The Diversification Puzzle

Abstract

The levels of diversification in U.S. investors' equity portfolios present a puzzle. Today's optimal level of diversification, measured by the rules of mean–variance portfolio theory, exceeds 300 stocks, but the average investor holds only 3 or 4 stocks. The diversification puzzle can be solved, however, in the context of behavioral portfolio theory. In behavioral portfolio theory, investors construct their portfolios as layered pyramids in which the bottom layers are designed for downside protection and the top layers are designed for upside potential. Risk aversion gives way to risk seeking at the uppermost layer as the desire to avoid poverty gives way to the desire for riches. But what motivates this behavior is the aspirations of investors, not their attitudes toward risk. Some investors fill the uppermost layer with the few stocks of an undiversified portfolio; others fill it with lottery tickets. Neither lottery buying nor undiversified portfolios are consistent with mean–variance portfolio theory, but both are consistent with behavioral portfolio theory.

The levels of diversification in U.S. investors' equity portfolios present a puzzle. The benefits of diversification as measured by mean–variance portfolio theory have increased in recent years, yet the average level of diversification has not. It remains well below the optimal level.

The optimal level of diversification is reached when its marginal benefits exceed its marginal costs. The benefits of diversification in mean–variance portfolio theory are in the reduction of risk; the costs are transaction and holding costs. Risk is measured by the standard deviation of portfolio returns. Investors can choose to diversify in two ways—by assembling individual stocks into a portfolio or by buying a diversified portfolio in the form of a mutual fund. Investors who use a mutual fund save the cost of buying, holding, and selling stocks, but they pay, year by year, the cost of the fund.

Recently, the Vanguard Total Stock Market Index Fund contained 3,444 stocks and its annual cost was 0.20 percent. I estimated the benefit of an increase of diversification from fewer than 3,444 stocks to 3,444 stocks by calculating the value of the reduction of risk, expressed in units of expected returns. The relative benefits of diversification depend on the average correlation between stocks, the equity premium, and the cost of a portfolio versus the cost of investing through the Total Market fund. I found that the Total Market fund offers a better way to diversify than a portfolio of 300 or fewer stocks.

Although today's optimal mean–variance diversification exceeds 300 stocks, the average investor holds only 3 or 4 stocks. Large holdings of company (employer) stock in 401(k) accounts, concentration of portfolios in particular styles, and geographical bias add to the diversification puzzle.

The diversification puzzle can be solved, however, within the framework of behavioral portfolio theory. Whereas “mean–variance investors” consider their portfolios as a whole and are always risk averse, “behavioral investors” do not consider their portfolios as a whole and are not always risk averse. Behavioral theory posits that risk aversion and risk seeking share roles in our behavior. In behavioral portfolio theory, investors construct their portfolios as layered pyramids in which the bottom layers are designed for downside protection and the top layers are designed for upside potential.

The article shows that what is motivating this behavior of investors is aspirations, not attitudes toward risk. In behavioral theory, investors do not diversify fully because diversified portfolios leave them with too little hope of attaining their aspirations. But behavioral investors who select a few stocks for the upside-potential layers of their portfolios do not necessarily neglect the downside-protection layers. Some evidence shows that gamblers, for example, are more likely to have their future secured by Social Security and pensions than nongamblers.

The rules of diversification in behavioral portfolio theory are not as precise as the rules in mean–variance portfolio theory, but they are clear enough. The optimal number of individual stocks under the rules of behavioral portfolio theory is the number that balances the chance for an uplift into riches against the chance of a descent into poverty. Investors, financial advisors, and companies sponsoring 401(k) plans must be careful to draw the line between upside potential and downside protection so that dreams of riches do not plunge investors into poverty.

I thank Roger Clarke, Sanjiv Das, Ramie Fernandez, William Goetzmann, Mark Kritzman, Valery Polkovnichenko, and Jonathan Scheid, and acknowledge financial support from the Dean Witter Foundation.