Hedge fund strategies are often purchased because there are expectations that they will exhibit a beta similar to that of equity markets. Not all the betas will be the same, but they will generally run between .5 and .6 on the high side to zero or slightly negative on the low side. CTAs usually have the lowest beta but also likely have low alpha.
These betas or correlations will change with market conditions. The hope is that if there is an increase in beta, it is not because hedge fund managers are chasing the equity market with momentum trades, but rather because they are showing some market-timing skill. Evidence on market-timing the overall market is weak, so there should be concern when hedge funds exhibit higher short-run correlations with equity markets. Of course, hedge fund managers may have timing skills, but this is not the reason why most managers are buying these strategies.
Investors seek uncorrelated returns, so there is a general expectation that betas will be low and stable. Yes, that means that hedge funds will underperform versus the overall market on an absolute basis, but investors should not pay for unwanted beta.
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