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Abstract

Investors underdiversify because of solvency constraints and preferences for lottery-type outcomes. The relationship between underdiversification and positive skewness of portfolio returns breaks down somewhat in bear markets as co-movement between stocks increases.

What’s Inside?

The authors confirm the finding of earlier research that retail investors underdiversify compared with standard mean–variance portfolio theory. This finding is due in part to the impracticality of constructing diversified portfolios for investors with small portfolio values and in part to preferences for lottery-type outcomes (positive skewness of portfolio returns). The authors present a novel result—namely, that the relationship between portfolio skewness and diversification disappears in bear markets because of the greater “systematic” component in the variance of stock returns. Although investors prefer positive skewness, diversifying portfolios to reduce idiosyncratic risk also reduces portfolio skewness because portfolios with few stocks have positively skewed returns and portfolios with many stocks have negatively skewed returns.

How Is This Research Useful to Practitioners?

Several studies have highlighted the underdiversification of investor portfolios. The authors confirm that investors with less capital to invest in risky assets hold more-concentrated portfolios because of solvency constraints and transaction costs. In their 2003 and 2006 snapshots, more investors held only 1 stock in their portfolio (22%) than held 10 or more stocks (18%); the median investor held only 3 or 4 stocks. As wealth rises, there is a clear trend toward holding more-diversified portfolios. The authors also confirm that investors appear to like portfolios with positive skewness of returns, which comes at the expense of higher variance per unit of return than that of the portfolio prescribed by modern portfolio theory.

Examining a sample that contains clear bull and bear periods, the authors are able to investigate the relationship between portfolio diversification and portfolio skewness across these two regimes. By decomposing each stock’s variance into systematic and idiosyncratic components, they demonstrate that the proportion of idiosyncratic variance decreases, on average, during bear markets. The familiar result that the degree of co-movement increases in bear markets leads to the less familiar result that diversification becomes less effective in reducing portfolio skewness. In addition, the authors find evidence of the “home bias” puzzle in their sample of French investors, who largely invest in French stocks.

How Did the Authors Conduct This Research?

The authors obtain transaction data from a large French brokerage for all active accounts over 1999–2006. The data for each trade include the asset’s ISIN code, whether it was bought or sold, the quantity bought or sold, and the amount in euros. They are also able to control for investor heterogeneity because the data include information on each investor’s date of birth, gender, and region of residence. Price data are obtained from EUROFIDAI for stocks traded on Euronext and from Bloomberg for other stocks.

The authors construct three measures of diversification, ranging from a simple measure based on the number of stocks in the portfolio to a more sophisticated measure based on the ratio of the portfolio variance to the average variance of the individual stocks in the portfolio.

Regarding their key novel finding—that the relationship between underdiversification and portfolio skewness breaks down in bear markets—the authors calculate the rank correlation between the decrease in skewness owing to diversification and the proportion of “systematic” variance. In sum, they find strong statistical evidence (at the 1% level) that the tendency of diversified portfolios in bull markets to have lower skewness breaks down in bear markets because of the increased average variance owing to “common” factors.

Abstractor’s Viewpoint

The authors’ novel finding relates to the increased level of systematic variance across stocks in bear markets. It would be interesting to see whether the observed decreased reduction in portfolio skewness for diversified portfolios holds for other asset classes and other periods.

About the Author(s)

Antony Jackson CFA

Antony Jackson, CFA, is at the University of East Anglia.