There Is No Free Lunch – The Costs of Overdiversification

​By Neil Chapman, JD, CFA
Director, Chief Investment Officer

As investors, we have all heard that diversification – don’t put all your eggs in one basket - is a very important principle of successful investing. In more technical terms, as set forth in Modern Portfolio Theory, diversification reduces the risk of a portfolio. In fact, because diversification can reduce much of the inherent risk of equity ownership, it has often been called the only “free lunch” in investing. We may, however, be well-served to remember the words of economist Milton Friedman, who said, “There’s no such thing as a free lunch.”
 
Diversification of a Stock Portfolio

Much of the research, and discussion, on the concept of diversification relates to a portfolio of stocks. As described in modern portfolio theory, a part of the risk in any asset, such as a company’s stock, is unique to that asset. This risk is called “unsystematic” risk. As more stocks are added to a portfolio, the more diffuse the unique, or unsystematic, risk will be in the portfolio. In other words, unsystematic risk can be reduced by adding more stocks to the portfolio (the free lunch). This assumes a random selection of stocks. Some risk, however, is common to all investments in an asset class, such as the asset class of all common stocks. This risk is called “systematic” risk, or market risk, and cannot be diversified away by adding more stocks to the portfolio.   
 
The unsystematic risk of a portfolio can be reduced as the number of stocks increase. The risk level is reduced until it approaches the level of systematic risk (market risk), beyond which diversification no longer has a significant effect. How many stocks does it take to reduce almost all the unsystematic risk in a portfolio? The chart below shows the results of the seminal work, Modern Portfolio and Investment Analysis by Elton and Gruber, on the topic. 

As shown on the chart, the benefits of diversification taper off after the stock portfolio exceeds about 20 holdings. The red line shows the reduction in risk (standard deviation) until it approaches the dotted line, representing the level of systematic risk that cannot be diversified away.
 
Overdiversification occurs when diversification provides no further significant reduction in risk to the portfolio. In other words, the benefit of diversification has a limit. We must remember that diversifying across a number of stocks can reduce the unique risk of a stock, but it can also reduce the impact of the unique potential return of a stock. The primary danger, or cost, of over-diversifying a portfolio is to receive lower returns on your investment. Imagine a simple scenario: There are 5 stocks with expected returns of 10%, 12%, 14%, 16% and 18%. You could invest in the stock with 18% expected return and have a high return with high risk; or you could invest in all 5 stocks and lower your risk, but also lower your expected (average) return.
 
Diversification of a Multi-asset Class Portfolio
 
Diversification applies not only to the construction of a portfolio of individual stocks, but also to the construction of an overall portfolio, e.g., the total client portfolio, of separate asset classes – large cap growth, small cap value, developed international, etc. The general concept of diversification is the same. We can reduce the overall risk of the portfolio by adding additional asset classes so long as the additional asset classes have a low correlation to the other asset classes in the portfolio.
 
Correlation is the degree to which two variables move together. In this case, the variables are two separate asset classes. Correlation is expressed by a number ranging from +1 (the variables move exactly together), and -1 (the variables move exactly opposite). A correlation of 0 means that the variables move independently. Correlation is very important for the effectiveness of diversification. As an extreme example, the combined risk would be eliminated if two asset classes had a correlation of -1. Generally, in order to properly diversify a portfolio, asset classes with low correlation should be combined in the portfolio.

Correlations are not constant; they change over time. Therefore, the correlation of two asset classes should be looked at over a period of time. As an example, we can look at the correlation between developed international equities and US equities over two rolling periods as seen in the following chart.

​It is evident from the chart that the correlation between US and developed international markets has dramatically increased since the late 1990’s. The correlation between the two is now approximately .90. The two markets move almost exactly together, and therefore the diversification benefit of adding international equities to a portfolio of US equities is limited. Overdiversification can occur when asset classes are added to a portfolio with little or no reduction in risk. In light of the underperformance of international stocks compared to US stocks over the last several years, an argument could be made that there has also been a cost, consisting of lower returns by allocating a significant portion of a portfolio to the asset class. Of course, there are valid reasons to allocate to specific international equities.
 
Diversification Net of Fees
 
Investors, and investment professionals, must always be cognizant of the fees paid to managers/firms to manage the assets in their portfolio. Fees, or expense ratios for funds, are a quantifiable cost of investing. The fees charged by the manager of a large cap mutual fund, for instance, will reduce the investment return (a benefit of investing in the fund) received by an investor in the fund.    
 
The fees charged by a fund can also be thought of as reducing any diversification benefit the fund – or more specifically, the asset class in which the fund belongs - may provide for the portfolio. One study of the effect of fees on diversification benefits was conducted by Jennings and Payne, Journal of Portfolio Management (2016). They noted that a previous study showed that exposure to the US equity market is the key driver of risk for most asset classes and portfolios. This risk associated with the embedded US equity market exposure was defined as “allocation beta.” After accounting for the allocation beta, an excess or residual return remains, which is referred to as the “allocation alpha.” The allocation alphas, or excess returns, are uncorrelated with beta, and can be thought of as reflecting the risk-adjusted diversification benefits of the asset class. The following chart shows the allocation alphas for 45 asset classes, and the effect of the fees charged by managers in the asset classes.

​As shown in the chart, nine asset classes have no allocation alpha, or diversification benefit (allocation alpha below zero). More importantly, several asset classes with positive allocation alphas become negative after fees, and the diversification benefits for most asset classes are substantially reduced by fees. Although the authors do not identify all 45 asset classes, they note that the high fees for diversifying assets such as hedge funds and private equity significantly reduce or eliminate the diversification benefits. Overdiversification can occur by investing in asset classes that provide no diversification benefits and can be costly considering the fees charged by managers.
 
Conclusion
 
As an investor, you will be well-served by reviewing your investment portfolio to make sure it is diversified, but not overdiversified. Many investor portfolios consist of numerous mutual funds, each of which can be invested in 100 or more stocks. The combination of these funds can result in overdiversification, or in very little proper diversification.  In some instances, the combination of these holdings could look like a very expensive index fund rather than a properly diversified portfolio.  Diversification, when properly implemented, is very beneficial to a portfolio. It does, however, come with costs, and can be overdone.  The costs of diversification should not outweigh the benefits. There is no free lunch.