Answer: Strategy C offers the best expected return to the hedge fund, but the worst to the investors

The hedge fund earns a **2% management fee** on assets regardless of performance, plus a **20% performance fee** on profits. This makes the fund prefer **higher volatility / more convex payoffs**, because it participates in upside but does not share downside losses with investors. - **Strategy A:** profit is certain at $4.0m. - Management fee = $2.0m - Performance fee = 20% × $4.0m = $0.8m - Total expected fee = **$2.8m** - **Strategy B:** expected gross profit = 0.5 × 7 + 0.5 × 0 = $3.5m. - Expected fee = $2.0m + 20% × (0.5 × $7.0m) = $2.0m + $0.7m = **$2.7m** - **Strategy C:** expected gross profit = 0.5 × 18 + 0.5 × (−15) = $1.5m. - In the profitable state, fee = $2.0m + 20% × $18.0m = $5.6m - In the loss state, fee = $2.0m only - Expected fee = 0.5 × 5.6 + 0.5 × 2.0 = **$3.8m** So **Strategy C** gives the **highest expected return to the hedge fund** because it produces the largest expected fee income, while it is the **worst for investors** because the expected net return after fees is lowest (indeed negative).

Author: Manit Arora