BlackRock Inc.'s largest mutual fund has been adding to its bet on the Japanese stock market, a company note said on Wednesday, calling it one of the few markets to offer a bargain and warning that U.S. stocks may disappoint.

Nearly 10 percent of the $45 billion BlackRock Global Allocation Fund is made up of Japanese stocks, as of July 29, about double the 5 percent held by its benchmark, a BlackRock website showed.

"During the month of July, we added to Japanese equities as we view the reappointment of (Japanese Prime Minister) Shinzo Abe's coalition combined with attractive valuations and corporate governance trends as a positive for risk assets in Japan," a note from the funds' managers said. "Looking across the broad array of asset classes globally, few are unambiguously cheap. Investors with a strong U.S. bias may become particularly disappointed."

Abe and his ruling coalition won a landslide victory last month in an election for parliament's upper house.

Institutional shares of the Global Allocation Fund have returned -0.57 percent over the last year, through July, trailing its longer-term record. The fund is managed by Dennis Stattman, Dan Chamby and Aldo Roldan.