Explanation

Let's break this down step by step:

Given:

• Management fee: 2%
• Incentive fee: 20% (on net return after management fees)
• Target return after fees: 20%
• Let R be the required return before fees

Step 1: Calculate return after management fee After management fee = R - 2%

Step 2: Calculate incentive fee Incentive fee = 20% × (R - 2%)

Step 3: Calculate return after all fees Return after fees = (R - 2%) - 20% × (R - 2%) Return after fees = (R - 2%) × (1 - 0.20) Return after fees = (R - 2%) × 0.80

Step 4: Set equal to target return and solve (R - 2%) × 0.80 = 20% R - 2% = 20% / 0.80 R - 2% = 25% R = 27%

Verification:

• Before fees: 27%
• After 2% management fee: 25%
• 20% incentive fee on 25%: 5%
• Return after all fees: 25% - 5% = 20% ✓

Therefore, the hedge fund needs to earn 27% before fees to provide investors with a 20% return after fees.