Putting the Portfolio Odds in Your Favour

July 29, 2013

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.

{ 18 comments… read them below or add one }

Alan M July 29, 2013 at 10:01 am

It would be interested to know whether research like this and other confirmatory pieces alter your Couch Potato Portfolio mixes or ETF suggestions/recommendations in any way, or simply reinforce the current recommendations (which may understandably change over time as some ETF’s track better or cost less).

Canadian Couch Potato July 29, 2013 at 10:15 am

@Alan M: Research like this confirms why trying to outperform the market with actively managed funds is a colossal waste of time. The odds are low, and even if you win, the payout is often trivial. The specific ETF choices used in the study are really not that important. I hope the that’s part of the takeaway message here: just capture market returns and you’re already ahead of 80% to 90% of investors.

Alan M July 29, 2013 at 11:29 am

That information came through clearly in your piece, no worries there. For those of us already living the Couch Potato approach, I was simply curious if this research provides any additional insight into selection/balance of holdings when constructing a couch potato portfolio. Your articles are always informative and I look forward to each one — thanks for the ongoing education!

Canadian Couch Potato July 29, 2013 at 12:01 pm

@Alan: No, the research didn’t really look at that piece of the puzzle. But if you’re interested in the specifics of the more complex portfolios, see page 15 of the white paper, which has a breakdown of the 10-fund portfolio.

madMike July 29, 2013 at 1:00 pm

Another great piece, very informative. this is the type of concise article that I tell people to look at when I explain my investment strategy – trying to get my friends to stop asking how “my RSP has done lately”, i.e. the last 3-4 years.
Sometimes I think people are afraid to read and to think – they’ve been conditioned for so long to believe that “fund managers are experts, they’re educated, they know about financial stuff, this is how they make a living, their fees must be justified”, etc.
Pure numbers-backed, scientific research cannot be refuted rationally.

calvin1 July 29, 2013 at 3:16 pm

I am curious to hear your response to a semi-active/semi-passive strategy called BTSX proposed by Dr. David Stanley which uses the same methodology as Dogs of the Dow. In the latest August Canadian Money Saver, this strategy beats the S&P/TSX 60 index in 20 out of the past 26 years since 1987, by an average of over 32%, with lower volatility. If Canadian Couch Potato can be back-tested to the same past 26 years, what would be its relative performance?
Thank you.

Canadian Couch Potato July 29, 2013 at 4:09 pm

@calvin1: The annualized return of the S&P/TSX Composite Index from 1987 through 2012 was 8.2%. So my first question would be: would that have been adequate to meet your financial goals?

I would put the BTSX strategy in the same category as all of the others that make similar market-beating claims: they might give you good results if you actually executed them perfectly for many years. After all, it is really just a type of value strategy: buy whatever is most beaten down every year. But remember that this strategy requires a discipline that precious few investors possess. My guess is the number of investors who have followed it faithfully and actually achieved those returns is close to zero. It’s also important to note the BTSX strategy involves buying just 10 Canadian stocks. That is wholly inadequate diversification. What do you do with the rest of your portfolio?

taran July 29, 2013 at 5:07 pm

@CCP i have a question, as starting up investor for long term in RESP(14+) if i buy Vanguard Total Stock Market (VTI), is my money protected from default of Vanguard? Is there justification to buy ETF from bmo/ishares.ca (ZSP +XSU) as they are covered by CIPF?

second question should i hold on to diversification for few years as bonds are likely to give negative yields and my time horizon is far in future?

jamie July 29, 2013 at 7:04 pm

Thanks for all this work Dan! I always check out your blog to see what’s up.

Canadian Couch Potato July 29, 2013 at 7:14 pm

@taran: It’s very important to understand the risks of ETFs accurately. When you invest in any ETF in the US or Canada, the assets are held by a third-party custodian, so the fund provider has no claim on your assets. If the fund provider were to become insolvent, they can’t use your investment to pay their debts. So this is really not a concern, especially with a huge well-established firm like Vanguard.

However, this protection has nothing to do with CIPF, which covers brokerages and investment dealers, not fund providers. So selecting Canadian ETFs does not offer any advantage over US-listed ETFs in this respect.

As for how to invest your RESP, I encourage you to keep things very simple. US-listed ETFs are almost certainly the wrong vehicle, because the high cost of trading in US dollars is likely to overwhelm the lower MER in a small account. I usually recommend using no more than two to four index mutual funds in RESP, where the most important driver is by far your contribution amount, not the returns on your investments:

DL July 29, 2013 at 8:13 pm

Dan, a lot of your articles have extolled the virtues of passive index investing. Through your excellent and informative posts, you have persuaded many to diversify and invest using broad market index ETFs. Please keep it up!

One post I do want you to write in the near future is the downside of index investing. There’s always a good and bad to everything. For example, one article I read in the Globe today was not so glowing about the passive approach (http://www.theglobeandmail.com/globe-investor/personal-finance/financial-road-map/can-a-boglehead-approach-to-investing-work/article13484317/).

I hope, with your balanced view of index investing, you can bring forth a strong view of why indexing works.

Andrew July 29, 2013 at 9:20 pm

The ten index fund on page 15 is interesting as it is equal weight but 50% equities, 10% REITs the rest bonds. What is interesting to me is the resulting relatively high allocation to small/mid cap and emerging (30%) for a balanced portfolio. Large cap is just 20% of the portfolio maybe less as I don’t know the constituents of the the international equity index 10% which may contain small/mid. Some adherents to Ray Dalios all weather portfolios equal weight assets that perform best under inflation, deflation, growth and contraction with the result of different weights than in the study.

I like the simplicity of equal weight because it is easy to understand and implement.

Overall though the study is more evidence for a great need in the wealth management business, namely algorithmically driven portfolios with MERs in the sub 0.5% range all in like Betterment.com’s product.

Canadian Couch Potato July 29, 2013 at 11:07 pm

@DL: Thanks for the comment. I will let the rest of the financial industry write about the downside of index investing. That Globe article you linked to is embarrassingly bad: I couldn’t have made active advisors look worse if I tried.

If you’re interested in the evidence for index investing, there are several books on my resources page that can start you off. My own Perfect Portfolio lays out the case, as does Ferri’s The Power of Passive Investing and Swedroe’s The Quest For Alpha.

taran July 29, 2013 at 11:12 pm

@CCP thanks ccp, any other risks to watch out with ETFs, other than asset allocation, MER?

Thanks for RESP link, yes i think splitting into too many funds is going to add transaction cost. i have added 2500 and i am thinking ZSP or VTI. i need to check if i could buy td index funds from CIBC Investers edge.


DL July 29, 2013 at 11:44 pm

Dan: Just to follow up on your blog post and some of your previous postings, many of the statistics you have posted focuses on long-term. It is with good reason, as many investors need to keep a long-term perspective. However, would you suggest the same type of indexing for, say, seniors who have a shorter time frame (e.g., 5 years), and who are just starting to invest in the current markets because they are not satisfied with low bank account/GIC rates?

I ask this because, on a long term perspective, everyone understands that the markets would peak and dip in cycles, but ultimately would rise in the long term. As index investors, we are investing based on the average. Over the long-term, passive investing beats active investing. However, on a shorter term perspective, we have the S&P 500 that is at all time highs, TSX composite that is near its highs, and fixed income that is generating almost a 0% return. Would seniors, with a short horizon and investing in today’s markets, benefit from active management?

PeterH July 30, 2013 at 12:23 am

Interesting post. I would like to add some technical comments. Some notation will be helpful. Let the random variable T denote the performance of the Vanguard portfolio minus that of a randomly sampled portfolio (one of the 5000). Let X, Y, and Z denote the corresponding differences for the components of the portfolio: US equities, international equities, and US bonds. Since all portfolios use the same component weights, we have

T = .4 X + .2 Y + .4 Z

Ferri and Benke compare the probability of outperformance P(T>0) with the linear combination of component probabilities

LCP = .4 P(X>0) + .2 P(Y>0) + .4 P(Z>0) .

They observe that, in their simulation study, the first probability is larger than the second. They refer to this phenomenon as a passive portfolio multiplier (though it is not clear what is being multiplied).

My first reaction was to question the performance criterion. One might argue that the expected value of performance E(T) is more relevant than the probability of outperformance P(T>0) . There is no multiplier effect for the expected value criterion because we have

E(T) = .4 E(X) + .2 E(Y) + .4 E(Z)

for all joint distributions of (X,Y, Z). The multiplier effect is thus related to a specific criterion.

I also questioned whether the multiplier effect might be a fluke, specific to the chosen time period and the Vanguard portfolio. The probabilities P(T>0) and LCP depend on the joint distribution of (X,Y,Z). The performance of the Vanguard funds over the specified period affects only the mean of this distribution. The pattern of variation is determined entirely by variation in performance among the 5000 sampled portfolios. Is there good reason to expect that a multiplier effect will occur over the next 20 years?

To get some insight about what aspects of the joint distribution lead to a multiplier effect, I considered a simple family of models. Suppose (X,Y,Z) has a trivariate normal distribution with the same variance = 1 for all three variables and the same correlation = rho for all pairs of variables. I obtained Monte Carlo estimates of P(T>0) and LCP (based on 50,000 simulated random vectors) for various values of rho and for two mean vectors:

mu1 = (0.74, 0.33, 1.34) and mu2 = (0.84, 0.84, 0.84) .

For mu1 we get essentially the same component probabilities as those in the paper:
P(X>0) = 0.77, P(Y>0) = 0.63, P(Z>0) = 0.91, and LCP = 0.80 .

For mu2 all component probabilities equal LCP = 0.80 .

My results are shown in the following table.

rho P(T>0) P(T>0)
for mu1 for mu2
0.0 0.934 0.921
0.2 0.902 0.888
0.4 0.876 0.861
0.6 0.855 0.839
0.8 0.834 0.818
1.0 0.815 0.800

Note that multiplier effect decreases as rho increases, and is smaller when the component probabilities are equal. The effect disappears (i.e., P(Y>0) = LCP = 0.80) when rho = 1 and the means are equal; i.e., when X = Y = Z.

The assumptions of normality, equal variances, and equal correlations are likely NOT realistic. However, these calculations leave me with some confidence that the multiplier effect is real, not just a fluke.

One last minor comment: The paper reports median shortfall and outperformance for funds and portolios. The median shortfall (outperformance) for the Vanguard portfolio is defined as the median of the conditional distribution of T given T 0 respectively). There is no general formula relating these conditional medians to the unconditional median. However, there is a simple formula for the corresponding expected values that holds for all distributions:

E(T) = E(T given T<0) P(T<0) + E(T given T≥0) P(T≥0)

Canadian Couch Potato July 30, 2013 at 12:24 am

@DL: Time horizon doesn’t affect the active v. passive decision, only the asset allocation decision. This post may be helpful in explaining this point:

Neil Murphy August 11, 2013 at 12:33 pm

Great article. Active management is a dubious exercise particularly in the realm of the average investor.

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