Massachusetts Secretary of State William F. Galvin on Wednesday charged a unit of Boston-based ­Putnam Investments with deceiving investors about $3 billion in investments in mortgage-related securities that went on to lose money.

According to Galvin’s office, ­Putnam Advisory Co. allowed a prominent Illinois hedge fund, Magnetar Capital, to help select securities for collateralized debt obligations, vehicles made up of risky sliced-up mortgages that imploded in the financial crisis. But Magnetar was in a position to gain if the securities, many of them subprime, defaulted.