Diversifer or complement - What type of hedge fund do you want?

There is an ongoing discussion of how to classify hedge funds. A simple approach can be divide hedge funds by their style whereby you can have equity long/short, convertible arbitrage,  event risk, or global macro to name a few. But, from a portfolio perspective, there may be more important ways to classify alternatives based on what they can do for you. Call it classification in context.

A recent Campbell and Co research piece "The Taming of the Skew" discusses how hedge fund can be classified as being either diversifiers or complements.

• A diversifier will be a hedge fund that will lower volatility based on its lower correlation with the overall portfolio. Its objective is to increase the long-term Sharpe ratio. 
• The complement hedge fund will be one that provides value-added or diversification relative to a specific asset or a concentrated portfolio.  It attempts to exploit conditional correlation.

I could say that a hedge fund could be a macro diversifier or a micro diversifier. The micro diversifier or complement is a alternative that acts like a partial hedge for specific asset or pool of assets. The macro diversifier's benefit will always be in the context of what happens to overall portfolio's return to risk and not how it will interact with specific asset or situation.

Campbell looked at the difference in hedge fund styles in the context of managed futures. Some managers who have high crisis alpha will be a good micro hedge or complement against an equity portfolio while a diversifier may not have high crisis alpha but will have strong overall portfolio benefit. This is an interesting approach to thinking about hedge fund although there could be mental accounting issue with trying to match hedge funds with specific assets within the portfolio.