**Acknowledgements**

The views expressed in this paper are those of the authors and do not necessarily represent the views of the institutions with which they are affiliated. The authors acknowledge research from the FCT (NECE: UID/GES/04630/2019). The FCT NOVA's author acknowledges Fundação para a Ciência e a Tecnologia (FCT - MCTES) for its financial support via the project UIDB/00667/2020 (UNIDEMI).

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**Author details**

(IPL), Lisbon, Portugal

Caparica, Portugal

Engineering, FCT NOVA, Caparica, Portugal

provided the original work is properly cited.

\*Address all correspondence to: hvgn@fct.unl.pt

Raúl D. Navas1,2, Sónia R. Bentes1,3 and Helena V.G. Navas4,5\*

2 Research Center in Business Sciences (NECE), Covilhã, Portugal

3 BRU - The Business Research Unit, Lisbon University Institute, Portugal

4 NOVA School of Science and Technology, Universidade NOVA de Lisboa,

5 UNIDEMI - Research and Development Unit in Mechanical and Industrial

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Lisbon Accounting and Business School (LABS) – Lisbon Polytechnic Institute

*Optimized Portfolios: All Seasons Strategy DOI: http://dx.doi.org/10.5772/intechopen.95122* *Optimized Portfolios: All Seasons Strategy DOI: http://dx.doi.org/10.5772/intechopen.95122*

*Quality Control - Intelligent Manufacturing, Robust Design and Charts*

tives years which is still better than the benchmark (3 versus 7).

(linear and "classical" portfolios).

The results enforce the MPT from [2, 3].

**Acknowledgements**

followed by portfolios 6 and 3. Portfolio 1 shows a strong sharp ratio equal to 4, presenting though, very low volatility but with lower returns when comparing to portfolios 6 and 3. None of this mentioned portfolios show a negative year during the period of 2000 to 2018. Portfolio 3 presents a high performance (14,15% annually). For an aggressive investor portfolio 2 is the best choice because it maximizes the overall return. It is the most volatile portfolio, but it may generate an average income superior to 15% annually. For a moderate investor, fan is wider but still we would exclude the portfolio 1 because it will not generate to much return and portfolio 2 may be a little volatile. Even that, portfolio 2 only presents three nega-

We went further in our research and we figure out that GRG is robust, and its returns exceeds the other models mentioned in the first paragraph of this section

Our contribution for this study is to provide a wider variety of portfolios that can be easily used by institutional and private investors and considering that nowadays there are plenty ETFs or funds available in the market is easy to everyone to apply one of the proposed models. Also, it is proved that it is possible to design very efficient portfolios, increasing returns and at the same time, lowering the risk.

As it happens in all models, there are, of course, some limitations as well. First, we may not guarantee that portfolios constitutions (1–6) will present the same results in the future because we are relaying in past returns and we would need, at least one more decade to understand if, for example, "good" decades present similar behavior between themselves. Another limitation found, the lack of the real VIX tracker (ETF/ETN). Available ETFs of VIX are a mix of mid-short term that do not reflect the actual index. Note that VIX plays an important role in GRG models.

The views expressed in this paper are those of the authors and do not necessarily represent the views of the institutions with which they are affiliated. The authors acknowledge research from the FCT (NECE: UID/GES/04630/2019). The FCT NOVA's author acknowledges Fundação para a Ciência e a Tecnologia (FCT - MCTES) for its financial support via the project UIDB/00667/2020 (UNIDEMI).

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