Portfolio Selection With Exploration of New Investment Opportunities

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