4Q 2022 AMVR “Cheat Sheets”: Correlation of Returns, “Closet Indexing,” and Fiduciary Liability

James W. Watkins, III, J.D., CFP Board EmeritusTM, AWMATM

First, note the new URL address. After years of having to explain the old “iainsight.wordpress.com” URL, we finally worked with WordPress to accomplish the re-branding. Kudos to WordPress for working with us and for their patience in helping us to accomplish the “fiduciaryinvestsense.com” re-branding and increase the InvestSense franchise.

Now, as for the “cheat sheets,” no real surprises here, as the six non-index-based funds in “Pensions & Investments” annual survey of the top mutual funds in U.S. defined contribution plans, based on total investment by plan participants, remain the same.

Just a reminder, InvestSense provides information based on the funds’ nominal numbers, or public reported performance numbers. These are the numbers see in the public ads and reports.

InvestSense uses the risk-adjusted returns (RAR) and correlation-adjusted costs numbers (CAC), as those numbers provide a more accurate picture of performance and costs. We advise plan sponsors, trustees and other investment fiduciaries, as well as attrorneys, to do the same for that reason as well.

None of the six funds qualified for an AMVR rating using either the nominal or adjusted numbers, as none were able to produce a scenario where the active fund’s incremental costs exceeded its incremental returns. Only two were even able to outperform a comparable Vanguard index fund.

Same story when analyzing the 10-year numbers. None of the six funds qualified for an AMVR rating using either the nominal or adjusted numbers, as none were able to produce a scenario where the active fund’s incremental costs exceeded its incremental returns. Only three were even able to outperform a comparable Vanguard index fund.

However, both charts provide a potentially significant lesson in connection with fiduciary risk management. Note the significant increase in effective incremental costs (AER column) for both Fidelity Contrafund and T. Rowe Price Blue Chip Growth when correlation of returns is factored in. Actively managed funds with a combination of high nominal incremental costs and a high r-squared. correlation of returns, number can expect to see similar high CACs and a failure to qualify as prudent investment options under AMVR standards.

Active Expense Ratio and Closet Indexing
I recently posted an article addressing the issue of closet and the poor response of the United States in general general in addressing the issue when compared to the response of other countries in recognizing and addressing both the issue and its negative impact on investors.

The AMVR uses Miller’s Active Expense Ratio (AER) to help expose potential cases of closet-indexing and evaluate the negative impact on 401(k) and 403(b) plan participants. People often ask me why we even calculate AER. Miller explained the value of the AER as follows

Mutual funds appear to provide investment services for relatively low fees because they bundle passive and active funds management together in a way that understates the true cost of active management. In particular, funds engaging in ‘closet’ or ‘shadow’ indexing charge their investors for active management while providing them with little more than an indexed investment. Even the average mutual fund, which ostensibly provides only active management, will have over 90% of the variance in its returns explained by its benchmark index.1

The AER supports Miller’s claim that the performance of most actively managed funds is overwhelmingly attributable to the it’s benchmark rather than the fund’s active management team. Part of the AER’s methodology requires that the user calculate the Active Weight (AW) of the mutual fund, the percentage of actual management provided by the active fund.

To calculate an actively managed fund’s AW only requires two pieces of data, the active fund’s correlation of returns to the comparable index fund and the fund’s incremental returns. For example, Contrafunds incremental cost is 69 basis point. (basis points is a term commonly used in the financial world. You do not need to understand it in calculating AW or AER.)

Contrafund’s r-squared, or correlation of returns0 number is 98 out of a possible 100. AW is then calculated as follows:

AW = SQRT(1 minus R-squared)/[(SQRT(R-squared) + (SQRT(1 minus R-squared.)]

Using our data, Contrafund’s AW is .1250, or an active weight of only 12.50%. Wonder how investors would react if they are only getting 12.50% of actual active management while actually underperforming the less expensive index funds and paying a fee approximately thirteen times higher for the privilege of receiving such underperformance.

To calculate an actively managed fund’s AER, simply divide the fund’s incremental costs by the fund’s AER. Here, Contrafund’s AER would equal 5.52 (0.69/.1250). Such a significant difference in the fund’s implicit expense ratio drastically reduces the fund’s relative cost-efficiency.

A high r-squared number is often a sign of a possible closet index fund. So why is so much international discussion and concern over closet-indexing? Martijn Cremers, co-creator of the Active Share metric, explains the reason for such concern.

[A] large number of funds that purport to offer active management and charge fees accordingly, in fact persistently hold portfolios that substantially overlap with market indices….Investors in a closet index fund are harmed by paying fees for active management that they do not receive or receive only partially….2

So should U.S. investors be concerned about possible closet-indexers? Most U.S. domestic equity-based funds are reporting r-squared of 90 or above, with many of the best-known funds reporting r-squared number of 95 and above. Both the 5 and 10-year cheat sheets demonstrate that trend.

The AMVR and Fiduciary Prudence: A One-Act Pla
I love working with my fiduciary risk management clients. During an initial meeting with a perspective client, I make my presentation using the famous InvestSense Fiduciary Liability Circle and several AMVR forensic analysis charts.

I often use an AMVR slide analyzing Fidelity Contrafund K shares since they are a common investment option within 401(k) and 403(b) plans.

I ask three simple questions:

1. Did the actively managed fund provide a positive incremental return, i.e., outperform the benchmark?
2. If so, did the actively managed fund’s incremental return exceed the fund’s incremental costs?
3. In accordance with the Restatement of Trusts’ Prudent Investor Rule (PIR), did the actively managed fund provide the highest level of return for the lowest level of costs and risks or, in the alternative, the lowest level of risk and costs for a given level of return?

If the answer to any of the three questions is “no,” then the actively managed is imprudent relative to the benchmark under the PIR standards. A quick check of the answers using the fund’s AER will often suggest that the fund may qualify as a imprudent closet-index fund.

At some point, the results of the three-question test usually results in something similar to the following scenario:

CEO: So, we are paying annual costs that are 8-10 times higher than the comparable index fund and essentially getting no commensurate return for the extra costs and risks of the actively managed fund? Why are we invested in this fund?
Investment Committee Member: Because our plan adviser recommended the fund.
CEO: Then why are we paying the plan adviser for such poor advice?
Investment Committee Member: They were highly recommended.
CEO: Just how much are we paying the plan adviser?
Investment Committee Member: $$$$$$$$$$$$$$$$$
CEO: Mr. Watkins, can we sue them?
Me: Yes and no. You agreed to a fiduciary disclaimer clause in the advisory contract, so they arguably have no fiducairy duty to you, the plan, or the plan participants. That said, the Supreme Court has ruled that you may be able to sue them based on common law grounds such as negligence, breach of contract and fraud.

At that point, the CEO asks how much potentially liability exposure they have and what their options are to address/”fix” the situation.

The SEC, Finra and the DOL have essentially buried their heads in the sand and have avoided discussing both the topic of closet-indexing and its harmful effects on plan participants. While there may not be any universally accepted standards for categorizing a fund as a closet-index fund, the quantitative analysis provided by an AMVR analysis can provide numbers reflecting the damage being inflicted on both plan participants and investors in general.


1. Ross Miller, “Evaluating the True Cost of Active Management by Mutual Funds,” Journal of Investment Management, Vol. 5, No. 1, 29-4.
2. Martijn Cremers and Quinn Curtis, Do Mutual Fund Investors Get What they Pay For?:The Legal Consequences of Closet Index Funds, https://papers.ssrn.com/sol/papers.cfm?abstract_id=2695133 (Cremers), 5, 42.

Copyright InvestSense, LLC 2023. All rights reserved.

This article is for informational purposes only, and is neither designed nor intended to provide legal, investment, or other professional advice since such advice always requires consideration of individual circumstances.  If legal, investment, or other professional assistance is needed, the services of an attorney or other professional advisor should be sought

About jwatkins

I am a securities and ERISA attorney. I am a CFP Board Emeritus™ and an Accredited Wealth Management Advisor™. I am a 1977 graduate of Georgia State University and a 1981 graduate of the University of Notre Dame Law School. I am the author of "CommonSense InvestSense: The Power of the Informed Investor" and " The 401(k)/403(b) Investment Manual: What Plan Sponsors and Plan Participants REALLY Need To Know. " As a former compliance director, I have extensive experience in evaluating the legal prudence of various types of investments, including mutual funds and annuities. My goal is to combine my legal and compliance experience in order to help educate investors and investment fiduciaries on sound, proven investment strategies that will help them protect their financial security and/or avoid unnecessary fiduciary liability exposure.
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