Hedge or Rebalance: Optimal Risk Management with Transaction Costs

Abstract

We solve the problem of optimal risk management for an investor holding an illiquid, alpha-generating fund and hedging his/her position with a liquid futures contract. When the investor is subject to a lower bound on net return, he/she is forced to reduce the total risk of his/her portfolio after a loss. In this case, he/she faces a tradeoff of either paying the transaction costs and deleveraging or keeping his/her current position in the illiquid instrument and hedging away some of the risk while keeping the residual, unhedgeable risk on his/her balance sheet. We explicitly characterize this tradeoff and study its dependence on asset characteristics. In particular, we show that higher alpha and lower beta typically widen the no-trading zone, while the impact of volatility is ambiguous.

Keywords

• optimal portfolio choice
• transaction costs
• hedging