My problem with this kind of compensation scheme is twofold:
1) Investment managers don't even need to beat the market to get a bonus. If the market as a whole goes up then the investment managers get rewarded, even if their performance lags the market as a whole!
2) By rewarding gains but not penalizing losses you get a scenario where investment managers may be incentivized to take greater risks for the possibility of bonuses since they are not penalized for 20% of the losses. In essence, they may benefit from increased variance.
But I'll admit that I don't know if providing a fee with no bonuses to the investment manager or managing company ends up being a better strategy.