Katsuhito Sasajima is looking into a double mystery. Why is the Bank of Japan's stock rising and why do the shares of the mega-banks usually follow?

BOJ shares surged 26 percent on four days through April 14.

The Mitsubishi UFJ Morgan Stanley Securities Co. analyst says he can't fathom why people buy the central bank's stock as there are minimal dividends and no voting rights. When the shares soared from 2012 to 2013 and in 2010, gains followed for Japan's three largest lenders, Mitsubishi UFJ Financial Group Inc., Sumitomo Mitsui Financial Group Inc. and Mizuho Financial Group Inc., he said.

"Mega-bank stocks have tracked BOJ stock rallies in the past," Sasajima wrote in a report dated Wednesday. "It is hard to identify any direct correlation between the two."

Since BOJ shares offer almost no income, investing in them is like buying a golf course membership, he wrote. He said the rally is being driven by individuals, who own about 40 percent of the shares and sometimes frame as a status symbol. "Even still, BOJ shares look like an odd investment," he wrote.