I think in theory you're right but in reality, this never occurs. Feb 11 '19 at 13:34