* Yen on course to post 3 straight quarters of gains
* Swiss franc hits one-mth peak vs dollar, 6-week high on euro
* Concerns about Deutsche Bank sour risk sentiment
* Sterling in longest losing quarterly streak since 1984
By Hideyuki Sano
TOKYO, Sept 30 (Reuters) - The Japanese yen looks set to log its third straight quarter of gains on Friday, while the Swiss franc held firm as concerns about the health of Deutsche Bank undermined investor risk appetite.
The yen traded at 101.20 yen to the dollar, bouncing back from Thursday's low of 101.845, and not far from a one-month high of 100.085 touched on Tuesday.
The yen, often seen as a safe-haven currency, rebounded as global share prices slipped on worries about Deutsche Bank , under pressure from a massive fine the United States demands over its sales of mortgage-backed securities.
The latest lurch came after Bloomberg reported that a number of hedge funds that clear derivatives trades with Deutsche had withdrawn some excess cash held at the lender.
The yen has gained 2.0 percent so far this quarter, on course to log its third consecutive quarter of gains, as investors suspect the Bank of Japan has reached a practical limit in stimulus and has lost clout in cheapening the yen.
For now, though, the dollar has been supported above 100, seen as a psychologically important level by many.
Speculation that Japanese investors may buy more foreign assets in their new business half-year starting from Oct 1. could stem the yen's gains in the near term.
Traders are also wary of possible attempts by Japanese authorities to talk down the yen, even though they think their intervention at this stage is unlikely.
"On the whole, I would expect the dollar to gradually weaken broadly, for as it stands now, Democrats are likely to win the White House, which means the Fed will remain cautious on raising rates," said a trader at a European bank.
The Swiss franc hit a one-month high of 0.9640 franc to the dollar. Against the euro, the franc hit a six-week high of 1.0833 franc per euro.
Also fanning flight-to-quality bids was India's military strike of Pakistan-ruled Kashmir on Thursday.
Indian officials said elite troops crossed into Kashmir and killed suspected militants preparing to infiltrate and carry out attacks on major cities, in a surprise raid that raised tensions between the nuclear-armed rivals.
The Indian rupee posted its biggest fall since June, sapping budding enthusiasm to the hunt for yields in emerging market currencies.
The euro was little moved at $1.1223, having stayed in a narrow trading range of just over two cents for the whole of September, the tightest since June 2014.
The British pound stood at $1.2972, weighed by expectations that the Bank of England might further ease monetary policy in coming months.
On the quarter, the pound lost 2.6 percent, which would be the fifth quarter of losses in a row, the longest such streak since 1983-84.
Some currency analysts think the pound's outlook remains bleak given worries that an exit from Europe's single market will drag Britain into a recession and blow out its ballooning current account deficit, already among the highest in the developed world.
"The current account deficit in UK is close to 7 pct. Budget deficit is close to 5 pct of GDP. We got political turmoil. And for that, it will give zero percent yield. How much of that would you like to buy?," said David Bloom, London-based global head of Forex strategy at HSBC. (Editing by Jacqueline Wong)