For a broker that is an intermediary and not holding the stocks then this is true to some extent. Their role is to connect those who are trying to sell a stock with those who want to buy it. They will receive a commission for this so in this respect they make money without risk. However on a broader level you consider them to be like a salesman, they will be competing with other brokers to get the connections and as such those under-performing are likely to lose out financially and in their career trajectory.

It is the traders and others who hold the stock that will have a greater risk as they will need the future price of the stock to change in order to resell/rebuy it and make a profit.

Agree with Peter when referring to institutional brokers. However, would add a couple of comments regarding non-institutional, i.e. normal household investors. Your question really depends on what type of broker you are talking about, and what type of trading you are referring to.

If you are referring to simple online broking platforms targeting "mum and pop" investors i.e. everyday households, and if you are referring to speculative "day trading," by your average non-institutional investor, then chances are you are right, the broker is making money on each transaction, with next to no risk to them. Day trading works on the premise that the individual assumes the stock price will move, sometimes by relatively small amounts, either up or down, and trades the stock to make a profit. Simple online trading platforms do not provide sophisticated advice, or allow for sophisticated financial instruments, and hence make most of their money by taking little risk, and also hence a small cut of each transaction.