Seeking Alpha

How Many Stocks Make Up A Well-Diversified Portfolio?

Includes: SPY
by: David Krejca

At some point, every investor must have asked what is the ideal number of securities in a portfolio.

Pioneering work on this topic by Evans and Archer (1968) shows that portfolio sizes beyond 10 stocks do not make much sense.

Even though some later studies proved the opposite, consensual answer to this decades-old question seems to be in accordance with the tenets of focus investing.

It has not been a long time since I submitted my dissertation on constructing and maintaining an optimal investment portfolio. As a part of the thesis, I revisited one of the most frequently asked questions regarding portfolio diversification and I tried to identify if there is any consensus on the optimal number of securities one should have in a portfolio.

First, it is absolutely essential to differentiate between two types of risk - systematic and non-systematic - which together form total portfolio risk, commonly measured by standard deviation of portfolio returns. Systematic risk, also known as market risk, is the uncertainty inherent to the entire economy stemming from events such as sudden changes in inflation rates, interest rates hikes or geopolitical conflicts. In contrast, non-systematic risk, also known as idiosyncratic risk, has its sources in firm and industry specific events.

Already in the early 1950s, Harry Markowitz presented an ingenious theoretical framework for portfolio risk reduction, which is still frequently used today. Markowitz (1952) demonstrated that it is possible to completely eliminate the non-systematic component of total portfolio risk through diversification across various assets with returns that do not co-vary with each other.

More than a decade later, Evans and Archer (1968) attempted to quantify this finding by performing two different statistical tests on the data of 470 securities listed in the S&P500 index (NYSEARCA:SPY) index from January 1958 to July 1967. The results of their analysis revealed that much of the non-systematic portfolio risk is taken away by the time 8th security is added to the portfolio. The paper also suggests that portfolio sizes beyond 10 securities might be hard to justify from an economic point of view as more resources are needed to analyze additional securities.

However, this conclusion is in sharp contrast with the practice of investment management industry, especially mutual funds. Sapp and Yan (2008) showed that the average mutual fund owns a portfolio of 91 stocks and that the top quintile of most diversified mutual funds holds on average 229 stocks. Surprisingly, there are few studies backing these numbers. For instance, Domian et al. (2007) remarked that one needs 100 securities or more with regard to portfolio shortfall risk in the long run. Another example can be Kryzanowski and Singh (2010) who essentially validated the thesis that portfolio sizes of over 100 stocks are required if one wants to achieve 90% of potential diversification benefits and meet a market rate as a target return.

Apart from different datasets, most of the studies also used different types of risk measures, which might be another reason for considerably disparate conclusions. Beginning with Evans and Archer (1968), standard deviation has become presumably the most popular measure and has been used in numerous writings such as Bird and Tippett (1986), Brands and Gallagher (2005) and Benjelloun (2010). Several other measures include variance; Johnson and Shannon (1974), Elton and Gruber (1977), Beck et al. (1996), mean absolute deviation; Fisher and Lorie (1970), Fielitz (1974), and terminal wealth standard deviation; O'Neal (1997) Brands and Gallagher (2005), Benjelloun (2010).

Ultimately, one of the latest works on the topic, by Alexeev and Tapon (2013), provides a comprehensive evaluation of the question based on daily data from five developed markets between the years 1975 and 2011. Unlike others, Aleexev and Tapon used extreme risk measures to account for black swan events as well and estimated confidence bands around central tendencies. According to their closing remarks, the ideal number of portfolio holdings to achieve most diversification benefits 90 percent of the time is somewhere between 38 to 49 depending on the country.

Indeed, consensual answer to the question seems to be in accordance with the tenets of focus investing. With respect to all the studies I have looked through, I would say that the ideal number of stocks to hold in a portfolio lies in the range of 20 to 40 depending on the circumstances. As legendary investor Peter Lynch pointed out, investors should be aware of negative consequences when their portfolios consist of too many stocks. After all, there is no point in constructing a portfolio with large quantities of holdings as one can simply buy an ETF that closely mimics the selected strategy benchmark.

Note: Feel free to check my Twitter, I'll try to share my dissertation on constructing and maintaining an optimal investment portfolio later this year. Your comments and feedback are welcomed and very much appreciated!

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.