Such an administration is considered less stable than a majority or coalition government, and so the analysts expect sterling to take a hit after the vote.
That applies regardless of whether it is Ed Miliband or David Cameron in Downing Street.
“The currency’s value should clearly decline to reflect the risk of extended policy uncertainty under minority rule,” said the note, written by economists Dean Turner and Bill O’Neill, as well as analyst Simon Bohn.
But the exact factors causing investors to panic do depend on which government comes to power.
If it is a Conservative government, then markets are likely to be worried by the chance of the UK leaving the EU in a referendum which David Cameron has promised for 2017 – a so-called Brexit.
By contrast if Ed Miliband wins, “Brexit fears will certainly fade, but these could be replaced by concerns about overall fiscal credibility and devolution, especially if Labour relies on the SNP for informal support,” said the note.
The different scenarios in the very tight election race will also have an impact on other markets.
A Conservative minority government would be expected to continue to reduce the deficit, pushing up gilt prices and allowing the Bank of England to keep interest rates low.
A Labour government would spend more, pushing borrowing costs up and encouraging the Bank of England to tighten monetary policy.
And the stock market would be affected by either party, with a Conservative-induced Brexit fear pushing down some shares, and Labour’s tax and regulation plans hitting other sectors.
Visit our General Election poll tracker to see how the polls changed in the build-up to election day.