A Theoretical Basis for Practitioners Heuristic 1/N and Long-Only Quintile Portfolio

The heuristic 1/N (equally weighted) portfolio and long-only quintile portfolio are both popular simple strategies in financial investment. In the 1/N portfolio, a fraction of 1/N of wealth is allocated to each of the N available assets. In the long-only quintile portfolio, first the assets are sorted according to some factors, e.g., expected returns, and then the strategy equally longs the top 20% (i.e., top quintile). Although they have been criticized for naiveness when proposed by practitioners, they have shown great advantage over some sophisticated portfolios. They are becoming more and more popular in practical investment due to their stable performance and easy deployment. In this paper, we formulate a mathematically meaningful robust maximum return portfolio design and show that it reduces to the two heuristic portfolios under different level of estimation error in the mean returns. A variance-adjusted uncertainty set is also proposed to derive an inverse-volatility portfolio, which shows consistent advantage over the heuristic portfolios in backtesting with real market data.