Combining the Active Management Value Ratio 2.0™ and the Active Expense Ratio – A More Meaningful Evaluation of Fiduciary Prudence

“The two variables that do the best job in predicting [a mutual fund’s] performance are expense ratios and turnover.”- Burton Malkiel, “A Random Walk Down Wall Street”

Registered investment advisers and their representatives are fiduciaries. The courts have consistently held that a fiduciary’s duties are “the highest standard of care at law or equity,” requiring that the adviser’s advice be truly disinterested. As legendary Justice Benjamin Cardoza stated, a fiduciary must act not simply with “honesty alone, but the punctillo of an honor the most sensitive….”

Fiduciary law is based primarily on common law trust and agency principles. While there are some differences between fiduciary duties under common law and ERISA, the duties are similar in many ways, especially the focus on cost control and risk management through effective diversification. This post will focus on cost control/efficiency, while the next post will focus on a fiduciary’s duties regarding effective risk management.

A fiduciary has a duty to control costs and avoid unnecessary expenses. As most fiduciaries are well aware, the issue of excessive fees has been, and continues to be, the subject of numerous multi-million dollar ERISA lawsuits and settlements.

InvestSense, LLC introduced its own metric, the Active Management Value Ratio 2.0™ (AMVR), which provides a means for evaluating the cost efficiency of actively managed mutual funds. The AMVR is a simple cost/benefit analysis that compares an actively managed fund’s incremental cost to its incremental return. More information about the AMVR and the calculation methodology, can be found in the white paper, “Management Value Ratio 2.0™ on this site and here.

The AMVR uses an actively managed fund’s stated annual expense ratio in calculating the fund’s incremental costs. However, given the fact that more funds are closement ely tracking their relevant benchmark, the actual contribution attributable to active management is reduced. Therefore, a fund’s stated annual expense ratio can understate the effective/implied cost of the active component of a mutual fund, and thus the overall effective cost of an actively managed fund.

The Active Expense Ratio (AER), a metric created by Professor Ross Miller of the University of New York, addresses this very issue. Like the AMVR, the AER is relatively simple to calculate, requiring very little information, all of which is freely available online at sites such as and

The first step in calculating an actively managed fund’s AER is to calculate the “active weight” (AWt) of the fund. The calculation simply requires the fund’s R-squared rating. Morningstar defines R-squared as the “measurement of the relationship between a portfolio and its benchmark….An R-squared of 100 indicates that all movements of a portfolio can be explained by movements in the benchmark….Conversely, a low R-squared indicates that very few of the portfolio’s movements can be explained by movements in its benchmark index.”

Using a fund’s R-squared rating, a fund’s AWt is calculated by using the equation

AWt = SQRT(1-R-squared)/[SQRT(R-squared) + SQRT(1-R-squared)]

AER is simply a fund’s incremental costs divided by the fund’s AWt (IC/AWt). The fund’s incremental costs are calculated as part of the AMVR calculation, making the calculation of AER that much easier.

The majority of domestic equity-based mutual funds currently have R-squared ratings above 90, with many domestic large-cap funds having an R-squared rating above 95. InvestSense uses 90 as the minimum R-squared rating for classification as a “closet index” fund. So using that number as a fund’s R-squared rating, 1.00 as the fund’s stated expense ratio, and 0.72 as the fund’s incremental costs, the resulting AER would be

AWt = SQRT(0.10)/(SQRT(0.10) + SQRT(0.90) = 0.3162/0.3162 + 0.9486 = 0.2499

AER = Fund’s stated expense ratio + (Fund’s incremental cost/AWt) = 1.00 + (0.72/ 0.2490) = 3.88

So, the actively managed fund’s effective annual expense ratio would be 3.88, or almost 300% higher that its stated annual expense ratio. The significant difference in expense ratios makes it extremely hard to successfully argue that the actively managed fund is cost efficient and a prudent choice, especially once the fund’s AMVR score is re-calculated using the fund’s AER. Bottom line, the higher a fund’s R-squared rating and/or the higher the fund’s incremental costs, the higher the fund’s AER and resulting effective expense ratio, and thus the less prudent the fund becomes.

A recent study by noted finance professors Eugene Fama, a Nobel laureate, and Kenneth French found that only the top 3 percent of active fund managers provided returns in excess of their fund’s costs. That number will likely be further reduced when a fund’s AER rating is incorporated into the calculation of the fund’s AMVR score.

Given the recent trend of a high correlation of returns between U.S. domestic equity funds and a resulting higher percentage of “closet index” funds, calculating a fund’s AMVR using its AER rating is both valuable and justifiable, as it provides a better perspective of the fiduciary prudence of a fund. Fiduciaries that recommend actively managed mutual funds that fail to provide investors with a commensurate return for the higher costs associated with actively managed funds face the risk of a breach of fiduciary claim.

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