Optimal Derivative Strategies with Discrete Rebalancing

Optimal asset allocation strategies are often derived in continuous time models, but have to be implemented in discrete time. It has been shown that in models with stochastic volatility or jumps, an investor who just uses the continuous time strategy in discrete time has to trade at least daily to profit from having access to derivatives. In this paper, we determine the optimal investment strategy when discrete rebalancing is explicitly taken into account. We find that the investor buys a more conservative portfolio and reduces extreme positions in the derivatives compared to the continuous time case. In particular, his exposure to volatility risk is significantly reduced. We show that even with monthly rebalancing, the investor profits from trading derivatives and can realize up to 63% of the utility gain from option trading in continuous time. He also profits from having access to a variance contract, since the more stable exposures of the variance contract to the risk factors over time allow him to take larger positions in volatility and jump risk.