This study re-examines two fundamental questions—how large must a portfolio be to ensure negligible firm-specific risk? And, at what point do gains from additional diversification become meaningless? Our analysis yields surprising answers. Contrary to conventional wisdom, there is no evidence investors can, or have ever been able to, form well-diversified portfolios and there are, and always have been, substantial diversification gains from holding much larger portfolios than traditionally recommended.
A portfolio is well-diversified when an investor is assured that the portfolio's firm-specific return will differ negligibly from zero (Ross, 1976). Determining the number of securities required to form such portfolios is fundamental to financial economics because of the central role well-diversified portfolios play in market efficiency, portfolio management, and asset pricing theories. These theories rely, at least in part, on arbitrageurs to risklessly correct mispricings and ensure that only systematic exposures are priced.
The idea that investors can easily eliminate firm-specific risk is ingrained and pervasive. Alexander, Sharpe, and Bailey (2001, pages 163 and 216), for example, note, "Roughly speaking, a portfolio that has equal proportions of 30 or more randomly selected securities in it will have a relatively small amount of unique risk. Its total risk will be only slightly greater than the amount of market risk that is present. Such portfolios are 'well diversified'" and "For a well-diversified portfolio , nonfactor risk will be insignificant." Similarly, Francis and Ibbotson (2002, page 399) maintain, "Diversifiable risk may be easily diversified away to zero in a portfolio that contains more than about 36 random stocks because the unsystematic pieces of good luck and bad luck from randomly selected assets tend to average out to zero."
The Securities Exchange Commission (2005) tells investors that, "You'll need at least a dozen carefully selected individual stocks to be truly diversified." Campbell, Lettau, Malkiel, and Xu (2001) suggest, however, that the decline in the average correlation between stocks and the rise in firm-specific risk over time has increased the number of securities needed for a well-diversified portfolio. The 2003 edition of Malkiel's classic "A Random Walk Down Wall Street," for instance, maintains the "golden number" has increased to 50.
