* Nikkei falls more than 3 pct for 6th time this quarter
* Real estate companies worst hit, exporters battered
* Yen stronger than most exporters' assumed FX rate
* Mothers market plunges 7 pct as investors lock in gains
By Hideyuki Sano
TOKYO, June 16 (Reuters) - Japanese share prices tumbled to four-month lows on Thursday, as the Bank of Japan's inaction, a cautious Fed that fuels the yen's strength and worries over Britain's possible departure from Europe all made for reasons to sell.
The Nikkei average fell 3.1 percent to 15,434.14, its lowest level since mid-April. It is the sixth time it fell more than 3 percent this quarter. Until mid-2015, a fall of over 3 percent was rare.
The broader Topix fell 2.8 percent to 1,241.56, its lowest level since mid-February.
"Fears are gripping fund managers. They are now reducing stocks and increasing cash to protect their funds," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.
"And when fears dominate, you could see some amazing pricings," he added.
The Nikkei volatility index rose to 35.6 percent, its highest level since February.
The BOJ refrained from introducing more stimulus. Although such an outcome was widely expected, there had been some speculation about easing due to the fragile state of the Japanese economy and BOJ Governor Haruhiko Kuroda's history of surprising markets with policy decisions.
Real estate companies were the worst hit, dumped by a minority of market players who had bought them earlier on hopes of s BOJ easing.
Real estate company subindex fell 4.2 percent, with Mitsui Fudosan dropping 4.6 percent.
Exporters were badly hit too, as the yen shot up to as high as 104 yen per dollar, its highest level in almost two years.
That level is stronger than the exchange rate assumed by even the most cautious exporters, such as Toyota Motor and Fanuc, which expect the dollar at 105 yen for the current business year.
Most other companies have assumed a dollar/yen exchange rate of 110-115 yen in the current financial year for their earnings estimate, suggesting many profit outlooks will have to be lowered.
Panasonic fell 3.9 percent while Hitachi shed 3.6 percent. Toyota dropped 3.3 percent and Fanuc fell 1.8 percent.
So far this week, the Nikkei has lost 7 percent and the market looks oversold in the short-term.
Yet, overriding worries about Brexit are so large that few investors expect a major rebound at least until the UK referendum a week from now.
"It is hard to buy risk assets unless we get past next Thursday," said Keita Kubota, investment manager at Aberdeen Investment Management.
As investors rushed to sell shares that still have some gains, the index for the Mothers start-up market plunged 7.1 percent. The index has fallen 17.7 percent this week though it is up 8.2 percent year-to-date, compared to a fall of almost 19 percent in the Nikkei.
Shares of Bio-pharmaceutical developer Sosei Group, a star performer since late last year, fell 10.2 percent. (Reporting by Hideyuki Sano; Editing by Sam Holmes and Richard Borsuk)