“The Incredible Shrinking Man,” starring Grant Williams, is a 1957 classic American black-and-white science fiction film. As the film’s plot progresses, Williams’ character continues to physically shrink. I think the film is the perfect analogy for what’s happening to the ability of active mutual fund managers to generate alpha today.

Charles Ellis published his wonderful book, “Winning the Loser’s Game,” in 1998. At that time, Ellis provided the evidence demonstrating that, while it is possible to win the game of active management, the odds of doing so are so poor that it isn’t prudent to try. He showed that investors have the greatest likelihood of achieving their financial objectives by investing in passively managed funds (such as index funds) that do not engage in any individual security selection or market timing.

Last year, in “The Incredible Shrinking Alpha,” my co-author, Andrew Berkin, and I presented the evidence demonstrating that, since Ellis wrote his book, there have been four major themes at work which have resulted in a persistent decline in the ability of active mutual fund managers to generate alpha. The four themes are as follows:

• Academic research has been converting what was once alpha into beta (a common factor easily accessed through low-cost, passively managed funds).

• The supply of sheep (victims) available to be sheared (exploited) by active mutual fund managers has been persistently shrinking as the percentage of the total market owned directly by individuals (the sheep) has fallen dramatically over the past 70 years.

• The skill level of the competition engaged in pursuing alpha has greatly increased.

• The amount of capital chasing this reduced supply of alpha has greatly increased as well.

Now, thanks to a recent study by Jeffrey Ptak, Morningstar’s director of global manager research, we possess further evidence that the likelihood of generating alpha not only has been declining, it’s collapsing. Consider the following.

Robert Arnott, Andrew Berkin and Jia Ye — authors of the study How Well Have Taxable Investors Been Served in the 1980s and 1990s?, published in the Summer 2000 issue of the Journal of Portfolio Management — found that just 22% of funds 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%; the average after-tax underperformance was 3.2%.)

In his new study, presented in the February/March 2016 issue of Morningstar magazine, Ptak set out to determine how many U.S. equity funds went on to beat their relevant index fund benchmark on an after-tax basis over the 10-year period ending October 2015.

Ptak, who assumes that the investor sells at the end of the period, found that out of the 4,993 funds he studied, only 205 beat their benchmark index fund on an after-tax basis. That’s just 4.1%. On a relative basis, 70% fewer funds outperformed on an after-tax basis than Arnott, Berkin and Ye found to be the case in their study, done just 15 years earlier. And what’s more, 10% fewer did so on an absolute basis.

Ptak also found that it didn’t matter which asset class he looked at; only a very small percentage of active funds outperformed on an after-tax basis. Keep this in mind the next time you hear arguments about active management outperforming in supposedly inefficient asset classes (such as small-cap stocks).

Ptak’s study provides powerful new evidence that the ability to generate alpha continues to shrink — while the “emperor” may not yet be completely naked, there are fewer and fewer clothes in his wardrobe.