It is still a widely held belief that 20 to 30 stocks make for sufficient diversification

A sizable body of literature covers the topic of single stock diversification. Unfortunately, many well-known studies approach the problem in an overly simplistic way. The idea that diversification benefits are minimal beyond a portfolio size of 20-30 stocks stems from the methodology pioneered by Evans and Archer (1968).

This approach calculates the average standard deviation of randomly drawn portfolios containing a certain number of stocks. Later publications such as Domian et al. (2007) already pointed out that this approach suffers from severe shortcomings.

Most importantly, it completely ignores returns and the fact that real-world investors only buy one portfolio and not the average of a range of simulated portfolios. Domian et al. (2007) showed that investors could significantly reduce return dispersion between randomly drawn portfolios and expected shortfall compared to a minimum return threshold by adding more than 30 stocks. They suggest that investors need no less than 174 stocks to remove 95% of diversifiable risk with 90% confidence.

In the attached paper, I go beyond this framework by testing the risk and performance of optimized portfolios utilizing the Bloomberg multi-factor risk model. In this context, it uses active risk compared to the market portfolio (in this case, the STOXX 600 Index and the S&P 500 Index) as the primary measure of risk, to minimize.

It shows that concentrated holdings of 20, 30, and even more than 50 stocks can result in substantial performance deviations, even if the market participants try to stay as close to the market as possible. The results are even more extreme when we form portfolios that actively target the value factor.

Furthermore, I find a pronounced negative correlation between the number of stocks and portfolio turnover, implying that investors can meaningfully reduce transaction and active risk at the same time by increasing the number of stocks held.

Factor or risk premia investing is only one possible application of our optimization-based approach. Resource-constrained investors with strong views on a limited number of securities could also use a similar strategy to build around their core picks and thus reduce risk and improve diversification without losing the opportunity to generate alpha through informed single stock picks.

In either case, the still widely held belief that 20 to 30 stocks make for good diversification results from a dangerous misunderstanding.