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Analysis | diversify? Volatility is more important than size


A pair of researchers from Boston-based financial advisory firm NDVR, Yin Chen and Roni Israelov, have come up with a new take on an age-old question for investors: How many stocks should you own for a well-diversified portfolio? The academic approach to finding an answer goes back to a 1968 article in the Journal of Finance by John Evans and Stephen Archer, which includes a chart that you can find versions of in almost every introductory finance book and in many articles on personal finance. They concluded that there was little additional diversification benefit once you got past 10 or 15 stocks.

Evans and Archer’s conclusion, echoed in much of the subsequent work on the matter, has some implications for the investors challenging Chen and Israelov:

• There is little incentive for index funds to bother holding 500 or more stocks; they could achieve similar diversification with less cost by holding 60 or 80 stocks or less

• Active managers should only have their 20 or 30 best ideas instead of ‘designing’ them into 60 or 80 positions to reduce risk

• Ordinary retail investors can efficiently hold small handfuls of stocks, few enough to pay attention to each stock

This chart shows portfolio volatility versus the number of randomly selected stocks in a portfolio. The orange dots represent actual data and the blue line is fitted to the data.

This isn’t the first newspaper to dispute Evans and Archer’s numbers. The literature, both academic and popular, seems to fall into three rough groups: the original 10 to 15 adherents (now usually 20 to 30), the 60 to 80 moderates, and the more-the-better-but-at least-200 extremists. There are many equity investment products that align with each of these ranges.

Chen and Israelov do a similar exercise to Evans and Archer, but present the results very differently. Instead of looking at volatility over a year, they look at total returns over 25 years. Instead of showing you the graph from their paper, I have estimated an equivalent calculation using the statistics generated for the Evans and Archer paper for an apples to apples comparison to the first graph. Chen and Israelov used a slightly different methodology and, of course, a different time period. But the base point is mathematical, in that a small change in annual volatility can lead to a big difference in results after 25 years with even moderate luck or bad luck.

This next chart shows someone’s wealth after 25 years per $1 invested versus the number of randomly selected stocks in a portfolio. The orange line represents 25% breakdown and the blue line represents 10% breakdown.

Evans and Archer found that portfolios of 20 stocks averaged 12.4% volatility per year, while portfolios of 40 stocks averaged 12.2%. Those numbers seem pretty close. But you don’t get 12.4% or 12.2% in every portfolio every year, but you get random draws that average for those numbers. In my extrapolation of Evans and Archer’s results, with moderate 25% bad luck (meaning you did better three quarters of the time, one quarter of the time you did worse) you ended the 25 years with $11.84 in a portfolio of 20 stocks versus $12.86 in a portfolio of 40 stocks and $14.50 in a portfolio of 500 stocks. With 10% bad luck (10% of the time you did worse) you have $8.50 in a 20 share, $9.74 in a 40 share and $14.29 in a 500 share. Those are noticeable differences.

Of course, if you’re lucky, you prefer to be in the more concentrated portfolios. If you pay a fee for active management, you presumably think your manager can achieve more than 50% results on average, so there is some temptation to aim for smaller portfolios. There is no reason to pay active management fees for closet indexing. But you need to weigh not only the cost of active management fees, expenses and taxes, but also of additional uncompensated volatility. Don’t look at the difference in annual volatility of active versus passive management, but how that difference is expected to grow over your investment horizon.

Another objection to this whole field of study is that no one picks stocks at random. People trying to get diversified portfolios with a limited number of stocks tend to spread their choice across all economic sectors (such as financials, technology, energy, consumer stocks, etc.) and perhaps by sector rather than evenly. Random selection biases portfolios towards smaller stocks since there are more small cap stocks than large cap stocks, but most people with concentrated portfolios will usually choose larger cap stocks.

These techniques can reduce the volatility of portfolios with fewer stocks and make them better track broad indices. But they do not change the basic mathematical point that small differences in annual volatility can make big differences in the distribution of long-term results. A carefully selected portfolio of 20 stocks can have the volatility of any portfolio of 50 stocks, but not a portfolio of 500 stocks.

None of this is saying that all stock investors should buy 500 or 5,000 shares. It does say that buying fewer stocks carries more risk over a long investment horizon, which is suggested by academic and popular articles that focus on annual volatility. Going beyond the specific points in these papers, I would add that ignoring diversification opportunities that may seem small based on their effect on annual volatility – such as international equities, real assets, bonds and alternative funds – leaves you in the dark. can cost a lot in the long run. run if you are moderately unlucky. Any time you fail to maximize diversification, whether you’re chasing active management, giving in to personal intuition or saving trouble, you need to think carefully about whether you’re getting paid enough for the extra risk. More from Bloomberg Opinion:

• The ‘Next Warren Buffett’ curse isn’t always deadly: Justin Fox

• Nasdaq 100 peak a year later: it was a bubble: Jonathan Levin

• The peak appears to be in, but the markets threaten to overdo it: John Authers

This column does not necessarily reflect the views of the editors or Bloomberg LP and its owners.

Aaron Brown is a former general manager and head of financial market research at AQR Capital Management. He is the author of ‘The Poker Face of Wall Street’. He may have a share in the areas he writes about.

More stories like this are available at bloomberg.com/opinion

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