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“Diversification, that’s for idiots.” – Mark Cuban

“Absolutely no one knows what the stock market is going to do tomorrow, let alone next year. Nor which sector, style, or region will lead and which will lag behind. Given this absolute uncertainty, the most logical strategy is to invest as broadly as possible, and benefit from the compounding dividend yields and long-term earnings growth of U.S. (and global) corporations—the ultimate winner’s game.” – John C. Bogle

These statements, from the Dallas Mavericks owner and the late Vanguard founder, represent what might be extremes in a long-running debate on portfolio diversification. The former has said he keeps his holdings in cash unless he spies an opportunity where he knows “something specific,” while the latter has advocated owning the entire stock market through low-cost index funds.

Even some advocates of diversification have said investors don’t need to hold that many stocks. Take, for example, a report by a George Mason University professor and two students published in 2021 on the CFA Institute’s “Enterprising Investor” site, which said: “For large-cap portfolios, there’s little to be gained by diversifying beyond 15 [stocks] or so. For small-cap portfolios, peak diversification is achieved with around 26 stocks.”

Such a conclusion typically points back to a mathematical model initially proposed by Evans and Archer in 1968, which assesses portfolio volatility relative to the number of stocks owned. Notably, the model convincingly shows most of the portfolio’s volatility reduction is exhausted with a mere few dozen stocks.

However, in a recent study on how many stocks you should own, my colleague Yin Chen and I challenge this conventional wisdom. We don’t dispute the math but question the premise: Is volatility the only risk investors should seek to mitigate?

We think relevant risks include price fluctuation, capital loss, and variability in terminal wealth (wealth at the end of an investment period). Focusing on terminal wealth variability is crucial for long-term investors who rely on stocks for growth.

Revisiting the accepted model, we looked at terminal wealth from the viewpoint of an unlucky investor. After all, diversification is intended to protect against bad luck. We defined the unlucky investor as someone at the 10th percentile of terminal wealth across a large set of randomly selected equal-weight portfolios after a 25-year investment horizon.

Our analysis revealed portfolios holding just a few dozen stocks run the risk of large, long-term shortfalls. For instance, the unlucky investor with 25 stocks had about 30% lower end wealth than the unlucky investor with 250 stocks. Such a haircut might cause one to question whether the potential diversification benefits had in fact been truly exhausted. Even owning 250 stocks didn’t perfectly protect against bad luck in our analysis, with the unlucky investor underperforming the expected terminal wealth of average investor who owned an equal-weight portfolio of 250 randomly selected stocks by a more tolerable 10%. Our results indicate that the marginal diversification benefits beyond 200 names are small.

Our analysis method was empirical. A recent research article by Markku Kurtti provides a new theoretical model, deriving the distribution of terminal wealth outcomes and yielding the same conclusions: “Conventional diversification analysis focuses on annualized standardized deviation of arithmetic returns, but long-term investors eventually care about compound terminal wealth…We find that, in the absence of stock-picking skill, the importance of diversification increases as time horizon increases.”

When it comes to concentration risk, luck compounds and time is the enemy.

Might careful stock selection and sector diversification help? While many articles argue that 20-30 well-chosen, sector-diverse stocks suffice, our findings on sector controls contradict this recommendation. We observe that stocks within sectors tend to demonstrate greater comovement than stocks in different sectors. Our analysis confirms that diversifying a portfolio’s sector exposure does tend to effectively, although modestly, reduce portfolio risk.

Still, stock-specific risk is significant. Concentrated individual stock exposure within the same sector can cause unnecessary performance dispersion, as illustrated by Nvidia‘s 225% vs. Intel’s 33% year-to-date performance (as of mid-July). A 25-stock portfolio that allocated to Intel would have underperformed one that allocated to Nvidia by over 7.5%, and this is over a short investment horizon of barely more than half a year.

These findings underscore the importance of defining what truly matters. If the concern lies in daily portfolio volatility, a few dozen stocks might suffice. However, if long-term outcomes are the focus—as they arguably should be for most investors—then portfolio volatility is an inadequate proxy for shortfall risk. Given the effectiveness of diversification in reducing portfolio volatility, it’s easy for investors to become complacent with what, in essence, is a concentrated portfolio, overlooking the fact that misfortunes can accumulate and compound over time.

Opinions on the optimal number of stocks for diversification vary significantly. While conventional wisdom endorses about two dozen stocks, our analysis recommends a more conservative figure of 200 or more for passive portfolios. In reconciling these opposing views, assess the potential risks: What repercussions might I face if effective diversification truly requires 200-plus stocks and I have only 25?

Most retirement savers are unlikely to have Cuban’s investment acumen and luck. They would likely be best served by sticking to a level of diversification closer to John Bogle.

Roni Israelov is the president and chief investment officer of NDVR, a wealth optimization firm based in Boston, Mass. He is responsible for managing the quantitative research team and overall corporate strategy. Previously, Roni served as principal at AQR Capital Management. He has a Ph.D. in Financial Economics from Carnegie Mellon University.