It’s well known that the majority of actively managed mutual funds underperform comparable index funds over any period longer than a few years. In fact, that statement has become so uncontroversial that even mutual fund salespeople freely acknowledge it. But a recent white paper co-authored by Rick Ferri, A Case for Index Fund Portfolios, takes this idea a step further.

Academic studies of mutual funds go back to the 1960s, and the well-known SPIVA scorecards are updated twice a year. So there’s no shortage of data on individual funds. But investors don’t use mutual funds in isolation: they build portfolios of funds in several asset classes. And there has been surprisingly little research on the performance of actively managed portfolios compared with passive alternatives.

Ferri introduced this idea in The Power of Passive Investing in 2011, and I wrote about his findings when that book came out. Now Ferri and his co-author Alex C. Benke have improved the analysis using more robust data. “The probability of outperformance using the simplest index fund portfolio started in the 80th percentile and increased over time,” the authors write in their summary. “A broader portfolio holding multiple low-cost index funds nudged this number close to the 90th percentile.”

That finding is compelling, but it’s not particularly surprising if you’ve read the previous studies on individual funds. But Ferri and Benke’s research turn up some more surprising results that would only have become apparent when you looked at the data on a portfolio level. In the authors’ words: “An all-index fund portfolio performed better than the sum of its parts.”

The methodology

First, some background on the study. The authors compared index-fund and actively managed portfolios using six scenarios. The first simply looked at three-fund portfolios (40% US equity, 20% international equity, 40% bonds) from 1997 through 2012. Other scenarios used more complex portfolios or different time periods.

In all cases, the researchers started with a portfolio of Vanguard mutual funds or iShares ETFs. Then they compared this benchmark with 5,000 randomly generated portfolios of active funds drawn from the CRSP Survivor-Bias-Free US Mutual Fund Database.

The comparison starts in 1997 because that was the first year the three core index funds were available from Vanguard. Incidentally, for US equities the authors used the mutual fund equivalent of the Vanguard Total Stock Market (VTI), while for international equities they used the mutual fund equivalent of the Vanguard Total International Stock (VXUS), both of which are core holdings in my Complete Couch Potato.

The synergy of portfolios

In the simplest scenario, the three Vanguard funds outperformed 82.9% of the actively managed portfolios over the full 16 years. The median underperformance of the losing portfolios was –1.25%, while the median outperformance of the winners was 0.52%.

That means an actively managed portfolio had only about a one in six chance of outperforming the index funds, and among those lucky few winners, only half were rewarded with an excess return of more than half a point. That’s ugly enough, but it gets more interesting.

The authors broke down these results by measuring the probability that each individual component of the portfolio would outperform its peers in that asset class. Then they weighted those probabilities based on the 40%/20%/40% allocation of the portfolio. Here’s what they found:

Median Median
Fund or Portfolio % Win Shortfall Outperformance
US equities 77.1% -2.01% 0.97%
International equities 62.5% -1.75% 1.34%
US bonds 91.5% -0.99% 0.23%
Weighted 40%/20%/40% 79.9% -1.56% 0.74%
Actual results 82.9% -1.25% 0.52%

Let’s unpack these numbers. If you take the weighted average of the probabilities that each individual asset class would outperform, you would expect index funds to win 79.9% of the time. But in the 5,000 simulations, the index outperformance was actually three percentage points higher—a statistically significant amount. Likewise, a simple weighted average would lead you to expect the winners to outperform by 0.74%. But the median outperformance was significantly lower.

This finding is what Ferri and Benke call a Passive Portfolio Multiplier. “The first PPM we found was that index funds, when combined together in a portfolio, have a higher probability of outperforming actively managed funds than they do individually,” they write.

Later in the week I’ll take a look at the other Passive Portfolio Multipliers in the white paper. They’re even more surprising.