Japan's real estate investment trusts have soared in value to become the priciest in the world. More purchases by one of the biggest investors in the landlord business — the Bank of Japan — may help propel prices even higher.

Buying by the BOJ has helped boost premiums on J-REITs, which manage rental properties such as apartments, offices and malls, to 62 percent as of June 8, meaning investors would pay almost two-thirds more than the appraised value of properties they own, according to S&P Global Market Intelligence estimates. That gap makes J-REITs outliers compared with similar securities around the world and suggests that the BOJ's stimulus is stoking extreme price dislocations in this market.

"The BOJ's REIT buying is a big trigger for prices to increase," said Yoji Otani, an analyst at Deutsche Bank AG. "When they buy, everyone follows because they know that downside risk is limited. If the REIT index declines, the BOJ will just buy more, so everyone just buy, buy, buy."