How Many Stocks Do You Need for a Diversified Portfolio?

In my extrapolation from Evans and Archer’s results, with moderate 25% bad luck (meaning three quarters of the time you did better, one quarter of the time you did worse) you ended the 25 years with $11.84 in a 20-stock portfolio versus $12.86 in a 40-stock portfolio and $14.50 in a 500-stock portfolio.

With 10% bad luck (10% of the time you did worse) you have $8.50 in a 20-stock, $9.74 in a 40-stock and $14.29 in a 500-stock. Those are appreciable differences.

Of course, if you have good luck, you’d rather be in the more concentrated portfolios. If you are paying a fee for active management, presumably you think your manager can deliver above 50% results on average, so there’s some temptation to push for smaller portfolios.

There’s no reason to pay active management fees for closet indexing. But you have to weigh the cost not just of active management fees, expenses and taxes, but of additional uncompensated volatility.

Don’t look at the difference in annual volatility of active versus passive management, but how that difference can be expected to compound over your investment horizon.

More Issues to Consider

Another objection to this entire area of study is that no one picks stocks at random. People who try to get diversified portfolios with limited numbers of stocks will typically spread their picks out to cover all economic sectors (like financials, technology, energy, consumer stocks and so on) and perhaps weight by sector rather than equally.

Random selection biases the portfolios to smaller stocks, since there are more small cap stocks than large cap, but most people holding concentrated portfolios will pick mostly larger cap stocks.

These techniques can reduce the volatility of portfolios with fewer stocks and make them track broad indices better. But they don’t change the core mathematical point that small differences in annual volatility can made large differences to the distribution of long-term outcomes.

A carefully selected 20-stock portfolio might have the volatility of a random 50-stock portfolio, but not of a 500-stock portfolio.

None of this says that all stock investors need to buy 500 or 5,000 stocks. It does say that buying fewer stocks adds more risk over long investment horizons that has been suggested by academic and popular papers that focus on annual volatility.

Going beyond the specific points in these papers, I’d add that ignoring diversification opportunities that may seem small based on their effect on annual volatility — such as international stocks, real assets, bonds and alternative funds — could cost you a lot in the long run if you have moderate bad luck.

Any time you neglect to maximize diversification, whether to chase active management, indulge personal intuition or save trouble, you need to think carefully about whether you are getting paid enough for the additional risk.

Aaron Brown is a former managing director and head of financial market research at AQR Capital Management. He is author of “The Poker Face of Wall Street.” He may have a stake in the areas he writes about.

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