* European stocks fall 0.5 pct, spooked by U.S. politics
* Dollar steadies, peso rebounds after fall on Friday
* Oil slips as non-OPEC producers fail to back supply limits
* European bond yields eye biggest monthly rise in years
By Marc Jones
LONDON, Oct 31 (Reuters) - The dollar steadied but stock markets stayed spooked on Monday after news the FBI was investigating fresh e-mails linked to U.S presidential candidate Hillary Clinton's private computer server.
The weakest German retail sales in two years a fall in oil prices and one of the toughest month in years for bond markets all made for a shaky start in Europe where the STOXX 600 index .STOXX dropped 0.4 percent. .EU
A lacklustre day in Asia meant MSCI's 47-country 'All World' .MIWD00000PUS was flat and, at 1.7 percent lower, on course for its first monthly fall since June and its worst since a global shake down in January.
The dollar .DXY saw a recovery however, rising against the yen JPY= , euro EUR= and sterling GBP= on the day and heading for its best month - up 3.2 percent - against the world's top currencies in just under a year. /FRX
"The Clinton story of course has had an impact," said Richard Benson, co-head of portfolio management at currency fund Millennium Global in London.
"The polls are now roughly 50-50, but the probabilities are still hugely in favour of Clinton, given how the votes are spread out (per state). The question is whether people decide to reduce risk ahead of the election."
U.S. Federal investigators have secured a warrant to examine newly discovered emails, a source told Reuters on Sunday. had opened a recent lead over her unpredictable Republican rival Donald Trump in national polls, but it had been narrowing even before the email controversy resurfaced. An ABC News/Washington Post poll released on Sunday showed Clinton with a statistically insignificant 1-point national lead.
The Mexican peso MXN= , which has become a market proxy for the Clinton/Trump race, also rebounded in European trading after being knocked back on Friday.
South Africa's rand rallied too on hopes fraud charges would be dropped against its finance minister, though emerging market stocks .MSCIEF were down on the day and facing the prospect of an end to their four-month winning streak. EMRG/FRX
YIELDS BOIL, OIL TOILS
The jittery mood nudged investors back towards safe-haven government bonds but it has been the opposite story for most of the month.
German government bond yields were on track to end October with their biggest monthly rise since 2013, with sentiment fragile ahead of central bank meetings this week and a first estimate of euro zone inflation due shortly.
U.S. Treasury yields, which hit five-month highs last week, were poised for the biggest monthly rise since February 2015, while for Britain's gilts GB10YT=RR yields have risen almost 50 basis points, the biggest jump since Jan. 2009.
"Recent sharp falls in sterling's value vis-à-vis the euro and the U.S. dollar could reduce confidence in sterling and eventually threaten its role as a global reserve currency," said Standard and Poor's, which reviewed the UK's credit rating on Friday. could lower the rating if we conclude that sterling will lose its status as a reserve currency."
Oil prices extended their slide - driven by renewed oversupply concerns - and have surrendered most of the gains made in the first half of October. They are set to end the month with meagre gains.
The latest oil woes came after non-OPEC producers failed to make any specific commitment to join the Organization of Petroleum Exporting Countries in limiting output to support prices on Saturday.
U.S. crude CLc1 slid 0.4 percent to $48.52 a barrel on Monday, but looked set to edge up 0.6 percent for the month, while global benchmark Brent LCOc1 also retreated 0.4 percent to $49.50, up 0.9 percent in October.
"There was a lot of talk and nobody managed to agree on anything. That has been pushing the market down," said Jeffrey Halley, senior market analyst at OANDA brokerage in Singapore.
Adding to the list of potential market-moving events this week is a raft of factory activity surveys on Tuesday for many economies. There are also central bank policy meetings including Japan and Australia on Tuesday, the U.S. Federal Reserve on Wednesday and the Bank of England on Thursday, as well as U.S. October non-farm payrolls on Friday.