(Add details from speech)
* BoE's Cunliffe warns some funds may prove illiquid in crisis
* Says markets appear to have underprices risk of illiquidity
By David Milliken
LONDON, July 17 (Reuters) - Investment funds focused on emerging economies or high-yield debt may be unable to return investors' money promptly if turmoil hits markets, the Bank of England's financial stability chief warned on Thursday.
Many investment funds promise to redeem investors' shares within a day or two. But BoE Deputy Governor Jon Cunliffe said this may not be realistic when trouble strikes less liquid markets and droves of investors want to cut their losses.
"Market participants and investors will not always be able to sell what they want, where they want, and when they want," Cunliffe told a conference hosted by the Financial Reporting Council, a body that promotes corporate governance standards.
He said markets appeared to have underpriced the risk of investments proving illiquid, and that funds needed to have clearer discussions with investors about whether it was realistic to redeem shares quickly under all circumstances.
Investment funds have up to now been seen as posing few risks to financial markets, because they usually do not borrow money and operate a range of strategies.
But Cunliffe - who is responsible for financial stability at the BoE - said illiquidity was an issue in any market where a small number of investment funds or hedge funds pre-dominated, and cited emerging markets and high-yield bonds as areas where this may be a problem.
"Investment funds can pose risks to financial stability. They very often offer same- or next-day redemptions despite holding assets for which secondary-market liquidity can be uncertain," he said.
"(This) could disrupt systemically important markets."
Speculation last year that the Federal Reserve would slow the pace at which it pumped money into the U.S. economy caused a brief rout in emerging market assets, and Cunliffe said it was hard to predict what the consequences would be when global monetary policy started to tighten in earnest.
Some 4.5 trillion pounds ($7.7 trillion) of assets were managed in Britain at the end of 2012, according to the Investment Management Association, an industry body. Blackrock , Legal & General, Prudential's M&G unit and State Street are major players. ($1 = 0.5844 British Pounds) (Reporting by David Milliken Editing by Jeremy Gaunt)