An overwhelming body of evidence demonstrates that the majority of investors who engage in the active management of stock and bond portfolios underperform with great persistence. This evidence led Charles Ellis to call active management the “loser’s game” — while it’s possible to win, the odds of it are so poor that it isn’t prudent to try.

What’s more, the evidence even applies to endowments and investors in tax-advantaged accounts, such as IRAs and 401(k) plans, who don’t pay taxes. However, the already-poor odds of winning become dramatically worse for taxable investors.

After-tax returns are the only returns that matter for taxable accounts because dividend and realized capital gains distributions are subject to state, local, and federal taxation. Yet most individual investors remain focused on pre-tax results. One explanation for this behavior is that investors are unaware of just how devastating an impact taxes can have on returns. Another may be that they are subject to “mental accounting”: returns they earn go into one pocket, but come April 15, when their accountant hands them the tax bill based on IRS Form 1099 distributions, they pay it from a different pocket and never tie the two together.

In their quest for alpha, the greater turnover of actively managed mutual funds makes them tax inefficient relative to passively managed funds. The literature provides us with a large body of evidence demonstrating that taxes are often the largest expense taxable investors will face — greater than management fees or fund trading costs. In other words, the quest for pre-tax alpha can generate negative after-tax alpha.

Morningstar’s Jeffrey Ptak adds to the research on the effect of taxes through his recent study comparing the after-tax returns of domestic actively managed mutual funds with after-tax returns of comparable Vanguard index funds.

The study, which included more than 4,500 funds, covered the ten-year period ending October 2015. The methodology Morningstar uses for determining the after-tax returns follows SEC guidelines, which are based on the following assumptions: the investor sells the holding at the end of the time period and pays capital gains taxes on any appreciation in price; distributions are taxed at the highest prevailing federal tax-rate and then reinvested; state and local taxes are excluded; only the capital gains are adjusted for tax-exempt funds, because the income from these funds is nontaxable; and the total return is adjusted for the effects of sales loads. A summary of the results can be found in the table below.

The success rate calculations in the table don’t contain any survivorship bias ‒ the study assumed any funds which started the period but did not finish the period was a failure ‒ but the average returns are survivorship biased, since there was no ten-year post-tax return to average for the obsolete funds. Thus, the average returns as well as the returns of the losers are likely overstated (worse than shown).

Note that in not a single case were even 11% of actively managed funds able to outperform their Vanguard index fund benchmark on an after-tax basis. And what’s more, the average underperformance ranged from -0.67% to -1.45% (because of survivorship bias, the true level of underperformance is even worse). Observe that in each case only a small minority of active funds outperformed, and that the margin of outperformance earned by these very few winners was much smaller than the margin of underperformance posted by the much larger number of losers. In other words, the odds of outperforming were not only poor, but the times when funds did outperform, the margin of outperformance tended to be small (from 0.56% to 0.95%). When a fund lost, the margin of underperformance was much greater (from -1.16% to as much as -1.71%).

Using the large blend category as an example, we can calculate the risk-adjusted odds of outperformance. With the 95.2% of active funds that underperformed managing to do so by an average of -1.17%, and with the 4.8% of active funds that outperformed doing so by an average of 0.76%, the risk-adjusted odds of outperformance were 31:1.

The risk-adjusted odds of outperformance for the other categories are: large growth‒18:1; large value‒13:1; mid blend‒61:1; small blend‒46:1; small growth‒23:1; and small value‒13:1. The average risk-adjusted odds of outperformance when equally weighting all seven categories were 29:1. Again, keep in mind that because of survivorship bias, the risk-adjusted odds of outperformance are actually worse than these already abysmal figures suggest.

As you consider this data, it’s important to understand that because of the two major bear markets we experienced in the first decade of this century, the impact of taxes on returns over the period that Ptak examined is likely to have been less than the long-term experience. As a result, it’s important to look at data from prior periods; with this in mind, we’ll now look at that research.

In their 1993 study, Is Your Alpha Big Enough to Cover its Taxes, Robert Jeffrey and Robert Arnott found that, during the ten-year period they studied, 21% of actively managed funds beat passive alternatives on a pre-tax basis, while just 7% did so on an after-tax basis. They concluded: “The preponderance of evidence is so convincing we conclude that the typical approach of managing taxable portfolios as if they were tax-exempt is inherently irresponsible, even though doing so is the industry standard.”

Robert Arnott, Andrew Berkin and Jia Ye, authors of the study “How Well Have Taxable Investors Been Served in the 1980s and 1990s?,” investigated the pre- and after-tax efficiency of actively managed funds, the likelihood of pre- and after-tax outperformance, and the relative size of outperformance versus the relative size of underperformance. The following is a summary of their findings:

• The average fund underperformed its benchmark by 1.75% per year before taxes and by 2.58% on an after-tax basis.

• Just 22% of funds managed to beat their benchmark on a pre-tax basis. The average outperformance was 1.4%; the average underperformance was 2.6%. However, on an after-tax basis, only 14% of funds outperformed. The average after-tax outperformance was 1.3%, while the average after-tax underperformance was 3.2%. The risk-adjusted odds against outperformance were about 17:1.

This story is actually worse than it appears, because the data above contains survivorship bias: 33 funds disappeared during the time frame covered by the study. Also, because the study only covered funds with more than $100 million in assets, it is likely that the survivorship bias is understated. Funds with successful track records tend to attract assets, while funds with poor records tend to lose assets or are “put to death,” never reaching the $100 million threshold used in the study.

Arnott and Berkin, along with Paul Bouchey, updated this study in 2011. They concluded that the typical approach for managing taxable portfolios, acting as if taxes cannot be reduced or deferred, remains the industry standard. Yet they estimated that the typical active fund needs to generate a pre-tax alpha of more than 2% per year to offset the tax drag from their active strategies — and most cannot accomplish that feat. The finding of a tax drag in excess of 2% is consistent with the findings from other studies.

In our book, “The Incredible Shrinking Alpha,” my co-author, the aforementioned Andrew Berkin, and I present the evidence demonstrating that over time it’s become persistently more difficult to generate pre-tax alpha. Ptak’s findings are consistent with the evidence that we presented, since they show an even smaller percentage of active funds are generating after-tax alpha than had been found in prior studies. In other words, while active management has been a loser’s game for decades, the odds of winning are persistently falling because the competition is becoming ever more skillful as the losers (the less skillful) abandon the game.

In fact, the evidence is so overwhelming that Ted Aronson of AJO, an institutional fund manager with roughly $26 billion in assets under management, offered this advice: “Once you introduce taxes, active management probably has an insurmountable hurdle.”

Given the evidence, it’s not surprising that most mutual fund managers focus on pre-tax returns. However, ignoring the impact of taxes on the returns of taxable accounts is one of the biggest mistakes you can make. You can avoid this error if you keep the following points in mind:

• Because of the important impact on returns, passively managed funds that are also tax-managed should generally be the preferred investment vehicles for taxable accounts.

• Exchange-traded funds are also appropriate vehicles to consider because their structure generally enables them to be highly tax efficient.

• If you do choose to use actively managed funds, they are best held in a tax-deferred account, where their tax inefficiency won’t impact after-tax returns. Of course, in the vast majority of cases, you’re better off avoiding their use altogether.