A comprehensive evaluation of constrained mean-expectile portfolios with short selling

Abstract

Owing to its unique property of being both coherent and elicitable, expectile has recently been studied as an alternative risk measure to value-at-risk (\({{\,\textrm{VaR}\,}}\)) and conditional value-at-risk (\({{\,\textrm{CVaR}\,}}\)). Analogously, as a risk measure, it is defined as expectile value-at-risk (\({{\,\textrm{EVaR}\,}}\)). This study proposes to enhance the Mean-\({{\,\textrm{EVaR}\,}}\) portfolio optimization model to incorporate short selling strategy. To assimilate different practical arrangements of a short-sale transaction, we analyze constraints such as proportional bounds, \(l_1\)-norm constraint, bounded budget, and turnover constraints. We conduct extensive in-sample and out-of-sample analyses using historical data of stocks from the CNX NIFTY 50 (India), Hang Seng (Hong Kong), FTSE 100 (UK), and DAX 100 (Germany) indices over 10 years using a rolling window strategy. While the \(l_1\)-norm constraint and the bounded budget help to restrict the total short-sale budget, the turnover constraint helps in tuning the portfolio turnover, thereby reducing the overall transaction cost. The empirical results highlight the benefits of choosing specific constraints to assist practical decision-making for the short-selling strategy in the proposed model. We further perform a comparative study of Mean-\({{\,\textrm{EVaR}\,}}\) model with the 1/n portfolio strategy and two popular portfolio optimization models, Mean-Variance and Mean-\({{\,\textrm{CVaR}\,}}\) under a similar setting and observe the financial benefit of the proposed model indicating its importance in investment practices.