These days a lot of the money in Hedge Funds is institutional. Typically institutional investors coming to funds already have a specific allocation to an investment style, market, or asset class that they are trying to fill. So they already have an idea of whether they want market exposure, which would be benchmark oriented and should have high correlation to the benchmark/market, or whether they want no market exposure, which would would have low to zero correlation to the market (they also could want exposure anywhere in between). So in long only (no shorting) funds benchmarks can be arbitrary (though are usually indexes), but they are fixed and agreed upon by manager and investor.

The mandate for the manager in benchmark oriented strategies is to track the agreed upon benchmark with a correlation (or more accurately Beta) of as close to 1 as possible, while still beating it by a certain margin. So if the benchmark is up 10, the fund should be up 15. If the benchmark is down -10 the fund should be down -5. Technically, this margin is often measured not as the difference between the fund and the benchmark but as the annualized standard deviation of the difference, known as the Tracking Error(TE). The TE is typically agreed upon between the fund and investor(s).

It's very common for a fund to charge only a management fee in benchmark oriented strategies. In a benchmark oriented fund with a target TE it would not really make sense to charge performance fee on the magnitude total fund performance since that will largely (or completely) be a function of the benchmark/market - remember correlation should be 1. It also would not make sense to charge performance fee on the excess return over the benchmark because that is incorporated into the TE and should be relatively constant over time (in the example earlier the fund should always beat the benchmark by %5.

So usually there is just the management fee. The reasoning is that if a fund can yield consistently high returns with a consistently low risk (as measured by vol/std. dev. of excess returns a.k.a. TE) then they have some skill and should be compensated accordingly. The excess returns adjusted by risk of excess returns is called Information Ratio (IR). IR is analogous to Sharpe Ratio(SR) in non benchmark oriented funds. In a long/short fund, the higher the SR the higher the fees usually. Similarly, in the long only benchmark oriented fund, the higher the IR the higher the management fee.

This is how fees usually are determined for funds that have benchmarks.

I'm not an investment expert, but wouldn't there be virtually unlimited upside in an optimal hindsight strategy? I.e. you could use derivatives and other financial instruments to gain an arbitrary amount of leverage and hence return, since there would be no risk.

Expanding on this, this idea of looking backwards as a method determining what returns you could have made is actually the root of a lot of _bad_ investment advice.

People often look back and try to determine some type of optimal portfolio that they claim is the best in all economic environments because they found it to be the best portfolio in the certain timeframe they looked, but they had the benefit of checking hundreds of different potential sets of funds and if you were to actually calculate the probability that composition of funds is better than any other composition you'd find that it was just random chance it provided the best returns over that time frame.

Granted there is a lot to learn from looking back, but it's also very imperfect if you're not taking in to the benefit of hindsight.

Compensating for this effect of training may be done by properly discounting the measure using the Deflated Sharpe Ratio or similar corrected SR's. I always ask any interviewee who cites experience producing these measures a question with this effect as the crux. Few come back with a correct answer.