Aplicación de la simulación de Monte Carlo para determinar el α objetivo en un FIC

Abstract

This report applies Monte Carlo Simulation to estimate the target alpha of a mixed Collective Investment Fund (CIF) within the framework of a professional internship at Banco Davivienda S.A. The study is conducted using publicly available data for illustrative purposes, and the proposed methodology is generalizable to any Collective Investment Fund by replacing the underlying assets, their historical unit values, and the benchmark portfolio weights. The methodology consists of generating multiple random combinations of portfolio weights around the benchmark using a normal distribution, calculating the alpha of each portfolio based on actual historical returns, and estimating the fund’s expected alpha as the average of all simulated outcomes. The mathematical foundation of the methodology relies on the Law of Large Numbers, which ensures that this average converges to the expected alpha of the fund as the number of simulations increases. The results make it possible to establish a reasonable and attainable target alpha for the fund manager, supported by quantifiable historical evidence.