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Expert Analysis and Commentary

Portfolio Diversification: How Many Stocks Are Enough?

Larry Swedroe Feb 17, 2015



But, despite the benefits of diversification, many investors hold only a limited number of securities. Among the explanations for this behavior are:

  • Investors confuse the familiar with the safe. Following Peter Lynch’s misplaced advice, investors tend to buy the stock of companies they believe they know well.
  • Investors are overconfident in their ability to identify and purchase stocks that will outperform. Diversification is only for those investors who don’t have a clear crystal ball.
  • Investors have a preference for investments with the characteristics of a lottery ticket. Investors are lured by the potential for large gains, while large portfolios and diversification guarantee “mediocrity.”
  • Investors are unaware of just how many stocks are needed to effectively reduce risk. Or, perhaps, they may be relying on old data.
    With this last point in mind, we’ll take a close look at some of the findings from academic research on the number of stocks needed to effectively diversify a portfolio.


How Many Stocks Are Needed?


The authors concluded that an investor needed to construct a portfolio containing as little as 15 randomly selected stocks before the benefits of diversification, as measured by the standard deviation, were basically exhausted. A similar study from the same era found that 90 percent of the diversification benefit came from just 16 stocks, and 95 percent of the benefit could be captured by just 30 stocks.

For about 30 years, these studies provided the intellectual support for limiting the number of stocks an investor needed to hold to reduce portfolio risk to an acceptable level.

More recent studies — including a 2000 paper, “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,” by John Campbell, Martin Lettau, Burton Malkiel and Yexiao Xu — found a greater need for diversification. This need, they discovered, is caused by the increased volatility of individual stocks, although not increased volatility of the market. That has led to decreased correlations among individual stocks. Declining correlations among equities implies that the benefits of portfolio diversification have increased over time. The authors found that while a portfolio of about 20 stocks was sufficient to reduce the excess standard deviation of a portfolio to 10 percent in the 1960s, by the turn of the century that figure had risen to 50 stocks.


A Different Approach


But instead of examining how many stocks were needed to reduce tracking error risk to an acceptable level, the authors examined the risk of a portfolio having end wealth below that of a risk-free rate. The authors randomly selected portfolios from 1,000 large U.S. stocks and calculated the shortfall risk over a 20-year holding period (1985–2004).

At the start of this period, the 20-year Treasury bond (the riskless instrument for the timeframe in question) had a yield to maturity of 11.70 percent. The following is a summary of the authors’ conclusions:

  • Fifteen to 30 stocks are woefully inadequate for long-term investors who wish to outperform riskless Treasury bonds. Based on the sample period, investors need at least 164 stocks to have at most a 1 percent chance of underperforming Treasury bonds.
  • The shortfall probability for a 10-stock portfolio was 40 percent. The shortfall probability drops to 29 percent for 20 stocks, 22 percent for 30 stocks and 13 percent for 50 stocks. It was still 4 percent for 100 stocks. For a 200-stock portfolio, the figure dropped to 0.4 percent.
  • Using 1 percent, 5 percent and 10 percent levels of statistical significance, portfolios of 164, 93 and 63 stocks, respectively, were required to meet the shortfall risk test.
  • Although slightly lower risk can be achieved in small portfolios by diversifying across industries, a greater reduction in risk is obtained by simply increasing the number of stocks.
  • The 2002 study “How Much Diversification is Enough?” came to a similar conclusion. In this case, the author found that the optimal level of diversification, measured by the rules of mean-variance portfolio theory, exceeds 120 stocks.

The most recent study on the subject — a November 2014 paper, “Equity Portfolio Diversification: How Many Stocks are Enough? Evidence from Five Developed Markets,” by Vitali Alexeev and Francis Tapon — examined the evidence from five developed markets (U.S., U.K., Australia, Japan and Canada) over the period from 1975 through 2011. They also considered various measures of risk, including volatility and shortfall. The following is a summary of their findings:

  • The number of stocks needed to diversify risk increases during periods when markets are in financial distress.
  • For the U.S., even to be confident of reducing 90 percent of diversifiable risk 90 percent of the time, the number of stocks needed on average is about 55. However, in times of distress it can increase to more than 110 stocks.
  • For the U.K., Japanese, Canadian and Australian markets, the figure for equities needed in times of distress is as high as 86, 97, 39 and 81 stocks, respectively.
    The number of stocks needed to reduce idiosyncratic risk to an acceptable level is not only far greater than most investors believe, but far greater than is reasonable for the vast majority of individual investors to efficiently manage.

But, even though the evidence demonstrates that large numbers of stocks are needed to reduce portfolio risk to acceptable levels, most people hold concentrated portfolios. This led Meir Statman, a professor of finance at Santa Clara University to conclude: “People who hold undiversified portfolios, like people who buy lottery tickets, behave as gamblers since they accept higher risk without compensation in the form of higher expected returns.”


The Bottom Line



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