Norm constrained minimum variance portfolios with short selling

Short selling is a wealth-building trading procedure which, when included in the portfolio construction, not only helps increase the return on investment but also reduces the investor’s overall exposure to the market risk. In this study, we incorporate it in the minimum variance model by analyzing several constraints that aptly consider the different practical settings of a short sale transaction. We propose to utilize the short-rebate gain by maximizing this additional interest due to short sales in the objective function. In constraints, we impose the bounds on 1- and 2-norm that respectively generate sparse and diversified portfolios. Along with the norm constraints, we also bound the budget constraint to homogenize the allocations in long and short and avoid the dominance of one strategy over the other. We present empirical results highlighting the effect of the specific choice of constraints and, thereafter, conduct a comparative analysis of our proposed models vis-a-vis several related models from literature across eight global data sets using the rolling window scheme. We observe that our proposed models outperform the others in terms of several performance measures. In particular, the 1-norm constrained model generates statistically significant portfolios as compared to other related models in terms of variance and Sharpe ratio. Additionally, the threshold parameter of the 1-norm constraint provides the flexibility to tune the short sale budget, proving more favorable for a short sale scenario.