Morgan Stanley raises interest rates on cash. It’s a sign of pressure in the industry.

For years, investors’ uninvested money has been a lucrative source of revenue for the asset management industry. Firms have paid clients paltry interest on that money, while rates have generally risen over the past two years, in many cases allowing firms to earn much higher returns than they paid their clients. That’s starting to change.

Morgan Stanley will raise fees on some clients’ uninvested money in advisory accounts, a spokeswoman confirmed Wednesday. Effective Aug. 1, clients with $250,000 or more…