It turns out many so-called alpha funds actually lack it.
The average five-year alpha for funds with the word "alpha" in their name is a negative 0.42 percent, according to Morningstar.
Alpha measures how much better a fund does against a specific benchmark. In other words, if the posted returns of 3 percent over a specific period and a fund returned 6 percent, then that fund's alpha is 3 percent.
The fund with the worst five-year alpha in the group is the Oppenheimer SteelPath MLP Alpha Plus Y with an average five-year alpha of negative 5.32 percent, according to Morningstar.
Funds with the word "plus" in their name don't do much better, either. Morningstar's data show the five-year alpha for these funds is negative 0.01 percent.
"I think alpha and plus are mainly marketing names. They are more aspirational than factual," said Russel Kinnel, director of manager research at Morningstar. "Also, it isn't easy to add alpha."
To be sure, some funds have delivered alpha to investors over five years, including the AlphaCentric Hedged Market Opportunity I, which has an average five-year alpha of 7.15 percent.
Actively managed funds have suffered dearly in recent years despite an eight-year bull market in stocks. For example, not a single large-cap fund manager who beat the S&P 500 in 2013 managed to do so three years later.
But things may be turning around for large-cap money managers. Nearly two-thirds of large-cap money managers beat their benchmarks in April and the average fund outperformed by 18 basis points.
—CNBC's Evelyn Cheng contributed to this report.