Create Better Diversified High-Conviction Equity Portfolios using the Portfolio Diversification Index

We investigate the construction of well-diversified high-conviction equity portfolios, building on Rudin and Morgan (2006) who introduced the Portfolio Diversification Index (PDI) as a new measure of portfolio diversification applied to long/short equity hedge funds in an in-sample period. We are the first to investigate the out-of-sample properties of the PDI. Our research applies a novel portfolio selection algorithm to maximize the PDI of a portfolio of stocks in the S&P 500 Index over 2000 to 2009. We construct equally-weighted, well-diversified portfolios, consisting of 5 to 30 stocks and compare these with randomly selected portfolios of the same stock sizes. Our results indicate that investors using our algorithm to maximize the PDI can improve the diversification of high-conviction equity portfolios. For example, a portfolio of 20 stocks constructed using the algorithm with the PDI behaves out-of-sample as if it contains 10 independent stocks, i.e. a PDI score of 10. Although this is less than the PDI score of 15 achieved in-sample, it is a significant improvement over the PDI score of 7, which occurs with a randomly selected portfolio. Our research is robust with respect to the number of stocks in the investment portfolio and the time period under consideration.