Investors wishing to achieve a particular level of diversification may be misled on how many stocks to hold in a portfolio by assessing the portfolio risk at different data frequencies. High frequency intradaily data provide better estimates of volatility, which translate to more accurate assessment of portfolio risk. Using 5-min, daily and weekly data on S&P500 constituents for the period from 2003 to 2011, we find that for an average investor wishing to diversify away 85% (90%) of the risk, equally weighted portfolios of 7 (10) stocks will suffice, irrespective of the data frequency used or the time period considered. However, to assure investors of a desired level of diversification 90% of the time (in contrast to on average), using low frequency data results in an exaggerated number of stocks in a portfolio when compared with the recommendation based on 5-min data. This difference is magnified during periods when financial markets are in distress, as much as doubling during the 2007-2009 financial crisis.