The conclusion by Evans and Archer, echoed in much of the subsequent work on the issue, has some implications for the investors that Chen and Israelov challenge:
• There’s little reason for index funds to go through the trouble of holding 500 or more stocks; they could achieve similar diversification with less expense holding 60 or 80 stocks or less
• Active managers should hold only their 20 or 30 best ideas rather than “deworsifying” into 60 or 80 holdings to reduce risk
• Ordinary retail investors can hold small handfuls of stocks efficiently, few enough so they can pay attention to each one
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 is not the first paper to dispute the Evans and Archer numbers. The literature, both academic and popular, seems to fall into three rough groups: the original 10 to 15 stocks (now usually 20 to 30) supporters, the 60 to 80 moderates, and the more-the-better-but-at-least-200 extremists. There are many investment products with stock holdings consistent 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 one year, they consider total return over 25 years. Rather than show you the graph from their paper, I estimated an equivalent calculation using the statistics generated for the Evans and Archer paper for an apples-to-apples comparison with the first chart. Chen and Israelov used a somewhat different methodology and, of course, a different time period. But the basic point is mathematical, in that a small change in annual volatility can compound to a large difference in results after 25 years with even moderately good or bad luck.
This next chart shows one’s wealth after 25 years per $1 invested versus the number of randomly selected stocks in a portfolio. The orange line represents 25% bad luck and blue line is 10% bad luck.
Evans and Archer found that 20-stock portfolios averaged 12.4% volatility per year, while 40-stock portfolios averaged 12.2%. Those numbers seem pretty close. But you don’t get 12.4% or 12.2% every year in every portfolio, rather you get random draws that average to those figures. 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.
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.More from Bloomberg Opinion:
• The ‘ Next Warren Buffett’ Curse Isn’t Always Fatal: Justin Fox
• Nasdaq 100 Peak a Year Later: It Was a Bubble: Jonathan Levin
• The Peak Looks In, But Markets Risk Overdoing It: John Authers
This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
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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