“Humble Arithmetic,” Prudence, and Successful Investing

Facts do not cease to exist because they are ignored. – Aldous Huxley

In 2005, John Bogle, of Vanguard fame, spoke at the 60th anniversary conference of the Financial Analysts Journal. Mr. Bogle’s presentation, entitled “The Relentless Rules of Humble Arithmetic,” suggested that the argument over the EMH, the efficient market hypothesis, was essentially meaningless and that time would be better spent examining the CMH, the Cost Matters Hypothesis.(1)

In support of the CMH, Bogle referenced a quote from Louis Brandeis, one of America’s great legal jurists. Brandeis, in addressing issues within the investment industry and the rampant investment speculation at that time, commented on the “relentless rules of humble arithmetic.”(2) Bogle noted that “the relentless rules of humble arithmetic” devastate the long-term returns of investors.”(3)

In addressing “the relentless rules of humble arithmetic,” Bogle stated that

No matter how efficient or inefficient markets may be, the returns earned by investors as a group must fall short of the market returns by precisely the amount of the aggregate costs they incur. It is the central fact of investing.(4)

Costs matter, period. Far too many investors see a 1 percent annual fee for a mutual fund and dismiss it as only 1 percent. Throw in an additional 1 percent advisory fee and now the investor is looking at a cumulative fee of 2 percent.  If the investment is a variable annuity, throw in an additional 1-1.5 percent, for a cumulative 3-3.5 cumulative fee.

Some investors will still believe that it is only 3 percent without calculating the actual dollars and costs involved. If we assume no taxes and a tax-deferred account, a starting principal of $50,000, an annual return of 7 percent, and an investment period of twenty years, our end wealth would be approximately $193,484.22. Increasing the fees by 1 percent (reducing the annual return to 6 percent) would reduce the investor’s end wealth to $160,356.77, or a reduction of 17.1 percent.

Add another 1 percent of fees (reducing the annual return to 5 percent) and the investor’s end return is reduced to $132,664.89, or a reduction of 31.4 percent. And finally, add yet another 1 percent of fees (reducing the annual return to 4 percent) and the investor’s end return is reduced to $109,556.16, or a reduction of 43.4 percent.

Costs matter.

Charles Ellis, noted industry leader, has recently suggested that the value of active management should be evaluated based upon the investment’s fees as a percentage of incremental return rather than as fees as a percentage of assets under management.(5) Ellis correctly points out that investors already own the assets in their accounts, so such assets should not be evaluated in terms of an advisor’s services or in computing advisory fees.

Ellis also suggests that evaluating fees based on the incremental return investors receive from an advisor’s services can also prevent misleading representations. As an example, Ellis points out that a stated fee of 1 percent,based on assets under management, can actually be considered as an effective fee of 12.5 percent if the incremental return to the client is only 8 percent, since the real contribution of active management would only be the incremental return.

The investment industry often counters with the argument that the additional fees allow for professional money management and improved returns for investors. And yet, the evidence on historical performance seems to indicate otherwise. Standard and Poor’s publishes various reports comparing the performance of indices and actively managed funds. The reports, known as the SPIVA reports, have consistently shown that the majority of actively managed funds do not outperform their relative indices.

The SPIVA end-year 2012 reports found that

Performance lagged behind the benchmark indices for 63.25% of large-cap funds, 80.45% of mid-cap funds and 66.5% of small cap funds.

The performance figures are equally unfavorable for active funds when viewed over three-and five-year horizons. Managers across all domestic equity categories lagged behind the benchmarks over the three-year horizon. The five-year horizon yielded similar results, with large-cap value emerging as the only category that maintained performance parity relative to its benchmark.(6)

Other studies have produced similar reports of the underperformance of actively managed mutual funds.  One of the most detailed studies ever conducted reported analyzed the twenty year period ending in 1998. The study found that

  • Over the twenty year period, the average actively managed mutual fund underperformed the Vanguard S&P 500 Index Fund by 2.1 percent a year;
  • Over a fifteen year period, the average actively managed mutual fund underperformed the Vanguard S&P 500 Index Fund by 4.2 percent a year; and
  • Over a ten year period, the average actively managed mutual fund underperformed the Vanguard S&P 500 Index Fund by 3.5 percent a year.(7)

Now go back and look at the previous data on the impact of lower returns. Is paying higher fees for less return than a simple index fund prudent?

The same study examined the pre-tax performance of actively managed mutual funds and found that

  • Over the twenty year period, investors had a 14 percent chance of beating the Vanguard S&P 500 Index Fund, with an average margin of outperformance of only 1.9 percent and an average loss of 3.9 percent.
  • Over the fifteen year period, investors had a 5 percent chance of beating the Vanguard S&P 500 Index Fund, with an average margin of outperformance of only 1.1 percent and an average loss of 3.8 percent.
  • Over the ten year period, investors had a 2 percent chance of beating the Vanguard S&P 500 Index Fund, with an average margin of outperformance of only 1.4 percent and an average loss of 2.6 percent.(8)

Do those numbers present evidence of prudent investment choices? I actually have the report’s findings of performance on an after-tax basis. Rather than list more statistics, let’s just say the results do not improve.

Costs matter, whether such costs are in terms of fees or the opportunity costs that result from a fund’s underperformance. One study estimated that between 1996 and 2002, the underperformance of broker-sold actively managed mutual funds cost investors approximately $9 billion dollars a year, with such funds producing an annual return of 2.9 percent over the time period, as compared to an annual return of 6.6 percent for directly purchased index funds.(9) Another study estimated that for the period 1980-2005, actively managed mutual funds produced an annual return of 7.3 percent, compared to an annual return of 12.3 percent for index funds.(10)

The last example of the value of humble arithmetic is my own proprietary metric, the Active Management Value Ratio (AMVR).  Given the evidence that suggests that even when actively managed equity-based mutual funds do outperform similar index funds they only do so by a slim margin, a logical question is whether the actively managed funds are cost efficient for investors.

Rather than go through the entire calculation process again, I will direct readers to my previous posts and white paper on this blog.  Using simple subtraction and division, an investor can evaluate the cost efficiency of an actively managed mutual fund in approximately one minute. And yet, this humble arithmetic process can result in significant savings for investors.

In one analysis, I used the AMVR to evaluate the performance of twenty-three of the most common  actively managed mutual funds used within pension plans. I calculated the AMVR score for the funds for both a 5-year and 10-year period, setting an AMVR score of 1.5 or lower as the acceptable standard for cost efficiency. An AMVR score of 1.5 or less would indicate that the active portion of a fund’s annual fee was less than 50 percent greater than the portion of the fund’s return attributable to active management

The 5-year AMVR analysis resulted in only nine of the funds qualifying for an AMVR score at all, and only four of the twenty-three funds having an AMVR score of 1.5 or less.  The 10-year AMVR analysis resulted in twelve funds qualifying for an AMVR score, and only four of the twenty-three funds achieving an AMVR score of 1.5 or less.

Costs matter with regard to cost efficiency.

Those who promote actively managed mutual funds will offer various arguments against the evidence presented in this post.  I suggest that investors perform the easy calculations required by the AMVR. Perhaps Upton Sinclair summed up the active management opposition best when he noted that “it is difficult to get a man to understand something when his salary depends on his not understanding it.”

So it is easy to understand the motive behind proponents of actively managed funds promoting such funds. However, in light of the evidence presented herein, what is not so easily understood is the fact that according to the 2013 Investment Company Factbook, 82.6 percent of the money invested in equity-based mutual funds was invested in actively managed mutual funds!

Whether this fact is due to salesmanship skills or lack of information, the disparity between investments in index funds and actively managed fund suggests that investors may be suffering millions of unnecessary financial losses annually due to both the high costs usually associated with actively managed funds and the underperformance often shown by actively managed mutual funds. As David Swensen, the highly respected chief investment officer of Yale University, has pointed out

at the end of 2007, index funds accounted for only slightly more than 5 percent of mutual fund assets, leaving almost 95 percent of assets in the hands of wealth-destroying active managers. In a rational world, the percentages would be reversed.(11)

While the disparity has improved to 17.4 percent of investors’ assets invested in index funds, the statistics indicate that investors are still acting irrationally and fiduciaries using actively managed mutual funds may be violating their fiduciary duty of prudence. 

What I have provided in this post is essentially the same prudence/due diligence strategy that I use in litigating or providing expert witness services in ERISA and breach of fiduciary duty cases.  While the nature of such cases often requires extensive use of statistics, the beauty and strength of the strategy is its simplicity and easy verification using “humble arithmetic.” With an increasing number of actively managed mutual funds having high R-squared numbers and, in essence, acting as “closet index” funds, it is becoming more common to see situations where the active component of the fund’s annual expenses greatly exceeds the benefit derived from such active management, in many cases by 300-400 percent, or more.

Winston Churchill once said “men occasionally stumble over the truth, but most of them pick themselves up and hurry of as if nothing ever happened.” Hopefully, this post will help some investors realize the “truths” discussed herein and the need for a closer evaluation of mutual funds in terms of cost and its impact on returns, opportunity cost, and cost efficiency, by using the resources referenced herein. For those who value their financial security, the relatively small time required for such analysis will prove to be time well spent.

© 2013 InvestSense, LLC. All rights reserved.

This article 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.


1. John Bogle speech, “The Relentless Rules of Humble Arithmetic,” available online at https://personal.vanguard.com/bogle_site/sp20060101.htm.
2. Louis D. Brandeis, Other People’s Money, New York:F. A. Stokes (1914).
3. Bogle Speech.
4. Bogle Speech
5. Charles D. Ellis, “Investment Management Fees Are (Much) Higher Than You Think,” Financial Analysts Journal, May/June 2012, Vol. 68, No. 3:4-6
6. http://www.spindices.com/resource-center/thought-leadership/spiva/
7. Robert Arnott, Andrew Berkin and Jia Ye, “How Well Have Taxable Investors Been Served in the 1980s and 1990s?” Journal of Portfolio Management, Summer 2000, Vol 26, No.4.
8. Arnott, Berkin and Ye.
9. John Bogle, The Little Book of Common Sense Investing:The Only Way to Guarantee Your Fair Share of Stock Market Returns,” New York:John Wiley and Sons (2007), 103
10. Bogle, “Common Sense Investing,” 51
11. Charles D. Ellis, Winning the Loser’s Game: Timeless Strategies for Successful Investing, 5th ed., New York:McGraw Hill (2010), xii

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