Portfolio Selection With Exploration of New Investment Opportunities

58 Pages Posted: 6 Aug 2020 Last revised: 7 Oct 2021

See all articles by Luca De Gennaro Aquino

Luca De Gennaro Aquino

Southern University of Science and Technology; Grenoble Ecole de Management

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute; Southern University of Science and Technology; Tokyo Institute of Technology

Moris Simon Strub

Southern University of Science and Technology - School of Business

Date Written: June 12, 2020

Abstract

We introduce a model for portfolio selection with an extendable investment universe where an agent with mean-variance preferences faces a trade-off between exploiting existing and exploring for new investment opportunities. When the agent chooses to explore, a new risky asset is discovered and the agent subsequently invests in the extended universe. We first provide conditions for wellposedness and characterize the optimal amount devoted to exploration. Our model shows that incremental exploration does not pay off, that it is increasingly worthwhile to explore in worse market environments, and that investment performance measured by the Sharpe ratio is increasing in the initial wealth of the agent indicating that richer agents can make better use of new investment opportunities. We further generalize our model and verify the robustness of the main findings with regards to various modeling assumptions.

Keywords: portfolio selection, mean-variance optimization, exploration vs exploitation, investment universe, alternative investments

JEL Classification: C61, G11

Suggested Citation

De Gennaro Aquino, Luca and De Gennaro Aquino, Luca and Sornette, Didier and Strub, Moris Simon, Portfolio Selection With Exploration of New Investment Opportunities (June 12, 2020). Swiss Finance Institute Research Paper No. 20-57, Available at SSRN: https://ssrn.com/abstract=3625492 or http://dx.doi.org/10.2139/ssrn.3625492

Luca De Gennaro Aquino

Southern University of Science and Technology ( email )

No 1088, xueyuan Rd.
Xili, Nanshan District
Shenzhen, Guangdong 518055
China

Grenoble Ecole de Management ( email )

12 Rue Pierre Semard
Grenoble, Cedex 01 38000
France

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Southern University of Science and Technology

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Tokyo Institute of Technology

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

Moris Simon Strub (Contact Author)

Southern University of Science and Technology - School of Business ( email )

1088 Xueyuan Ave
Shenzhen, Guangdong
China

HOME PAGE: http://sites.google.com/view/morisstrub/home

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