Salim Ramji is betting the path to Vanguard Group customers’ hearts is still through their wallets. In the first major initiative in Ramji’s six-month run as chief executive, Vanguard on Monday slashed the fees on nearly half of its U.

Vanguard Group Inc.’s biggest salvo yet in its campaign to cut fees for the investing masses presents industry rivals with a painful choice. Follow suit and lose potentially hundreds of millions in revenue — or hold the line and risk losing badly needed market share.

Malvern-based Vanguard is pricing active funds cheaper as it competes with Schwab, Fidelity, and other mass-market money managers.