A hedge fund that requires incentive fees to be calculated only on the portion of returns above a benchmark return is said to have a:

In a hedge fund’s fee structure, a hard hurdle rate means that incentive fees are earned only on returns in excess of the benchmark return. A soft hurdle rate means that incentive fees are calculated on the entire return, but are only paid if the return exceeds the hurdle rate. A high water mark specifies that incentive fees are only paid on returns that increase an investors account value above its highest previous value.