Tracking Stock Exchange Index with considering the limitation of loss aversion with using the new approach of Big Bang - Big Crunch

One of the causes of underdevelopment stock in developing countries such as Iran is inadequate growth of decision-making tools for the investors, especially beginners. Therefore, in this study an index tracking model with regard to loss aversion limitation and restriction of Integer constraints on selected assets, to create an index tracker basket (portfolio) has been applied. The key difference of this study to other similar national researches is in considering of loss aversion, this means that the influences which investors accepted from positive and negative fluctuations in their own portfolio’s output, has not the same utility and hence their impact on investment model is not equivalent. The space of the solution of this problem is discrete and non-convex, so common numerical methods for solving this problem are not usable. Other innovations from this research, the use of the Bing bang - Big Crunch algorithm as a new meta-heuristic algorithms for the solution and it’s comparison with differential evolution algorithm with using of stock’s daily price data available on the Dow Jones index from 2000 to 2006. The obtained results indicate good performance of the algorithm of the Big Bang-Big Crunch toward differential evolution algorithm according to performance criteria. Then this algorithm has been used for Index tracking of 30 largest companies in Tehran Stock Exchange from (2012-2014) 1391 to 1393 A.H.S that the result of it was achieving to an efficient portfolio and a risk equivalent to index of 30 companies in Tehran Stock Exchange.