Great question, Adam. Peter's conclusion is absolutely correct, but it's useful to present investors' actual experience in hedge funds and look at their portfolios with and without the hedge fund allocation. In fact, for that purpose let's look at the largest, most sophisticated investors in the entire country.
That's exactly what CEM Benchmarking did. The company collects data on the actual investment results of hundreds of large public and corporate pension funds, and it summarized those actual returns in a report published in 2014 called "Asset Allocation and Fund Performance of Defined Benefit Pension Funds in the United States Between 1998-2011." (The report, which was sponsored by NAREIT, my employer, is available for download at http://reit.com/data-research/research/cem-benchmarking-defined-benefit….)
Hedge funds were the absolute worst among all 12 asset classes, according to CEM Benchmarking's data. Net total returns over the 14-year historical period averaged just 4.77% per year: worse than all three categories of equity investments, worse than all four categories of alternative investments (other than hedge funds), and even worse than all four categories of fixed-income investments!
As for investing their portfolios "with and without the hedge allocation," CEM Benchmarking did exactly that, calculating the marginal impacts of a 1% increase in the allocation to each asset class. A marginal increase in the hedge fund allocation would have REDUCED average pension fund returns by 2.1 basis points per year. Only three other asset classes showed negative marginal impacts, and only one of them (U.S. large cap equities during what was called the "lost decade") had a larger negative marginal impact than hedge funds.
While you're at it, check out "Higher Risk, Lower Returns: What Hedge Fund Investors Really Earn" by Ilia D. Dichev & Gwen Yu, published in Journal of Financial Economics and available at http://www.people.hbs.edu/gyu/HigherRiskLowerReturns.pdf. Using data for the period 1980-2008 they found that "dollar-weighted returns are reliably lower than the return on the S&P 500 index, and are only marginally higher than the risk-free rate as of the end of 2008. The combined impression from these results is that the return experience of hedge fund investors is much worse than previously thought."