A couple of researchers at financial advisory firm NDVR in Boston, 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 properly diversified portfolio?
The academic approach to finding an answer goes back to a 1968 Journal of Finance paper by John Evans and Stephen Archer that included a graph that you can find versions of in almost any introductory finance book and many personal finance articles today. They concluded there was little additional diversification benefit once you got beyond 10 or 15 stocks.
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:
1. 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.
2. Active managers should hold only their 20 or 30 best ideas rather than "de-worsifying" into 60 or 80 holdings to reduce risk
3. Ordinary retail investors can hold small handfuls of stocks efficiently, few enough so they can pay attention to each one
One chart in the report 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.
The Role of Good Luck, Bad Luck
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.
Another 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.
