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Investors have beaten the money managers. Their next adversary will be even more difficult: themselves.

It’s impossible to overstate the magnitude of the changes that have swept through the investment industry over the last decade. Until recently, investors looking to grow their money encountered high fees everywhere, from brokerage commissions to fund and advisory fees. The combined tolls routinely amounted to more than 2% of their savings every year and much more in some cases. There were few avenues of escape despite mounting evidence that higher fees lead to lower returns, the industry’s emphatic denials notwithstanding.

After the 2008 financial crisis, however, a wave of investors decided they had enough. Aided by a burgeoning line of low-cost exchange-traded funds and robo-advisors offering online money management for a fraction of the cost of traditional advice, investors fled to cheaper options. They plowed roughly $3.8 trillion into index mutual funds and ETFs from 2010 through October while yanking $250 billion from traditional actively managed mutual funds, according to Morningstar. Investors have also handed an estimated $250 billion to robo-advisors, much of it invested in index funds.

Granted, more money is still managed the expensive way, but the gap is closing. Roughly $1.6 trillion was invested in index mutual funds and ETFs at the end of 2009, compared with $6.2 trillion in actively managed mutual funds. Now those numbers are closer to $8.1 trillion and $11.8 trillion, respectively. And sure, robo-advisors still manage a pittance compared with the money invested elsewhere, but no one doubts that online investing will continue to gather adherents, which is why Wall Street firms are rolling out robo-advisors of their own.

In any event, arguments about the significance of the flows to low-cost options miss the essence of the decade’s revolution, which is that investors now have myriad options to invest cheaply and thereby bolster their savings. And enough of them are focused on cost that financial firms are warring over who can offer the cheapest investments. There are now zero-fee funds and zero commissions, both unthinkable a decade ago. Even the once inviolable 1% asset management fee is on the chopping block.

Still, declaring victory would be premature because there are other — arguably even more stubborn — costs to cut: the ones investors impose on themselves. They sit on cash too long, chase investment fads during booms and panic-sell during busts, to name just a few common cognitive and emotional lapses. But too little attention is paid to those mistakes, and for obvious reasons. It’s easier for investors to blame the financial industry for their sagging portfolios than confront their own poor choices. It’s also easier — and more lucrative — for financial firms to pander to investors’ worst instincts than help subdue them.

How costly are those mistakes? It’s hard to know exactly, which is yet another enabler. It’s far easier to quantify the cost of fees on portfolios than the impact of behavior, which gives investors a convenient excuse to avoid introspection. But there are some reasonable attempts to estimate the so-called behavior gap, or the difference between the return of an investment and how much of that return investors manage to capture.

One of them is Morningstar’s recently released “Mind the Gap” study. The study estimates the behavior gap for U.S. mutual funds and ETFs over 10-year periods ended each year between 2014 and 2018, and the same number of five-year periods for a handful of other countries.

First, the bad news. The average behavior gap in the U.S. was  -0.45% a year across all investment categories, including stock, bond, alternative and asset-allocation funds. That’s roughly the difference between the average expense ratio for traditional actively managed funds and index funds. The behavior gap was only worse in Europe (-0.53%) and Singapore (-1.19%).

The good news is that the details behind the headline numbers offer hints about how investors might close the gap. One clue is that the gap varies drastically depending on investment type. In the U.S., for example, stock and bond investors gave up 0.56% and 0.55%, respectively, while the gap for asset-allocation funds was a positive 0.22%.

Why did investors in allocation funds fare so much better? As the study notes, allocation includes target-date funds held almost exclusively in 401(k)s, where savers tend to invest regularly and pay little attention. That combination of disciplined investing and benign neglect also appears to have contributed to the success of investors in Australia and South Korea, which boast a positive behavior gap of 0.65% and 0.26%, respectively, due in part to broad adoption of systematic investing that keeps savings flowing to markets regularly.

Another clue is that the gap appears to be related to the volatility of the investment. Morningstar sorted stock, bond and allocation funds into quintiles based on standard deviation, a common measure of risk. In the U.S., the behavior gap worsened across all three categories as volatility rose. For the most volatile quintile of stock funds, the gap was a whopping -1.86%. The results were generally similar around the world. The key insight is that just because an investment promises a higher return in exchange for more risk doesn’t mean investors will capture it; when humans are involved, sometimes less risk translates into a higher return.

There are some caveats around all this. One is that investors don’t always control the timing of their investments, so some of the behavior gap may be attributed to luck rather than behavior. Also, more data is needed. The numbers in the U.S. stretch back to 2005, so they include just the one bear market around the 2008 financial crisis. And outside the U.S., the numbers begin in 2010. Given the apparent link between volatility and behavior, the gaps are likely to widen during the next downturn.

The last decade will be known for the low-fee revolution. Let’s hope the next one is equally revolutionary when it comes to changing investors’ behavior.

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