FOMO and the optimal portfolio size

One of the most influential studies on portfolio construction was published by Meir Statman in 1987. He found that with as few as 30 to 40 stocks, one can diversify away practically all idiosyncratic risk. A new study from Erasmus University claims that one needs far more stocks than that, especially in an ESG portfolio.

The key differences between Statman’s study and the new study are that the new study uses global stocks, not just US stocks and that the new study uses a Monte Carlo simulation of randomly selected equity portfolios rather than a theoretical formula based on correlation and standard deviation metrics.

The charts below show the most important results for our discussion, so let’s go through them one by one.

Volatility and returns of equity portfolios by number of stocks

Source: Brogger et al. (2025)

Panel A shows the volatility of the randomly drawn portfolio of global stocks as a function of how many stocks are in the portfolio. The grey area shows the range that 95% of random portfolios fall into. The vital thing to notice here is that volatility declines significantly even if one adds 100 or 250 stocks to the portfolio. Hence, they conclude that one needs way more than 30-40 stocks to diversify away idiosyncratic (i.e. stock-specific) risk and possibly as many as 750 stocks in a global portfolio.

The reason why this happens is that stock returns are highly concentrated in a few winners. In contrast, far more stocks go to zero (and thus have extremely high volatility towards the end of their existence) than theory suggests. Thus, a random selection of stocks in a portfolio needs to have more stocks in it to have a decent chance of owning the multibagger stocks that drive returns and reduce volatility.

Panel C shows the simulation results for returns in a global stock portfolio. Again, you see that one needs to own hundreds of stocks to narrow the range of possible returns to something close to the median because the true outperformers are few and far between.

Panels B and D on the right-hand side repeat the exercise for ESG portfolios, where the probability of picking a stock is given by its ESG score (stocks with a higher ESG score have a higher chance of ending up in the portfolio). Again, you need some 250 to 500 stocks to diversify away idiosyncratic risk but the return distribution converges even slower in Panel D than in the baseline case in Panel C.

Astute readers may remember that I am a big fan of concentrated portfolios for active managers, where portfolio managers focus their portfolio on their high-conviction stock picks. Does this study challenge my preference for concentrated portfolios?

Not really.

The main reason why I am a fan of concentrated portfolios is that it allows investors to identify more easily (and quicker) if a manager has skill or not, because if the manager has skill, performance differences vs. a passive benchmark will be greater. The whole point of picking a skilled manager is that she should be able to select outperforming stocks with a higher probability than a random draw.

But the study discussed here selects stocks with a random draw (or an ESG-score weighted probability, which is a random draw for an ESG investor). Hence, what the study here shows is that if you face an unskilled manager, it requires hundreds of stocks to get a similar result as you would get by buying simply an index tracker fund.

And that is the crucial bit. If you think portfolio managers don’t have skill, you buy index trackers. If you think a portfolio manager has skill, you want her to run a concentrated portfolio to increase the potential outperformance vs. a passive benchmark and get a faster signal if you were wrong, the portfolio manager doesn’t have skill even though you thought she had.