This paper will explore how “concentrated” portfolios perform using the historical performance of mutual funds, and will determine the relative impact of different types of concentration on an absolute-return, a risk and a risk-adjusted basis.
Past research on portfolio concentration has tended to note the potential benefits of concentrated portfolios over less-concentrated portfolios, although the approaches to defining “concentration” have differed considerably. In perhaps the most expansive study, Kacperczyk, Sialm and Zheng  found that mutual funds with higher levels of industry concentrations yield an average abnormal return of 1.58 percent per year before deducting expenses and 0.33 percent per year after deducting expenses. Kacperczyk et al. attribute this outperformance to superior stock selection ability and also note that the trades of concentrated portfolios added more value than the trades of diversified portfolios.
Brands, Brown and Gallagher  conducted a study of active Australian equity managers and found a positive relationship between portfolio concentration and fund performance at the stock, industry and sector levels. They defined portfolio concentration as “the extent to which the portfolio weights held in stocks, industries and sectors deviate from the underlying index or market portfolio.”
Ivkovich, Sialm and Weisbenner  found that stock investments made by households that choose to concentrate their brokerage accounts in a few stocks outperform those made by households with more diversified accounts (especially among those with large portfolios). They found that when controlling for households’ average investment abilities, their trades and holdings perform better when their portfolios include fewer stocks. Ivkovich et al. use the term “concentrated” to refer to investors who hold only one or two stocks in their brokerage accounts, and use the term “diversified” to refer to investors who are not as highly focused with their portfolio (i.e., hold three or more stocks).
The Benefits Of Diversification
The benefits of portfolio diversification have been well-documented. In one of the first studies on portfolio stock diversification, Evans and Archer  noted that there is little diversification benefit beyond holding eight to 10 stocks for an equal-weighted portfolio. This confirmed earlier advice from Benjamin Graham, who in his 1949 book, “The Intelligent Investor,” recommended owning from 10 to 30 stocks to achieve proper diversification based on instinct and experience. More recent research by Statman , though, suggested that a well-diversified portfolio of randomly chosen stocks must include at least 30 stocks for a borrowing investor and 40 stocks for a lending investor.
While the number of securities necessary to achieve diversification has varied, according to past research (and over time, according to Campbell, Lettau, Malkiel and Xu ), adequate diversification is an important consideration when addressing the risk component of a portfolio. De Wit  has noted that even a well-diversified portfolio can benefit from additional diversification. Holding multiple stocks does not necessarily create a diversified portfolio, though, if the correlations among the stocks within a portfolio are high (Goetzmann and Kumar ). Often, the reason a portfolio manager increases the total number of holdings is not out of a desire to own the new stocks per se, but rather as a means to accommodate mutual fund inflows (Shawky and Smith ).
Since there is no clear consensus on the number of securities necessary for adequate portfolio diversification, Figure 1 has been provided as a reference. Figure 1 includes the 95th (worst 1 in 20), 80th (worst 1 in 5), 50th (median), 20th (best 1 in 5), and 5th (best 1 in 20) percentile returns for randomly created equal-weighted portfolios holding differing numbers of securities. The portfolios’ number of holdings range from one stock to 400. The securities included in the portfolio are the components of the S&P 500 as of June 10, 2008, with available full-year 2007 performance (which reduced the test set to 490 securities). For each security set (e.g., five stocks, 100 stocks, 250 stocks, etc.), 1,000 equal-weighted random combinations were tested (from which the percentile bands are determined). The performance of the percentiles is compared against the performance for the equal-weighted full stock portfolio for the period.
Figure 1 demonstrates that as the number of securities in a portfolio increases, the more likely it will achieve a return that is similar to the composite index, and vice versa. Portfolio managers who wish to exhibit low levels of tracking error are more likely to hold more securities and to weight the portfolio similarly to the benchmark index. While increasing the number of securities decreases tracking error, it increases monitoring costs and reduces the ability of the portfolio manager to exploit his or her “best ideas.”