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.
Highlights
Many investment instruments are illiquid and costly to trade
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
Summary
Many investment instruments are illiquid and costly to trade This makes the corresponding optimal risk and performance management a highly complex task: 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 cost and deleveraging or keeping his/her current position in the illiquid instrument and hedging away some of the risk with more liquid instruments (such as, e.g., futures contracts). Using the explicit solution of Kallsen and Muhle-Karbe (2017), we show that the optimal policy consists of keeping the asset position inside an explicitly given no-trade region around the target asset position in the frictionless model; we study the behavior of this no-trade region
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