Semi-Universal Portfolios with Transaction Costs

Online portfolio selection (PS) has been extensively studied in artificial intelligence and machine learning communities in recent years. An important practical issue of online PS is transaction cost, which is unavoidable and nontrivial in real financial trading markets. Most existing strategies, such as universal portfolio (UP) based strategies, often rebalance their target portfolio vectors at every investment period, and thus the total transaction cost increases rapidly and the final cumulative wealth degrades severely. To overcome the limitation, in this paper we investigate new investment strategies that rebalances its portfolio only at some selected instants. Specifically, we design a novel on-line PS strategy named semi-universal portfolio (SUP) strategy under transaction cost, which attempts to avoid rebalancing when the transaction cost outweighs the benefit of trading. We show that the proposed SUP strategy is universal and has an upper bound on the regret. We present an efficient implementation of the strategy based on nonuniform random walks and online factor graph algorithms. Empirical simulation on real historical markets show that SUP can overcome the drawback of existing UP based transaction cost aware algorithms and achieve significantly better performance. Furthermore, SUP has a polynomial complexity in the number of stocks and thus is efficient and scalable in practice. ∗This work was partially supported by the NSFC (71401128), the SRF for ROCS, SEM, the Key Projects of FRM of Shanghai MCST (14JC1400300), the NSF of Shanghai (15ZR1408300), Shanghai Key Laboratory of Intelligent Information Processing (IIPL-2014001) and Singapore MOE tier 1 research grant (C220/MSS14C003).