Deworsification [WONKISH]

If you are not interested in the mathematics of portfolio construction you can safely skip this post. This is a (relatively) plain language summary of a research paper published in The Financial Analysts Journal. It is not investment advice and should not be used as the basis for any investment decision.

One of the issues that I have been interested in for a long time is the issue of overdiversification in investment portfolios. We are conditioned by portfolio theory to accept diversification as a universal good. However, depending on the investor’s objectives diversification can be counterproductive–particular when higher cost investment strategies are involved. This post examines the research paper, “What Free Lunch? The Costs of Over Diversification” by Shawn McKay, Robert Shapiro and Ric Thomas, which offers a rigorous treatment of the issue.


The authors use empirical and simulated data to develop a framework for assessing the optimal number of active managers in an investment allocation. They find that as one adds managers to an investment allocation, the active risk (a.k.a “tracking error”) decreases while investment management expenses remain constant or even increase. This leads to the problem of “overdiversification” or, more colloquially, “deworsification.”

Source: McKay, et al.

The authors propose two measures to analyze the impact of overdiversification:

Fees For Active Risk (FAR) = Fees / Active Risk

Fees For Active Share (FAS) = Fees / Active Share

All else equal, one would like the FAR and FAS ratios to be as low as possible.

Source: McKay, et al.

However, perhaps the most important conclusion the authors reach is that as active risk decreases, the security selection skill needed to deliver outperformance versus a benchmark rises exponentially:

Holding breadth [portfolio size] constant allows us to develop a framework that illustrates the trade-offs between active risk and the information coefficient for various levels of expected return. Each line in Figure 5 is an isometric line, highlighting various combinations that give a fixed level of expected return. The curve at the bottom shows all combinations of active risk and the information coefficient in which the excess return equals 1% when holding breadth constant at 100. The two other lines show the same trade-offs for breadth levels of 60 and 20, respectively.

As expected, the required information coefficient increases as tracking error declines, but it rises exponentially as we approach lower levels of active risk. Allowing for greater breadth shifts the line downward, beneficially, but in all cases, there is a similar convex relationship.

Source: McKay, et al.

Practical Implications

  • The more diversified your allocation, the more difficult the relative performance game gets due to increasing fee drag on decreasing levels of active risk.
  • Investors who are aiming for significant outperformance via active management should concentrate capital with a small number of managers.
  • Investors who desire highly diversified portfolios are thus better off allocating to a passive, factor and enhanced-index funds than dozens of highly active equity managers.
  • Capacity and fiduciary constraints make it extra challenging for capacity constrained investors such as large pension funds to generate substantial alpha at the portfolio level, as it is imprudent for them to run highly concentrated portfolios. For these investors in particular, a core-satellite approach likely makes sense.

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