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Abstract:
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This paper is concerned with the creation of an optimal portfolio selection from a given range of assets. We are looking to create a vector, in which each asset is represented as an element in the vector, 1 for present and 0 for not present, that will yield a portfolio under a metric such as the highest Sharpe ratio. Let's assume that A is the set of all admissible assets. Our goal is to find a subset {x_1, x_2, … x_n} of A such that: a) the weight attributed to each asset is great than or equal to zero, b) the weights sum up to one, c) the number of assets chosen is smaller than some prescribed maximum n< N, and d) while a given objective function f(w_1,w_2, … ,w_n) is at its maximum. This "portfolio cut" problem can be solved by stepping w_i on certain discrete grid with increments of say 0.5%, starting from zero. To illustrate its complexity, if N = 500 (e.g. the S&P 500 stock components), the number of combinations to split the assets into two subsets is C = 1.6 X 10^150. This is a computationally time-consuming if not intractable for a typical set of available assets to choose from. This paper aims to present different computational results achieved to solve "portfolio cuts".
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