A simheuristic algorithm for the portfolio optimization problem with random returns and noisy covariances

The goal of the portfolio optimization problem is to minimize risk for an expected portfolio return by allocating weights to included assets. As the pool of investable assets grows, and additional constraints are imposed, the problem becomes NP-hard. Thus, metaheuristics are commonly employed for solving large instances of rich versions. However, metaheuristics do not fully account for random returns and noisy covariances, which renders them unrealistic in the presence of heightened uncertainty in financial markets. This paper aims to close this gap by proposing a simulation–optimization approach – specifically, a simheuristic algorithm that integrates a variable neighborhood search metaheuristic with Monte Carlo simulation – to deal with stochastic returns and noisy covariances modeled as random variables. Computational experiments performed on a well-established benchmark instance illustrate the advantages of our methodology and analyze how the solutions change in response to a varying degree of randomness, minimum required return, and probability of obtaining a return exceeding an investor-defined threshold.