Cash Management with Futures in Passive Investment - Proceedings AFIR 2001 - Toronto, Canada

Despite of the importance of effective cash management in passive investment, few analytical results could be found in this area except Connor & Leland(1995). They analyzed the cash management as a stochastic control problem. But futures are not taken into account in their model. Though the use of futures in hedging has disadvantages of possible large tracking error and extra trading cost due to rollovers, it has advantages such as low trading cost. This paper tries to prove the effectiveness of the use of futures through the stochastic analysis and numerical experiments. First, we formulate "spot model"(without futures) and "spot and future model"(with futures) respectively as a discrete Markov chain. We then calculate the expected tracking errors under several cash management policies of threshold type. The comparison of calculation indicates that there is not large difference of the expected tracking errors, but spot and future model performs well for all threshold values while performance of spot model can degrade considerably depending on the threshold levels. We also compare the average interval of trading index portfolio, and find that spot and future model has longer interval, which enables us to reduce office cost. Finally, we research robustness against fluctuation of parameters with sensitivity analysis and illustrate that spot and future model is robust enough for practical use.