Why does all this matter to proprietary trading? A bank could sneakily use market making to mask its proprietary trading ambitions. For example, if a bank wants to bet that Apple's stock will decline, it can sell a bunch of call options on the company's stock to its clients. Then, it could just keep the exposure to itself, instead of selling it to different investors with a bearish view on Apple.
That example, however, would be pretty transparent to regulators. There's probably a pretty liquid market for investors who would like to bet for or against the stock of a company like Apple. But in the market for over-the-counter derivatives, it isn't so easy to find an investor to take on the exposure to a security that was highly customized for another client. That's where things get tricky.
The Volcker Rule study recognizes this issue, saying:
The ability to hold inventory in this context is a principal complexity: the same inventory built with the intention of facilitating liquidity for clients could also be built with the intention of engaging in impermissible proprietary trading. Consequently, a key challenge is the identification of inventory levels that are appropriate to facilitate client-driven transactions but not to take prohibited proprietary risks.
There are no clearly great solutions to deal with this problem, as it's pretty difficult to differentiate between legitimate market making and proprietary trading. But here are a few potential solutions, none of which are perfect.
If a bank is really making a market for some security, then that implies that a customer has asked the bank for that security. That should be somewhat documentable. For example, if a copper mining firm wants a customized derivative to hedge its risk, then it can request that a bank make a market for that security. In doing so, it can be asked to sign a declaration that it requested the security, and that the bank did not solicit the firm to create it instead. Regulators could audit such declarations.
If a proprietary trading desk is hidden through market making, it would still need some ability to solicit in order to make the bets it believes in. If it can't solicit investors, then reaching its investment goals will be very difficult. While an investor may come around from time to time requesting precisely the opposite side of a trade that a prop trader is looking for, this won't always be the case. That will make executing a specific investing strategy relatively difficult.
Moreover, this wouldn't necessarily mean that market-making traders couldn't solicit any business. There could be an exception to this rule if a trade is made to offset exposure a bank already has in its inventory due to a previous transaction as a part of its market making function. And if the bank wants to generally advertise its market-making services, it can do so, as long as it doesn't suggest that its clients buy securities with some specific type of exposure.