Portfolio Valuation Under Liquidity and Expected Shortfall Constraints

In the standard approach to fund valuation, it is often assumed that markets are perfectly liquid and hence assets have unique prices. In practice, however, as has been widely documented, this is not the case. Asset values are impacted by deterioration of market liquidity (market depth). However, the work by Acerbi and Scandolo (Quantitative Finance, 2008, 8(7), 681) highlighted, in addition, the key role that the liquidity policies of the fund can have on the fund value. Funds with the identical positions but differing liquidity policies have different values. In this paper, we describe and analyze, the relationship between the fund value and the liquidity policy (constraints that can potentially be called upon, and that are imposed externally on the fund manager). These constraints, for example, can be a requirement to be able to generate an amount of cash (due to possible adverse redemption), a minimum weight requirement per asset, or a market risk constraint such as a maximum expected shortfall (ES). We employ a power-law Marginal Supply-Demand Curve (MSDC) to model market depth, together with various types of liquidity policies. These liquidity restrictions affect, to a varying degree, the liquidation process of illiquid and high volatility assets. We find that as the liquidity policy becomes stricter with the portfolio ES constraint, the liquidity costs increase significantly