lending money to people for shorting on stock from math perspective I am trying to understand why would someone lend you stocks despite commissions for you to short on stock exchange market. If you borrow stocks from someone and price of stocks goes down, you get money, but he looses it. before: 1_stock = 100 USD now: 1_stock = 75 USD In this case 1_stock lost value. Now the lender gets his stock back and he lost 25$. I don't see any reason why people would lend their stock. Is there any math behind, like probability calculation on earning on fees or something?

They lose the same money if the stock goes down, whether or not they lend it to you. Either way, they own stock whose price went down.

But by lending you the stock, they collect the fees and interest you pay them.

(Compare: why would a bank lend you money when they _know_ that because of inflation it will have less value when you pay it back? They guess how much inflation there will be and charge an interest rate that exceeds the likely inflation rate. And the money would lose the same value from inflation whether or not they lent it to you.)