Efficient portfolio valuation incorporating liquidity risk

Abstract

According to the theory proposed by Acerbi and Scandolo (2008) [Quant. Finance, 2008, 8, 681–692], an asset is described by the so-called Marginal Supply–Demand Curve (MSDC), which is a collection of bid and ask prices according to its trading volumes, and the value of a portfolio is defined in terms of commonly available market data and idiosyncratic portfolio constraints imposed by an investor holding the portfolio. Depending on the constraints, one and the same portfolio could have different values for different investors. As it turns out, within the Acerbi–Scandolo theory, portfolio valuation can be framed as a convex optimization problem. We provide useful MSDC models and show that portfolio valuation can be solved with remarkable accuracy and efficiency.

Keywords:

• Liquidity risk
• Portfolio valuation
• Ladder MSDC
• Liquidation sequence
• Exponential MSDC
• Approximation

Classification:

• C60
• G11
• G12

Acknowledgments

The authors would like to thank Dr Carlo Acerbi (MSCI) for his kind help and fruitful discussions on the theory and the MSDC models. We also thank the anonymous referees for providing us with insightful comments on our first version. The views expressed in this paper do not necessarily reflect the views or practises of RBS.

Notes

For example, the optimality conditions in the interior point algorithm will not apply at non-smooth points of the ladder MSDC. See Boyd and Vandenberghe (2004) for more information.

The computer used for all experiments has an Intel Core2 Duo CPU, E8600 @3.33 GHz with 3.49 GB of RAM and the code is written in MATLAB R2009b.