A linearized value-at-risk model with transaction costs and short selling

• A linearized VaR model (LP4) by applying the mixed 0-1 programing to advance Benati and Rizzi (2007) P2 and Lin (2009) P4 models is proposed.
• Short-sales and transaction costs are modeled.
• LP4 portfolios yield the global optimum and demonstrate the higher performance than P4.
• LP4 show the usefulness in the real world.

Though value-at-risk (VaR) has been widely applied by finance industry, a possibility of multiple optimums that is caused by the nonlinearity in modeling can challenge its application. To deal with this technical issue, we propose a linearized VaR model that employs the mixed 0-1 programing in Lin (2009) P4 model. We further advance the previous models with considering various transaction costs and the optimization of short-selling weights. We compare the performance of buy-and-hold (BH) strategy, the mean-variance (MV) model, the original P4 model, and our linearized P4 (LP4) model by rebalancing a wide scale of international and alternative investments during a period between 2001 and 2012. The results of numerical tests show the superior performance of the VaR models to the BH and the MV portfolios. The LP4 model yields the global optimum and outperforms the corresponding P4 model in both return and risk. The stability of portfolio value generated from the LP4 model supports its higher effectiveness in risk management than the P4 model.