Portfolio Selection With Exploration of New Investment Opportunities

28 Pages Posted: 6 Aug 2020 Last revised: 10 Aug 2020

See all articles by Didier Sornette

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 - Division of Information Systems and Management Engineering

Date Written: June 12, 2020

Abstract

We introduce a model for portfolio selection with an extendable investment universe where the agent faces a trade-off between exploiting existing and exploring for new investment opportunities. An agent with mean-variance preferences starts with an existing investment universe consisting of a risk-free and a number of risky assets. However, rather than being limited to these assets, the agent has the option to devote a part of his/her wealth for exploring new investment opportunities. If this option is exercised, a new risky asset is discovered and the agent subsequently invests in the extended universe. We show that the problem is well-posed when the Sharpe ratio of the newly discovered asset has reasonably asymptotic elasticity, and determine an equation characterizing the optimal amount devoted to exploration. We determine that incremental exploration does not pay off: one must put a significant amount at risk in order to harvest the potential benefits of exploring for new investment opportunities. We further find that the investment performance as 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.

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

JEL Classification: C61, G11

Suggested Citation

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

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 - Division of Information Systems and Management Engineering ( email )

1088 Xueyuan Ave
Shenzhen, Guangdong
China

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
176
Abstract Views
826
rank
199,949
PlumX Metrics