Liquidity-constrained index tracking optimization models

This paper examines optimization models that use liquidity constraints to track an index. Liquidity is relevant from a risk management perspective but has hardly been explored in the portfolio optimization literature. The liquidity aspect is especially critical in emerging markets. We present two modeling approaches to instill liquidity in index tracking portfolio optimization. The first one defines the portfolio liquidity as the weighted average of assets’ liquidities and accounts for financial volume, turnover, and Amihud’s metric. The second one models liquidity with the introduction of financial practice parameters related to the liquidation level and the monetary value of the constructed portfolio. An extensive empirical analysis is conducted to replicate two Brazilian stock market indices: Ibovespa and SMLL. As expected, liquidity-constrained portfolios show higher liquidity and higher tracking errors. A counter-intuitive result is observed for the first liquidity-constrained approach in which the number of assets included in the portfolio decreases as the liquidity requirement gets tighter. In the second approach, as liquidity becomes tighter, the number of assets in the portfolio increases. This observation is confirmed by investigating the diversification of the constructed portfolios using the Gini index.