NEW YORK—Consumers are saving more than they’re spending, and that has investors worried.

Stocks capped a choppy week of trading with a mixed finish Friday after the Commerce Department reported that personal spending, incomes and savings all rose in May. What troubled investors was that the savings rate soared to 6.9 percent, a 15-year high, while spending rose by a modest 0.3 percent.

The trend suggests consumers are being very careful with their money. That’s good for the individual, but not great in the short term for the overall economy, which relies heavily on con...

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