Share your insights or perspective on the financial matter presented in the input.

Why do Dealers/Brokers hold Inventory in Stocks?
The difficulty is that you are thinking of a day as a natural unit of time.  For some securities the inventory decisions are less than a minute, for others, it can be months.  You could ask a similar question of "why would a dealer hold cash?" They are profit maximizing firms and, subject to a chosen risk level, will accept deals that are sufficiently profitable.  Consider a stock that averages 1,000 shares per day, but for which there is an order for 10,000 shares.  At a sufficient discount, the dealer would be crazy not to carry the order.   You are also assuming all orders are idiosyncratic.  Dividend reinvestment plans (DRIP) trigger planned purchases on a fixed day, usually by averaging them over a period such as 10 days.  The dealer slowly accumulates a position leading up to the date whenever it appears a good discount is available and fills the DRIP orders out of their own account.  The dealer tries to be careful not to disturb the market leading up to the date and allows the volume request to shift prices upward and then fills them.