Strongest performance during the preceding year and

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strongest performance during the preceding year and puts more money into the weak- est. Increased ending wealth is consistent with the market overreaction hypothesis presented by De Bondt and Thaler (1985, 1987). The most important similarity between the two samples is the finding that effec- tive portfolio diversification requires more than 100 stocks. To illustrate, a 100-stock portfolio in the 1965 1984 period has a mean of $7.61 and the 10th percentile is $6.34. Thus there is a 10% chance that ending wealth will be at least 16.7% below the mean of the distribution. Many investors would find this unacceptable. 8. Conclusion This study offers new insights into the question of how many stocks are required to diversify a portfolio. Traditional wisdom from the 1960s and 1970s is that eight to 20 stocks are sufficient. In contrast, we believe that even 100 are not enough. From 1985 to 2004, 25% of randomly constructed 100-stock portfolios produced ending wealth at least 18% below the mean stock portfolio. In accordance with the Safety First criterion, 164 stocks are needed to have a 1% chance of underperform- ing Treasury bonds. These findings are consistent with the recent Statman (2004) study. We consider both random diversification, in which portfolios are drawn from the entire 1,000-stock sample, and industry diversification, in which the portfolio composition is equally distributed across ten industry groups. Industry diversification has no effect on larger portfolios, and only a small effect on the lowest percentiles of small portfolios. In contrast, annual rebalancing improves portfolio performance, but further research is needed to determine whether the diversification benefits outweigh taxes and transactions costs. References Aizcorbe, A.M., A.B. Kennickell, and K.B. Moore, 2003. Recent changes in U.S. family finances: Evidence from the 1998 and 2001 Survey of Consumer Finances, Federal Reserve Bulletin 89, 1 32. Campbell, J.Y., M. Lettau, B.G. Malkiel, and Y. Xu, 2001. Have individual stocks become more volatile? An empirical investigation of idiosyncratic risk, Journal of Finance 56, 1 44. De Bondt, W.F.M. and R. Thaler, 1985. Does the stock market overreact? Journal of Finance 40, 793 805. De Bondt, W.F.M. and R. Thaler, 1987. Further evidence on investor overreaction and stock market seasonality, Journal of Finance 42, 557 581.
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570 D. L. Domian et al./The Financial Review 42 (2007) 557 570 de Vassal, V., 2001. Risk diversification benefits of multiple-stock portfolios, Journal of Portfolio Man- agement 27, 32 39. Domian, D.L., D.A. Louton, and M.D. Racine, 2003. Portfolio diversification for long holding periods: How many stocks do investors need? Studies in Economics and Finance 21, 40 64. Elton, E.J. and M.J. Gruber, 1977. Risk reduction and portfolio size: An analytical solution, Journal of Business 50, 415 437. Evans, J.L. and S.H. Archer, 1968. Diversification and the reduction of dispersion: An empirical analysis, Journal of Finance 23, 761 767.
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