The paper’s authors, Christopher Philips, Francis Kinniry Jr., Todd Schlanger and Joshua Hirt, begin by observing the importance of understanding that active investing is a zero-sum game. Since all stocks must be held by someone, and passive investors earn the return of the market, then as a group active investors must also earn the return of the market.

Put simply, the sum of the parts must equal the whole. Thus, if one group of active investors outperforms over a particular period, then others must underperform over the same timeframe. Obviously, this holds true whether there’s a bull or bear market, and for all asset classes. And that’s before expenses, such as commissions, management fees, bid-ask spreads, administrative costs, market impact and, for taxable accounts, taxes. Not only is active investing a zero-sum game before expenses, but since active investors incur higher expenses than passive investors, it must be a negative-sum game after expenses. And this must be true whether the market is informationally efficient or inefficient. Of course, that doesn’t mean that all active investors will underperform. And that’s why some investors hold onto the hope of outperformance.

The authors go on to present performance data and show that in almost all cases the active funds they studied underperformed, even before accounting for the well-known problem of survivorship bias. The authors then attempted to control for the impact of this bias. To highlight the importance of this issue, they commence by showing that in the 12-month period prior to a fund closing or being merged out of existence, these dead funds underperformed their benchmark by 2.0 percent a year. In the 18 months prior to their disappearance, they underperformed by a whopping 3.7 percent a year.

Once survivorship bias was accounted for, the percentage of active managers who underperformed increased, in many cases by a large amount. For example, in the case of U.S. large-cap value equity funds, at the 10-year horizon, the adjustment for survivorship bias increased the percentage of underperforming funds from 66 percent to 82 percent. In the 3-year, 5-year, 10-year, and 15-year periods, at no time did a majority of active equity managers outperform in any of the 12 asset classes the authors examined.

Of particular interest is that Vanguard found a significant majority of actively managed funds in so-called inefficient sectors, such as small-cap and emerging market stocks, underperformed their benchmark, particularly when accounting for those funds that were closed. This exposes as myth the belief that actively managed funds have an advantage in market segments perceived as inefficient.

The authors then turned to evaluating the likelihood that investors would be able to identify beforehand the relatively small group of future outperformers. Their findings were consistent with prior research, which has found that while there’s little evidence of persistent outperformance beyond the randomly expected, there’s evidence of persistent underperformance among losing funds (likely due to high expenses).

For example, they discovered that “the percentage of highest-quintile active funds falling to the lowest quintile (28%) exceeded the probability that the funds would remain in the top quintile (12%). Stated another way, of the 5,945 funds available to invest in 2008, only 145 (2%) achieved top-quintile excess returns over both the five years ended 2008 and the five years ended 2013.”

For investors who for some reason are confident in their ability to pick the few future winners, the team at Vanguard noted the results of a 2008 study by Amit Goyal and Sunil Wahal, “The Selection and Termination of Investment Management Firms by Plan Sponsors,” were anything but encouraging. Goyal and Wahal concluded that when the sponsors of institutional pension plans — which typically hire outside consultants to help them perform due diligence — decided to replace their underperforming managers with outperforming managers, the fired managers went on to outperform the managers hired to replace them! Unfortunately, most pension plans ignore their own experience. They continue to act in a way that Einstein equated with insanity; they repeat the same behavior but expect a different outcome. Adding a bit of irony is that even Morningstar’s own study addressing an investor’s ability to identify future winners prospectively found that a fund’s expense ratio (which favors index funds) was a better predictor than their own star ratings.

The authors of the Vanguard study summarized the following benefits of indexing.

• Indexed strategies benchmarked to broad market indexes provide greater control of risk exposure in a portfolio. This avoids the problem of style-drift, which can occur with active managers.
• Index funds typically are more diversified than actively managed funds.
• Index funds typically are more tax-efficient, due to their lower turnover.
• Vanguard concluded with this warning: “Investors should not expect indexed strategies to outperform 100% of actively managed funds in a particular period. However, as a result of the zero-sum game, costs, and the general efficiency of the financial markets, consistent outperformance of any one active manager has been very rare.”

Vanguard could have gone much further. Most investors who choose active management don’t select just one fund in which to invest. Rather, they build diversified portfolios by hiring who they believe are the best managers in each asset class. But the odds that a portfolio of actively managed funds will outperform a portfolio of passively managed funds are much lower than the already low odds of one actively managed fund outperforming over the long term. The higher the number of active managers, the lower the odds of success. This, in fact, was precisely the finding from a 2013 study, “A Case for Index Fund Portfolios,” by Richard Ferri and Alex Benke. Using live data from both index and actively managed funds, they performed 5,000 simulated trials by randomly selecting actively managed funds from each asset class.

The authors first looked at the performance of a three-fund portfolio for the 16-year period from 1997 through 2012. The index fund portfolio they created was allocated 40 percent to Vanguard’s Total Stock Market Index Fund Investor Shares (VTSMX), 20 percent to Vanguard’s Total International Stock Index Fund (VGTSX) and 40 percent to the Vanguard Total Bond Market Index Fund (VBMFX). This portfolio outperformed 83 percent of the simulated active fund portfolios.

Using the Sharpe ratio as their measure, they also examined the risk-adjusted odds of an active portfolio outperforming its benchmark. The odds of success fell from about 17 percent to about 14 percent.

The authors also tested whether using more than one active fund in each asset class improved the odds of an active portfolio’s success. They found that using one active fund provided a 17 percent chance of outperformance while employing two active funds in each asset class reduced the odds of success to just 13 percent. And using three active funds in each asset class reduced the odds to just 10 percent. It’s important to note that the authors only examined pre-tax returns.

They then built a portfolio that consisted of 10 different asset classes. Given the limited availability of index funds for each of the asset classes included, the study only covered the 10-year period from 2003 through 2012. The index portfolio used in the study had 10 percent allocations to each of the following asset classes/funds:

• Large-cap U.S. equity: Vanguard 500 Index Fund (VFINX)
• Mid-cap U.S. equity: Vanguard Mid-Cap Index Fund (VIMSX)
• Small-cap U.S. equity: Vanguard Small-Cap Index Fund (NAESX)
• Real estate (REITs): Vanguard REIT Index Fund (VGSIX)
• Developed international equity: Vanguard Developed Markets Index Fund (VDMIX)
• Emerging markets equity: Vanguard Emerging Markets Stock Index Fund (VEIEX)
• Short-term Treasury bonds: iShares Barclays 1-3 Year Treasury Bond Fund (SHY)
• U.S. investment-grade bonds: Vanguard Total Bond Market Index Fund (VBMFX)
• U.S. inflation-protected securities: iShares Barclays (TIP) (2004-2012), Vanguard Inflation-Protected Securities (VIPSX) (2003 only)
• Tax-exempt bonds: iShares S&P National AMT-Free Muni Bond Fund (MUB) (2008-2012), Vanguard Intermediate-Term Tax-Exempt Fund (VWITX) (2003-2007)

The authors discovered that the index fund portfolio outperformed actively managed portfolios in 90 percent of their simulations.

Because the research demonstrates the main explanation for active management’s failure to generate alpha is due to expenses, the authors of the study performed one other test. They screened out the half of the active funds with the highest expense ratios. For the 16-year period from 1998 through 2012, the odds of success for the active three-fund portfolio did improve from 17 percent to 28 percent. However, that’s still a 72 percent failure rate. And it’s also pre-tax. Similar results occurred for the 10-fund portfolio that covered the 10-year period from 2003 through 2012. The odds of success for the active portfolio rose from 10 percent to 29 percent. But the failure rate was still 71 percent.

The conclusion we can draw from this research is that active management is the triumph of hype, hope and marketing over wisdom and experience. Choosing passively managed funds to implement your investment plan is the winning strategy — the one most likely to allow you to achieve your goals.