The Effects of Liquidity on Multi-period Portfolio Selection: A Case Study of American Sector ETFs

We study a multi-period portfolio optimisation problem incorporating liquidity cost. The objective is to maximise the expected utility of the final wealth over a finite investment horizon where the liquidity cost is formulated as an intermediate cost of rebalancing a portfolio. Our liquidity cost model is built upon the so-called Marginal Supply-Demand Curve which describes the asset price as a function of the trading volume. The main aim of our work is to empirically present how the performance of portfolios varies with different levels of liquidity, with emphasis on how to choose an optimal portfolio. We implement an extended least-squares Monte Carlo algorithm (detailed in [1]) on a portfolio investing in four major sector ETFs in the U.S. market. In terms of the empirical cumulative distribution function, the out-of-sample distribution and the real market performance, we benchmark dynamic strategy against several alternative portfolio strategies such as buy-and-hold strategy, fixed-mix strategy and liquidity-blind dynamic strategy. Our results show that dynamic strategy is dominant in the liquid markets while buy-and-hold strategy is more likely to outperform the others in the illiquid markets.