We propose a model for a manager of a hedge fund with a liquidity constraint, where he is seeking to optimize his utility of wealth, with one and multiple period horizons. By using stochastic control techniques, we state the corresponding multi-dimensional Hamilton–Jacobi–Bellman partial diﬀerential equation and we use a robust numerical approximation to obtain its unique viscosity solution. We examine the eﬀects of the liquidity constraint on managerial trading decisions and optimal allocation, ﬁnding that the manager behaves in a less risky manner. We also calculate the cost of being at sub-optimal positions as the diﬀerence in the certainty equivalent payoﬀ for the manager. Moreover, we compare the values of a benchmark hedge fund with another one having a risky asset with a higher rate of return but less liquidity, ﬁnding that higher rate of return with a liquidity constraint does not always lead to greater return.