We propose a new approach to measuring the effect of unobservable private information or beliefs on volatility. Using high-frequency intraday data, we estimate the volatility effect of a well identified shock on the volatility of the stock returns of large European banks as a function of the quality of available public information about the banks. We hypothesise that, as the publicly available information becomes stale, volatility effects and its persistence should increase, as the private information (beliefs) of investors becomes more important. We find strong support for this idea in the data. We argue that the results have implications for debate surrounding the opacity of banks and the transparency requirements that may be imposed on banks under Pillar III of the New Basel Accord.