A clear outcome on Tuesday, then, could set the market up for additional upside into the end of the year.
Historically, midterm elections correspond with market strength. Barclays noted that since 1928, the S&P 500 has posted a median return of 7 percent in the 90 days after a midterm, with returns positive 86 percent of the time.
Upside in mid-term election years has historically favored small-caps. Since 1990, the Russell 2000 has risen an average of 4.89 percent between Election Day and the end of the year, compared with a rise of 3.22 percent in the S&P over the same period and a rise of 2.28 percent in the Dow.
Those gains are close to the averages for all years, with the Russell 2000 rising 4.6 percent in the last two months of the year and the S&P up 3.2 percent in the last two months, according to the Stock Trader's Almanac.
Barclays Capital estimates a 64 percent to 90 percent chance that Republicans would win the Senate. With neither party likely to achieve a large enough majority to overturn vetoes or prevent filibusters, however, the actual party in power may not matter much on Wall Street.
A "new composition is unlikely to enact changes in the near term that will alter the direction of the equity market," Barclays wrote. "If the election results are a surprise and Democrats keep control of the Senate, we believe the market reaction would still be muted."
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There could be outsized moves in the energy and medical device sectors, two groups with ties to Republican-driven legislation. The GOP is generally opposed to the Affordable Care Act's imposition of a tax on medical device companies to fund the healthcare program, and the party is widely in support of the Keystone Pipeline project, which would connect Canadian oil sands with U.S. refineries.
"If the majority party of the Senate is in doubt, that would cause a lot of volatility for medical device names likeStryker and Medtronic, most likely with a downward bias," said Michael Mullaney, chief investment officer at Fiduciary Trust Co. in Boston.