The Limits of Diversification
How do stock pickers decide how many companies to hold in their portfolios? Modern portfolio theory suggests that diversification is one of the only “free lunches” in investment. But is the more really the merrier when it comes to diversifying investments? Or does diversification have its limits?
One reason stock pickers limit their holdings might be purely practical–it’s a lot to keep track of. Researchers have discovered that birds cannot count beyond the number three. To test birds’ ability to count, a hidden observer watched a flock of crows that hid in the treetops as quantities of men entered and left the forest. The observer found that when five men entered the woods and only four exited, the crows would make the mistake of flying to the ground to feed, even though predators were still present.
“Apparently, [the birds’] power of discrimination did not extend beyond three units—their perceptual-mathematical ability consisted of a sequence such as: one-two-three-many,” wrote Ayn Rand in her 1967 Introduction to Objectivist Epistemology. A 2014 scientific study of New Zealand robins found similar limited “proto-arithmetic awareness” of changes in quantity.
While humans have significantly more cognitive horsepower than crows and robins, the point is that there seems to be at least some fundamental limitations on the mind’s ability to track, conceive of and comprehend large quantities of discrete items.
Another reason for limiting portfolio holdings might be mathematical. For active funds with concrete strategies such as factor tilts (e.g., value, growth, momentum), adding incremental stocks to the portfolio can dilute the potency of the strategy through the inclusion of less desirable stocks. To illustrate, below are returns on Japanese equities since 2000 for a particular levered, small value–focused strategy, broken out by portfolio concentration. As the chart below suggests, investors with a winning strategy might “bleed” significant alpha as they continue to diversify beyond roughly 50 names, and they are rewarded with almost no reduction in volatility (standard deviation):
Figure 1: Performance Statistics on Levered Value Strategy for Japanese Equities (2000–2017)
Source: CapitalIQ, Verdad Research
We believe that diversification, like the human mind’s own ability to count, has its limits. Modern portfolio theory generally does not support the notion that diversification beyond ~50 securities reduces risk. The elimination of idiosyncratic risk among typically correlated stocks can be nearly fully accomplished with 50 names. Increasing one’s holdings from 50 to 100 stocks might not significantly change expected portfolio variance, and there might be almost no diversification benefits after that.
Figure 2: Portfolio Variance by Number of Holdings
Source: Elton & Gruber, “Risk Reduction and Portfolio Size: An Analytical Solution,” The Journal of Business, 1977
To drive home the point, we highlight a fascinating recent study from the bright folks at Greenline Partners. They found that the 30 large companies on the Dow Jones Industrial Average outperformed the 500 stocks on the S&P 500 since 1969 with reduced volatility. This is in part because, as diversification theory shows, the benefits of diversification might be drastically reduced past 40 stocks. It is also partially explained by the concentration of large, expensive tech stocks in the market cap–weighted S&P 500. The Dow, by its price-weighted index construction, has a much more random correlation among its securities.
“Finance theory suggests the S&P should earn higher returns with lower volatility,” the study’s authors observe, “because it includes more companies and holds some smaller companies which should earn higher returns. But historically, the Dow has actually earned higher returns with less volatility.” The safety of over 16x more stocks in the S&P 500 can be illusory.
There is significant nuance in determining the “optimal” diversification of a portfolio (e.g., international strategies may require more stocks), and every strategy should be rigorously tested. However, investors who believe they are reducing risk by investing in portfolios of 100+ stocks through mutual funds or ETFs may be engaged in “idiosyncratic overkill” at the cost of bleeding alpha from an otherwise profitable strategy or factor tilt. And yet a quick survey of the 120 US small value mutual funds, screened using Vanguard’s website, today finds a median of 100 and an average of 175 stocks per portfolio. We believe there is a better way to invest.