Goldman Sachs Group Inc. set higher financial targets Wednesday in an effort to turn a skeptical shareholder base into believers in Chief Executive David Solomon’s turnaround plan.

Speaking at the Wall Street bank’s first-ever investor day, Mr. Solomon said Goldman aims to hit a 13% return on equity over the next few years, which would put it closer to best-in-class rivals such as JPMorgan Chase & Co. That figure was 10% last year, dragged down by spending on new ventures like consumer banking and a big legal charge related…

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