Research On Enhanced Indexation Investment Model Based On Relaxed Second Order Stochastic Dominance Constraints

Second order stochastic dominance(SSD)is an important method of enhanced indexation investment models,but the SSD constraints are too conservative.In this paper,we propose two relaxed methods for an enhanced index investment model based on SSD constraints from the perspective of model and algorithm.For the model,the CVaR approximate model of the enhanced exponential model under SSD constraints is constructed,where the CVaR relaxed method is used to relax SSD constraints and the sample average approximation(SAA)method is as compute ways.The convergence property of the approximate model is proved.In the empirical study,based on the stock market index,the CVaR approximation model is studied on the NASDAQ 100,S&P 500 and FTSE 100 by different ways of back-testing,rebalancing and buying holdings for both in-sample and out-of-sample tests.Portfolios constructed by the CVaR approximation model with a certain confidence level are superior to the market index.The CVaR approximation model is a relaxation of the enhanced indexation model under SSD constraints,overcame the conservativeness of SSD constraints and obtain more competitive portfolios.Finally,the approximation model naturally selects a small number of stocks without imposing a cardinality constraint which is computational difficulties in exponential tracking models,and the corresponding transaction costs are also reduced.In addition,the enhanced indexation model is robust to small changes in datasets which with little or no rebalancing.A relaxation algorithm based on cutting plane method and VaR approximation is proposed.The solution of the algorithm is an approximate optimal solution to the indexation investment problem with SSD constraints.It not only overcomes the conservativeness of SSD constraints,but maintains the good nature of VaR approximation and avoids the difficulty in its calculation.This paper applies the relaxation algorithm to the empirical research of three markets:NASDAQ 100,S&P 500 and FTSE 100.With a certain confidence level,this relaxation algorithm can also obtain portfolios that are better than the index and portfolios of the indexation investment model with SSD constraints.