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Diversification refers to the idea that your investments ought to be spread out amongst many investments.  On average, a diversified portfolio will have the same expected return (but less riskvolatility) as a less diversified portfolio with similar characteristics.  When put that way, it is easy to see why diversification is beneficial — why have a more risky portfolio if you can't expect higher returns in exchange for taking on that additional risk? .

Daniel J. Burnside, Donald R. Chambers, and John S. Zdanowicz, "How Many Stocks Do You Need to be Diversified?," AAII Journal, July 2004. An excellent article.

John Y. Campbell, Martin Lettau, Burton G. Malkiel, and Yexiao Xu, " Have Individual Stocks Become More Volatile? An Empirical Investigation of Idiosyncratic Risk," Journal of Finance, February 2001, pp. 1-43 (1.95mb). This paper finds that, while several decades earlier, it may have been true that adequate diversification could be had with 15-20 stocks, it is no longer true.  The paper finds that, while volatility of the stock market as a whole has remained relatively steady, the volatility of individual stocks has increased.  This implies that correlations between stocks have decreased, which is confirmed by the paper's empirical results.  Thus, the benefits of diversification have increased, along with the need to hold more stocks to achieve those benefits.  This confirms the prudence of holding highly diversified mutual funds instead of individual stocks.  Also, see the Picerno summary article below.

John L. Evans and Stephen H. Archer, "Diversification and the Reduction of Dispersion: An Empirical Analysis," Journal of Finance, December 1968, pp. 761-767. This paper largely covers the same ground as the Fisher/Lorie paper below, but this paper only analyzed the period 1958-1967.

Lawrence Fisher and James Lorie, "Some Studies of Variability of Returns on Investments in Common Stocks," Journal of Business, April 1970, pp. 99-134. This is the paper usually cited by those who claim that a portfolio of 16 or so randomly selected stocks provides 90-plus percent of possible diversification benefit.  This may have been true in the 1926-1965 period studied, but as you can see from the Campbell/Lettau/Malkiel/Xu paper above and the Surz/Price paper below, it no longer appears to be true.

Zoran Ivković, Clemens Sialm, and Scott Weisbenner, "Portfolio Concentration and the Performance of Individual Investors," Working Paper, July 2004 (847kb).  This paper finds that individual investors with very concentrated portfolios tend to have higher returns than investors with more diversified portfolios.  This counterintuitive observation seems to support undiversified portfolios.  However, while the undiversified portfolios had (arithmetic) average returns that were 10% higher than diversified portfolios, they also had 50% more risk/volatility!  The risk-adjusted returns of undiversified portfolios were dramatically smaller than those of more diversified portfolios.  So this paper actually supports the prudence of diversification.  The higher arithmetic returns of an undiversified portfolio are likely to turn into lower geometric returns due to the increased risk/volatility (and geometric returns are what investors actually realize).

Henry A. Latané and William E. Young, "Test of Portfolio Building Rules," Journal of Finance, September 1969, pp. 595-612. "Diversification pays ... This advantage of diversification results entirely from the reduction of variance and hence increases in the geometric mean return.  It is not necessary to appeal to risk aversion on the part of investors to justify diversification."

Richard W. McEnally and Calvin M. Boardman, "Aspects of Corporate Bond Portfolio Diversification," Journal of Financial Research, Spring 1979, pp. 27-36. This paper analyzes how many individual corporate bonds are necessary in order to obtain diversification benefits.  Its conclusion is that, for high-grade bonds, there is limited diversification benefit, but that "something in the neighborhood of eight to 16 issues ... appear adequate to eliminate diversifiable risk in bond portfolios."  Note that this paper is considering diversifying volatility risk, NOT credit risk.

James Picerno, "Quantity Control," Bloomberg Wealth Manager, July/August 2000. A good summary of the Campbell/Lettau/Malkiel/Xu paper above.

Meir Statman, "How much Diversification is Enough?," Santa Clara University Working Paper, September 2002 (308kb).  "Lack of diversification is costly.  Investors who hold only 4 stocks in their portfolios forego the equivalent of a 3.3% annual return relative to investors who hold the 3,444 stocks of the Vanguard Total Index Stock Market Index fund.  Why do investors forego the benefits of diversification?"

Meir Statman and Jonathan Scheid, "Dispersion, correlation, and the benefits of diversification," Santa Clara University Working Paper, May 2004 (566kb). "Correlation is the common measure of the benefits of diversification but it is deficient for two reasons. First, the benefits of diversification depend not only on correlations but on standard deviations as well. Dispersion combines both effects. Second, dispersion, unlike correlation, provides an intuitive measure of the benefits of diversification. It is best to set aside correlation when we assess the benefits of diversification and focus on dispersion."

Ronald J. Surz and Mitchell Price, "The Truth About Diversification by the Numbers," Journal of Investing, Winter 2000, pp. 93-95 (60kb). This paper challenges the conventional wisdom that a randomly chosen portfolio of 15-20 stocks gives nearly all the diversification benefit of the market.  "Fifteen-stock portfolios, on average, achieve only 75%-80% of available diversification, not the 90%-plus typically believed.  Even 60-stock portfolios achieve less than 90% of full diversification."  This confirms the prudence of avoiding individual stocks in favor of highly diversified mutual funds.

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