WASHINGTON—Despite a week of budget wrangling that showed scant sign of abating, Wall Street investors shrugged off the federal government shutdown, presuming that lawmakers will find a solution before the U.S. loses its borrowing ability.

The Dow Jones Industrial Average rose 76.10 points on Friday to 15072.58, snapping a two-day losing streak. The 30-stock average declined just 1.2% during the week, despite the shutdown.

Many...