Portfolio Liquidity Risk Management with Expected Shortfall Constraints

In this thesis we quantify the potential cost of liquidity constraints on a long equity portfolio using the liquidity risk framework of Acerbi and Scandolo (2008). The model modifies the classical mark-to-market valuation model, and incorporates the impact of liquidity policies of portfolios on the liquidity adjustment valuation (LVA). Also, we suggest a quantitative indicator that scores market liquidity ranging from 0 to 1 (perfect liquidity) for a portfolio with possible liquidity constraints. The thesis consists of three major studies. In the first one, we compute LVA given the cash, minimum weight and portfolio expected shortfall (ES) liquidity policies on a long equity portfolio. Several numerical examples in the results demonstrate the importance associated the incorporation of the liquidity policy in the liquidity risk valuation. In the second study, we quantify the execution costs and the revenue risk when implementing trading strategies over multiple periods by employing the transaction costs measure of Garleanu and Pedersen (2013). The portfolio liquidity costs estimated from the model of Garleanu and Pedersen (2013) are compared with the costs estimated from the liquidity risk measure of Finger (2011). In the third study, we estimate the liquidity-adjusted portfolio ES for a long equity portfolio with the liquidity constraints. Portfolio pure market P&L scenarios are based on initial positions, and the liquidity adjustments are based on positions sold, which depend on the specified liquidity constraints. Portfolio pure market P&L scenarios and state-dependent liquidity adjustments are integrated to obtain liquidity-adjusted P&L scenarios. Then, we apply the liquidity score method (Meucci, 2012) on the liquidity-plus-market P&L distribution to quantify the market liquidity for the portfolio. The results show the importance of pricing liquidity risk with liquidity constraints. The liqiii uidity costs can vary greatly on different liquidity policies, portfolio MtM values, market situation and time to liquidation.