More Power in Passive Portfolios

Rick Ferri and Alex Benke recently collaborated on an interesting white paper called A Case for Index Fund Portfolios, which I introduced in my previous post. They compared index portfolios to thousands of randomly generated active portfolios to estimate the probability of outperformance. Passive came out ahead in about 80% to 90% of the trials, which is compelling enough. But there were some surprises, too. Let’s look at a few of them.

Indexing gets better with age

Ferri and Benke’s paper was novel in that it looked at portfolios rather than individual funds. They found that combining index funds led to greater outperformance than you would expect from examining the funds in isolation. In other words, the portfolios were greater than the sum of their parts. The authors called these factors Passive Portfolio Multipliers, or PPMs

One of these PPMs highlights the importance of taking a long-term view. Ferri and Benke looked at the five-year periods ending in 2002, 2007 and 2012. The first of those periods includes the dot-com bubble, while the last includes the worst market crash since the Great Depression. Not surprisingly, index funds did a little worse than might be expected during the bear markets, since active mangers could get defensive and move to cash or overweight bonds. The middle period was a strong bull market, the worst environment for active managers, who find it hard to keep up as the indexes charge ahead. Here’s the winning percentage for the index portfolios in each period:

Period Index % Win
1998–2002 66.1%
2003–2007 85.8%
2008–2012 77.5%
Average of above periods 76.5%
1998–2012 (all 15 years) 83.4%

Now the surprise. The average winning percentage for the three five-year periods is 76.5%, but over all 15 years it was much higher at 83.4%. “We concluded that the longer an index fund portfolio is held, the better its performance becomes relative to an all actively managed portfolio,” Ferri and Benke write.

Too many cooks

Look at the portfolios of many active advisors and you’ll probably be shocked to see how many funds are included. Who needs a total-market index fund when you can have two or three different active funds for each asset class? Advisors often call this “strategy diversification,” but Ferri and Benke’s findings suggest it’s worse than useless: it actually lowers your odds of market-beating performance.

The authors ran three trials using one, two and three active funds for each asset class and compared the success rate to a simple portfolio with one index fund for each category. Here are the results:

Portfolio Index % Win
One active fund per asset class 82.9%
Two active funds per asset class 87.1%
Three active funds per asset class 91.0%

Turns out using more than one manager is more likely to subtract value. “We conclude that while in general diversification of holdings is a good investing practice, diversifying fund managers is not,” write Ferri and Benke.

It’s not just about fees

There was one more surprising result in the white paper. Many people would argue the real problem with active funds is not the strategies per se, but the higher cost of implementing them. Surely low-fee active funds have a greater chance of outperforming index funds?

Ferri and Benke found this to be true, but the advantage was probably less dramatic than you’d guess. They compared portfolios of three, four and 10 index funds to randomly generated active portfolios, but this time they included only the active funds with lower-than-average MERs:

Index  Median Median
Portfolio % Win Shortfall Outperformance
3-fund portfolio (1997-2012) 82.9% -1.25% 0.52%
With below-average MER 71.5% -0.92% 0.53%
4-fund portfolio (2003-2012) 89.5% -1.24% 0.39%
With below-average MER 81.3% -1.00% 0.46%
10-fund portfolio (2003-2012) 90.0% -0.93 0.29%
With below-average MER 71.2% -0.57 0.33%

Even by sticking to cheaper-than-average funds, the best you could hope for was a success rate less than 30%. (And let’s remember fund fees in the US are much lower than in Canada.) “A common belief in the investment community is that low-fee actively managed fund portfolios have a meaningfully higher chance for outperforming an all index fund portfolio. We find no evidence to support this view.”

10 Responses to More Power in Passive Portfolios

  1. Matt Becker August 1, 2013 at 9:16 am #

    It’s amazing to me that people still pursue market-beating strategies, even with all of the evidence showing what a poor decision this is. I mean, you can basically replicate their 3-fund portfolio with a single Vanguard LifeStrategy fund, automate your contributions, never think about it again and rake in top 10-20% performance. You almost have to be crazy not to do that!

  2. Jan August 1, 2013 at 11:08 am #

    I enjoy reading these posts comparing a “couch potato”-like strategy to investing actively. One reason I haven’t yet made the jump is because I haven’t found any explanation for why a certain percentage of assets should be allocated to a certain asset class.
    The paper assumes 40-20-40 US equity – Int equity – US bonds, similar to the 20-20-20-40 of the Global Couch Potato. I know the “-40” is potentially variable depending on risk appetite, but how does one calculate the remaining components (the Complete Couch Potato has a 30-15-15 split)? Or is this split essentially arbitrary and any fixed proportion (within reason) should give similar results?

  3. Michael James August 1, 2013 at 1:57 pm #

    “Not surprisingly, index funds did a little worse than might be expected during the bear markets, since active mangers could get defensive and move to cash or overweight bonds.”

    This implies that portfolio managers are at least somewhat successful at market timing. Is this really true? One reason why active funds underperform by less in bear markets is because they must hold more cash than index funds. Is this not enough to explain the difference between bear and bull markets or do portfolio managers really succeed at market timing?

  4. Chris August 1, 2013 at 2:03 pm #


    Well, it depends what bubble you live in. Within the passive investor bubble, there is no other option. Branch out a bit, however, and you will find all sorts of curious market beating strategies.

    For instance, simply investing in the S&P 500 when it’s over the 200 MA (at the end of each month) has outperformed buy and hold (60-40) for over 100 years:

    This was further verified by another back test where the timing approach beat the 60-40 buy and hold for 170, 5-year periods 100% of the time.

    I know this will not convince any passive investor to actively manage their funds, but in the interest of fairness, I felt it should be mentioned.


  5. SV August 1, 2013 at 2:11 pm #

    Great article, you have convinced me that passive portfolios is the way to go.

    I am not sure how to use this information when it comes to RRSP though. My employer has a selection of funds for RRSP (with Great West Life), but I am pretty sure they are actively managed.

  6. PeterH August 1, 2013 at 5:25 pm #

    My long comment on the previous post described an attempt to understand the underlying reason for the passive portfolio multiplier. After further thought, it turns out there is a simple statistical explanation that applies to the “porfolio” example and to the “age” and “cooks” examples as well.

    Suppose A and B are random variables with the same positive mean (i.e., expected values E(A) = E(B) > 0), and with the variance of A less than the variance of B. Which random variable would you guess has the greater probabilty of being positive? I would pick P(A>0), arguing as follows. For typical “nice” distributions (i.e., unimodal, not heavily skewed, the mean fairly close to the median), the density of A will be more concentrated about its mean, hence putting more weight on positive values (in comparison with B). It is easy to construct counterexamples (e.g., distributions with substantial skewness, mean far from median) but those might be viewed as less typical.

    What are A and B? In the “portfolio” example from the previous post, we have a vector of random variables X = (X_1, X_2, X_3) where the component random variable X_j denotes the performance of a Vanguard fund minus the performance of a randomly sampled, actively managed fund. Let J be a random variable with probabilities P(J=j) representing the weight of fund j in the portfolio. Now define B as the random performance difference for a randomly selected component of the portfolio; i.e.,

    B = X_J

    Let A denote the random performance difference for the portfolio:

    A = sum of X_j P(J=j) over j=1,2,3

    Now those with some background in statistics may notice that A is the conditional expectation of B given the vector X. It then follows from the law of iterated expectations that E(A) = E(B) .

    Furthermore, the variance of the conditional expection of B given anything is always less than or equal to the variance of B, so the variance of A is less than or equal to the variance of B.

    Finally observe (by another application of the law of iterated expecatations) that the probability P(B>0) equals the linear combination of probabilities that component differences are positive:

    P(B >0) = sum of P(X_j > 0) P(J=j) over j=1,2,3

    For the “age” example, the argument is essentially the same. Here j indexes time periods and X_j is a performance difference for the portfolio during period j.

    For the “cooks” example, let X_1, X_2, and X_3 be independent and identically distributed random variables, each representing the difference between the index portfolio and a randomly selected, actively managed portfolio. Define

    C = X_1
    B = (1/2)(X_1 + X_2)
    A = (1/3)(X_1 + X_2 + X_3)

    We then have

    E(A) = E(B) = E(C)
    Var(B) = (1/2) Var(C)
    Var(A) = (1/3) Var(C)

    I am tempted to conclude by saying there is nothing surprising about the results in these examples. However, there are many examples of nonintuitive stochastic phenomena, and perhaps this is one of them. So I will instead conclude with Jack Aubrey’s aphorism about always choosing the lesser of two weevils (or variances).

  7. Chris August 1, 2013 at 6:08 pm #

    “We conclude that while in general diversification of holdings is a good investing practice, diversifying fund managers is not,” write Ferri and Benke.

    There seems to be a small problem with this conclusion. While the chance of beating the index decreases with more funds, presumably the chance of getting blown away by the index does as well. The real risk of choosing a single fund manager isn’t that your fund might trail the index by 0.2%… it’s that your fund might trail by 20%!

  8. Jas August 2, 2013 at 7:49 am #

    I would be curious to know what was the average MER of the “below average MER” portfolios. If the median out performance of index funds compared with below average MER is 029-0.53% , this could only represent the difference in MER between index funds and “low cost” active funds.

  9. Canadian Couch Potato August 4, 2013 at 1:32 pm #

    @Jan: There is no magic formula when it comes to splitting the equity allocation of a portfolio. In general it makes sense to start with the approximate market cap of the countries involved. The US comprises roughly half of the world’s stock markets, so as a US investor it probably makes most sense to hold half US and half internalize stocks. But investors all over the world have a pronounced home bias, so that’s a hard sell. There are also some good reasons to overweight your home country, including investing costs, taxes, and currency risk:

    In the case of the Complete Couch Potato, I would argue the equity split is 20-15-15 (Canada, US, international) and the remaining 10% is real estate, which is a separate asset class. My model portfolio uses Canadian REITs, but you could substitute global REITs if you wanted to, subject to the same caveats explained in the link above (global REITs may carry higher costs, higher taxes and currency risk).

    @Michael: I would agree that an important reason active managers outperform during bear markets is because they hold cash (which of course causes a drag during bull markets). However, during some bear markets there is a significant proportion of active managers who get defensive and protect against the worst losses. The problem, of course, is that they tend to underperform dramatically during the recovery. I wrote about this a while back:

    @Jas: The white paper does not give the median MER of the active funds. However, according to Morningstar’s Global Fund Investor Experience Report (2013), the median MER is 0.63% for fixed income funds and 0.82% for equity funds in the US.


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