Scalable, Efficient and Optimal Discrete-Time Rebalancing Algorithms for Log-Optimal Investment Portfolio - (:unkn) unknown (My University, 2014)
Portfolio rebalancing decisions are crucial to today's portfolio managers especially in high frequency algorithmic trading environment. These decisions must be made fast in dynamic market conditions. We develop computational algorithms to determine optimal rebalance frequency (ORF) of a class of investment portfolio for a finite investment horizon. We choose log-optimal investment portfolio which is deemed to be impractical and cost-prohibitive due to inherent need for continuous rebalancing and significant overhead of trading cost. Optimality of such portfolio is assured only when for very long term investor horizon. We study the question of how often a log-optimal portfolio be rebalanced for any given finite investment horizon. We develop an analytical framework to compute the expected log of portfolio value when a given discrete-time periodic rebalance frequency is used. For a certain class of portfolio assets, we compute the optimal rebalance frequency. We show that it is possible to improve investor log utility using this quasi-passive or hybrid rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and log-normality for sum of log-normal random variables, we find that the ORF is a piecewise function of investment horizon. One can construct this rebalance strategy function, called ORF function, up to a specified investment horizon given a limited trajectory of expected log of portfolio value (ELPV) when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm. Simulation studies show that an investor can gain significantly by adopting a discrete-time rebalancing periodically using ORF in lieu of continuous rebalancing. Finally we investigate the computational efficiency of the proposed algorithms to develop optimized versions which are scalable to portfolios comprising of large number of assets.
Keywords: Discrete Rebalancing; Log-Normal; Log-Optimal Portfolio; Portfolio Growth Rate; Portfolio Optimization; Rebalancing Frequency