Explanation

Fee Structure Analysis:

Given:

• Management fee: 2% of assets
• Incentive fee: 20% of net return (after management fee)
• Target return after fees: 20%

Let X = Required gross return before fees

Step 1: Calculate return after management fee

• Return after management fee = X - 2%

Step 2: Calculate incentive fee

• Incentive fee = 20% × (X - 2%)

Step 3: Set up equation for target return

• Return after all fees = (X - 2%) - [20% × (X - 2%)] = 20%
• (X - 2%) × (1 - 20%) = 20%
• (X - 2%) × 0.8 = 20%

Step 4: Solve for X

• X - 2% = 20% ÷ 0.8
• X - 2% = 25%
• X = 25% + 2% = 27%

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