Abstract
Portfolio selection has been the subject of extensive studies in order to obtain increased returns, minimizing the investment risk. However, the most appropriate risk measure to be considered is still an open problem. The aim of this work is to study different risk measures in the multiobjective portfolios optimization with cardinality constraint and rebalancing. The in-sample analysis compares the fronts of each algorithm, metric and range of cardinality, and out-of-sample analysis compares the results of each measure of risk with each other and with two benchmarks. The returns of portfolios are compared in terms of assets choice and assignment of weights. Statistical tests are performed to verify if any measure of risk shows some superiority. Results indicate that downside risk measures can reduce the cardinality and the risk of financial drawdown without reducing drawup, once they are able to reduce just the negative historical returns scenarios.
Highlights
The financial market generally allows investors to obtain higher profits, with the counterpoint of being exposed to greater risks
The highest concordance is obtained between Value at Risk (VaR)(v) and variance, as expected, and with Generalized Autoregressive Conditional Heterosedasticity (GARCH)
The results show the equality of variances just for the S-metric series generated by the Exponentially Weighted Moving Average (EWMA), GARCH and variance measures
Summary
The financial market generally allows investors to obtain higher profits, with the counterpoint of being exposed to greater risks. Investors are interested in simultaneously maximizing profits and minimizing risks. Using mathematical and computational models is proven to be decisively helpful in achieving optimal investments in stock markets. The higher the return, the greater the risk incurred, and there are two conflicting objectives. The investor must make a tradeoff between risk and return. A multiobjective model is considered here, which presents solutions of compromise between risk and return as the final answer. The model considers a cardinality constraint, with a given minimum and maximum quantity of assets to be included in the portfolio. The inclusion of the cardinality constraint greatly increases the algorithmic complexity of the solution (Cheng & Gao, 2015), so that the use of computational techniques as evolutionary algorithms is advisable to ensure good solutions in a reasonable time
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