There's no time like the present for Japan's pension whales to buy stocks and sell local bonds, according to Bank of America Merrill Lynch.

"Bond prices are high, and stocks are cheap, so it's a good opportunity to sell high and buy low," said Shuichi Ohsaki, the chief rates strategist at Merrill Lynch in Tokyo. "If they're going to do it, they should do it now."

The Government Pension Investment Fund and its three smaller peers, which manage a combined $1.9 trillion, have room to purchase $75 billion in Japanese stocks and offload $98 billion in domestic debt after an equity rout and tumbling yields sent the weightings in those securities veering off from their targets, according to Bloomberg calculations based on the money managers latest fiscal year results as of March.