Define the term "hedge fund"

What a misnomer. What exactly defines a "hedge fund" anyway?

All this hysteria about regulation because hedge funds are deemed more risky thant other funds is all much ado about nothing and actually only displays huge ignorance on the part of the regulators about risk, margin and volatility.

The term originated in 1949 when Alfred Wimslow Jones launched a "hedged fund" that both bought stocks and sold them short in order to hedge its exposure to the market's ups and downs. The term caught on, slightly altered, as shorthand for all unregulated investment funds.
Source: Fortune Magazine.

hedge strategy is to optimize total net return after risk, cost, intrest and tax
instead of benchmarking.

The regulation is not aimed at what the hedge funds are trading but rather how they handle investor funds.
Hedge funds are not generally more risky than any other type of derivative investment.

In fact, many hedge funds may not have a single financial derivative in them at all. You are quite right twalker when you say that its how they manage their investors that count. They in effect are outside the protection of "lay" investors. The one defining thing about hedge funds is that they take investment money from those the law deems a professional investor and as such they fall outside the protection that non-professionals would have. (e.g. a unit trust or pension fund)

The traditional textbook definition would be something like a pooled investment vehicle that is privately managed by professional inv managers & not widely available to the public. However nowadays it often just refers to any investment fund that isn't restricted to a long-only non-leveraged investment strategy.

Though reported peformance & risk can often be hard to trust as it will be influenced by survivorship & selection bias as well other biases caused by valuation problems (e.g OTC securities, distressed co. shares, etc), this will also affect the percieved volatility. Additionally although many many funds will have a 0 beta & low systematic risk this does not automatically imply low risk as many funds will carry a substantial specific risk.

Most funds are concerned with Relative Returns. Hedge funds are concerned with Absolute Returns and will achieve this for shorting anything that goes down and going long of anything that goes up. Futures and options play an important part of the strategy.

It's a prop desk that has outsourced everything it possibly can and is legally structured to fall outside the reach of regulatory authorities.