Random diversification over time

The case of five European countries surrounding the Euro introduction

Abstract

This article adds to the financial literacy of active individual investors who restrict themselves to a limited number of securities. Using monthly observations and a sample size of up to 5,177 stocks from five major European equity markets, this study provides evidence that the marginal benefit of adding a random stock to a portfolio is time varying. Moreover, for small portfolios, the marginal diversification benefits are less pronounced during times of high volatility than during periods of low volatility. Further, while we show that the relative risk of European equity markets has increased after the introduction of the Euro, our study demonstrates that in the post-Euro period a smaller portfolio size is necessary to achieve the same percentage average relative risk reduction than in the pre-Euro period. The highest average relative risk reductions are obtained in the larger equity markets, where a random portfolio of 15 stocks yields an average relative risk reduction of close to 50% of a two-stock portfolio. Our study implies that most individual investors, who enjoy direct investing and, hence, restrict themselves to invest in a small number of securities to reduce transactions cost, may not be as irrational and underdiversified as commonly thought.