The huge rally in U.S. stocks in 2013 had a downside for fund managers whose job it is to hunt for bargains: It has gotten harder to find undervalued names for their portfolios.

Value managers stress that they aren't saying the stock market can't continue its record-breaking rise just because there are fewer stocks they think are cheap. But cash is building up in their portfolios. The $1.5 billion Artisan Value fund, for example, was holding 9.1% of assets in cash at the end of November, up from 1% at the start of the year....