Are Index Funds the Only Rational Choice? 28 comments
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There are many experts who believe that investors ought to invest in funds that track a broad index [pdf file], and should not invest in smaller numbers of individual stocks. This idea has always rather bothered me because the arguments supporting it seem to be based on some simplistic assumptions. Is it really more intelligent to hold all 500 stocks in the S&P 500 than to hold a smaller number of stocks?
The arguments against holding individual stocks seem to hinge on the idea that investors have only two choices. They will either (1) buy an index fund or (2) randomly buy some number of individual stocks. This approach assumes that investors have no information at all to help them in distinguishing between stocks. The studies that support this thinking typically show that the returns of an index are disproportionately determined by a small number of big winners and that if you are picking stocks by chance, you have low odds of picking any of these rare but enormous winners if you pick a small number of stocks. Similarly, a random stock picker has reasonable odds of ending up with a portfolio that contains a higher exposure to individual stocks that suffer substantial losses, and thereby to suffer much higher losses than the index.
In essence, these arguments are based on a belief in large numbers—you will tend to closely match the average market index return only by buying large numbers of stocks in the index.
If investors can pick stocks no better than randomly, it will always be better to hold more stocks rather than fewer stocks. But is the world truly this random? To make the case that we can do no better than random selection is an incredibly strong assumption—and one that I believe is far from reality. There is evidence that funds that have smaller numbers of stock holdings than their peers tend to outperform and are, in fact, no more risky than their peers. The funds in these studies are real examples of portfolios with small numbers of holdings, in which managers can control for risk and diversification benefits, as opposed to the theoretical world of random stock pickers.
Well-known author and advisor William Bernstein did a study in which he created 98 randomly-selected 15-stock portfolios and then compared these to the performance of a portfolio which held every stock in the S&P 500 in equal proportion over a ten year period. What Dr. Bernstein found was that 3/4ths of the randomly-selected 15-stock portfolios under-performed the portfolio that held equal weights in every stock. The reason for this under-performance? Dr. Bernstein notes that a small number of stocks generated enormously high returns over this period (the ten year period ending in 11/30/99). If your fifteen stock portfolio did not hold one of these stocks, you would tend to under-perform. One of these “super stocks” in Dr. Bernstein’s study was Dell (DELL) computer, with a total return of 550% over this period. In retrospect, this argument seems a bit odd. Dell was trading at $51 a share in December of 1999. Today, it is trading at around $10. For the long-term investor, accidentally missing out on picking Dell might be one of the best things that ever happened---depending on where you start your analysis.
Dr. Bernstein notes that the S&P 500 returned an annualized 18.9% over this ten year period, whereas the portfolio that was equally weighted between all 500 stocks in the S&P 500 returned an annualized 24.2%. 35 of the 98 random portfolios generated less than 19% in annualized returns. This means that the majority (64%) of the randomly-selected 15-stock portfolios beat the S&P 500. The disparity between the conclusions one might draw using the equal-weight S&P 500 vs. the actual (market cap weighted S&P 500) is due to survivorship bias. There were stocks in the S&P 500 index that have collapsed over this ten year period and been de-listed. The S&P 500 index itself bears these losses, but a portfolio that is equally weighted among the 500 stocks currently in the S&P 500 does not. This means that the equal-weighted portfolio of stocks currently in the S&P 500 is biased upwards from what we would have if we had invested in all stocks currently in the index in each year in history.
There is also another issue that is important: the size effect. It is well known that smaller cap stocks tend to be both higher risk and have higher returns than larger cap stocks. An equal weighted portfolio of 15 stocks or of all of the stocks in the S&P 500 will have an average market cap well below that of the S&P 500. So Dr. Bernstein’s analysis is somewhat biased by the size effect.
The key issue that is missed in this type of study, however, is the assumption that investors pick stocks no better than randomly to build a portfolio of a certain number of stocks. An index contains stocks that have a vast range of risk levels, from the conservative to the massively risky. A random portfolio of stocks might end up with aggregate risk much larger or much smaller than the S&P 500. If one wanted to make this type of study more relevant, we could look at the projected portfolio risk of a series of possible portfolios.
In Dr. Bernstein’s analysis, he cites the an article showing that correlations between individual stocks are declining and that the volatilities of individual stocks are increasing. This article [pdf file] suggested that the next impacts on total market volatility canceled out (lower correlations tend to lower total market volatility).
Let’s say that we were standing at 11/30/1999, and trying to figure out what to do on the basis of Bernstein’s analysis. What do we know at that point? To address this issue, I have run Quantext Portfolio Planner (QPP) to predict risk and return for the S&P 500 and for a series of random portfolios using all default settings (and three years of data as input—my standard for testing). I have taken all of the stocks currently in the S&P 500 and created a set of ten portfolios, each with equal weights given to each of 15 random stocks from the S&P 500. This is the same process used by Dr. Bernstein, as far as I can tell.
After having built these ten random portfolios, I can look at the historical and projected risk levels for these portfolios, as compared to the S&P 500, for the nine years from 11/30/1999 to 11/30/2008.
To begin, I will note that the majority of these 15-stock portfolios were more volatility (risky) than the S&P 500, as expected. The table below shows the trailing three-year volatilities for each of the random portfolios (r1, r1,r3…r10) as well as the projected long-term volatility calculated using QPP.

Volatility is measured in terms of the standard deviation in returns. Riskier portfolios (those with higher volatility) will, by their very nature, have a larger variability in future outcomes than less risky portfolios---by definition. The first question that must be asked is whether it is even meaningful to compare the performance of these random portfolios to the S&P 500. Some of these portfolios are vastly more risky than the S&P 500 (r10 and r3, for example). To compare a portfolio with 51% higher volatility than the S&P 500 (r10) to the S&P 500 is fairly meaningless.
It is this enormous range in portfolio risk levels that largely leads to the enormous spread in annualized returns between portfolios. Dr. Bernstein emphasizes the enormous range of possible terminal levels of wealth in a random 15-stock portfolio—and he is correct. But the range would be much smaller if you constrained reasonable measures of portfolio risk in your 15-stock portfolio to be at or below the risk level of the S&P 500. The tendency towards higher risk portfolios is due, in part, to the size effect.
These random portfolios do not necessarily end up exploiting the level of industry diversification reflected in the S&P 500---odds are good that they don’t come close to the best that you can do. This is a major reason why a random portfolio with a small number of stocks will tend to be riskier than the total index, The bottom line here is that if you are going to create a portfolio of 15 randomly selected stocks, you could (and probably will) end up with a wide range of portfolio risk levels and a wide range of diversification benefits. This conclusion should not strike anyone as profound. This type of data in no way shows that a 15 stock portfolio is naturally more risky, less diversified, or less desirable than holding the S&P 500.
This does not mean that I am endorsing the idea that people get rid of their index funds and buy 15 stock portfolios—but rather that the conclusions that Dr. Bernstein draws is not well supported. Dr. Bernstein’s results (and those from related studies) apply only to random portfolios and say nothing about more rational approaches.
Now, our entire discussion will turn out to be somewhat theoretical if there is no consistent relationship between the projected volatility for a portfolio and the actual volatility for that portfolio. The results are summarized below:
The historical volatility, projected volatility (from QPP) and the realized volatility (what actually happened) over the subsequent 9-year period are closely related. Another way to look at these data is through the correlation matrix:
The correlation between the trailing volatilities for each portfolio (10 random plus the S&P 500) and the realized volatility for the subsequent 9-year period is 69%. The correlation between the Projected Volatility and the realized volatility is 77%. These correlations show that the QPP projections added value because the higher correlation means that the QPP projections were more useful in determining relative risk of all of the portfolios. That said, the 69% correlation between historical and realized volatility means that looking at the historical volatility is a useful guide in predicting future volatility for all of our candidate portfolios.
The two portfolios which were historically most risky are also most risky in the subsequent nine years (r10 and r3) and the least risky portfolio historically is the second least risky over the next nine years (r4). The correspondence is not perfect, but it is indicative. Most importantly, the fact that most of the random portfolios are more risky than the S&P 500 holds up over time. These results are easily shown by looking at the relative rankings of portfolio risk levels:
The correlation between the historical ranking of risk among these portfolios and the realized future ranking of risk is 63%, while the correlation between the QPP projected ranking of risk and realized future ranking of risk is 71%, mirroring the results from look at the volatilities themselves. Investors can do a remarkably robust job of sorting more risky portfolios from less risky portfolios, so why wouldn’t they do so?
These results mean that it would be irrational for any investor to randomly select a portfolio without first segregating on risk levels. Historical risk is a meaningful guide to future risk, so any attempt to build a stock portfolio should pay attention to historical risk. A forward-looking model like QPP adds even more information.
So what does all this mean for investors? The first takeaway for investors is to think more critically about whether the case for buying five hundred stocks in an index fund is as rock solid as it is often presented. I have cited William Bernstein and others, but this argument is found in many forms in many places. Ric Edelman uses this argument in his book called The Lies About Money (2008), as does Christopher Jones in The Intelligent Portfolio (2008). The basic premise of this argument is that we are all selecting stocks blindly. Even if you were to accept the argument that investors cannot time the market well, there is still abundant evidence that relative risk of portfolios is predictable to some extent. As such, arguments that start with the assumption that we cannot know anything about a portfolio of individual stocks are simply not well supported.
If you can say something intelligent about the relative differences between stocks chosen from the S&P 500, this implies that you can make a reasonable case for investing more heavily in on stock than another and that you can make the case for rejecting certain stocks entirely. It is not an enormous leap to then suggest that it might make sense for investors to own portfolios of stocks that do not simply mimic an index. In fact, recent research supports [pdf file] the idea that mimicking an index may be the best route to under-performance.
Does this mean that I think that investors should own a portfolio of only fifteen stocks? Not at all. Selecting individual stocks is fairly far down the list of important priorities for investors. I do, however, believe that owning individual stocks confers a range of advantages for the sophisticated investor.
The value of selecting individual stocks to supplement a well-designed portfolio will tend to increase in time of turmoil because of the general increase in correlations between broad indices in these conditions. The correlations between individual stocks are often much lower than the correlations between indices—and this is a trend that is increasing in time [pdf file]. I have made the case for exploiting individual stocks’ low correlations in earlier work.
If all an investor had done prior to the big market declines in 2008 was to identify a range of the riskiest stocks (which is related to the highest default risks) and rejected these, his/her portfolio would be much better off for it. In March of 2008, I wrote an article on how one might rationally estimate the risk of substantial or total losses from investing in individual stocks. The timing was quite good for such a study, and I included analysis of a range of stocks that turned out to have catastrophic losses in 2008. The results have turned out to look quite prescient (they suggested avoiding F, GM, WM, BZH, LEN, and PHM if you wanted to minimize default risk).
My conclusion is simply this: the conventional wisdom that investors must buy the entire market index (i.e. owning all 500 stocks in the S&P 500) or end up with disproportionate risk in their portfolios is simply not well supported. The body of academic research does support the notion that a random selection of stocks benefits from larger numbers of holdings, but there is a range of information available for individual stocks (risk and correlations, for example) that can inform the process of stock selection for building a well-diversified portfolio with a smaller number of stocks than the entire market.
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This article has 28 comments:
The problem is to predict which stocks these will be. Since the stock markets act on inside news before an individual has that information I do not believe it to be possible, and thus the best answer is to buy indexes.
Find a consistent stock picker and kill the whole game.
Your concern on avoiding the losers is address in the article I wrote--and cited above--on identifying high risk / troubled stocks.
Boubou:
My point is that this problem is NOT about stock picking--even if market timing and stock picking on fundamentals does not work at all, just selecting based on risk and correlation fundamentally changes the situation. There is consistent information embedded in risk--but the studies suggesting you need to own every stock in the S&P500 ignore that information.
To User 319912:
The point about getting one or more "super stocks" in Bernstein is misleading. DELL, for example, was a very high risk stock. In Bernstein's ten year analysis, DELL out-performed and in the subsequent ten years DELL massively under-performed. If your goal is to find stocks which in aggregate mimic the risk level of the S&P500, your universe of stocks probably will not include DELL, but neither will it include WM...Is there any evidence that having the super-stocks is more important than avoiding the "death stocks"? Showing statistical distributions in which all stocks are considered equal is misleading. Some companies are predictably far riskier than others.
What you fail to recognize is the cost/benefit of the time needed to research stocks. Most people would serve the economy better by just focusing on their jobs and not having to think about their investments. If every American was a Seeking Alpha reader perhaps your argument would carry some merit.
My only actual point though is this: I could have read the quarterly income statements of a dozen stocks in the time it took me to read this article. I think you should owe us some stock tips for wasting our time.
He started a fund company and offered these funds.
His funds massively underperformed, even before 2000. He closed the funds.
His analysis is superb in the book. To this day, i don't have a rational explanation for why it failed Others will use their 20/20 hindsight to tell me why O'Shaughnessy's analysis and portfolios didn't work. But his approach is the same presented by Mr. Considine.
The book is well worth your time.
The reason to invest in index funds is not to get a large number of stocks. The reason is to avoid the management and transaction fees that characterize an actively managed portfolio. Many studies, not linked by Mr. Considine, have shown that active managers can, in fact, select stocks that perform better than indexes. However, once you take out the management fees and the higher turnover costs that active management generates, the active management underperforms. Those fees and costs, often averaging 150 to 200 basis points, are too big a bogey for active management to overcome in a environment where they constitute 15% to 20% of the long term stock market return of approximately 11% per year..
A sample of "intelligently selected" portfolios of 15 stocks would probably beat an index, especially one based on a small number of stocks, until you factored in the management costs noted above. The diversification obtained by investing in an index with a large number of stocks is an ancillary benefit.
The statistical 'straw man' that I set up has been proposed by a range of experts and you can read this argument in many books and articles. Bernstein is no pushover. I am not talking about active management--I am talking about strategic asset allocation without needing to have hundreds of holdings. If this is correct--and obviously I believe it is--this has important implications for how people invest.
You can do Strategic Asset Allocation without investing in 500 stocks in the S&P500 to get exposure to large cap domestic equities, for example. This can be done as a passive investment strategy--not active.
To Weakonomist:
I am sorry you felt your time was wasted. Based on your response, I feel that you would probably prefer Jim Cramer...he is easily found. Good luck.
I think the biggest problem w/O'Shaugnessy's Funds were the timing. Fundamentals & Quantatative analysis didn't matter in the late 90's! When I first got into the investing game (1997) I tried to utilize these methods, got P.O.'d that the NASDAQ kept making everybody rich. So wanting my fair share I threw in the towel and joined the madness just in time (Feb 2000) to lose 40% of my portfolio (which thankfully was pretty small, but the loss still stung).
I'd love to see a study or something showing on how a portfolio using his method picked in 1995 would've held up. I'd not be surprised to find that the 1995-2008 returns probably would've been comprable to the S&P, DJIA, QQQQ with a lower Beta over the period.
Remeber when you buy SPY for every DELL, MSFT, and other star performer you also get stuck with overleveraged stinking corpses like AIG, F, GM, Enron, and WorldCom.
On Dec 15 01:11 PM BobHank wrote:
> One of the best sources on backtesting stocks is O'Shaugnessy's "What
> Works on Wall Street". He wrote this in 1995. He analyzed and came
> up with different portfolios, that he then went on to backtest. He
> came up with 5 different portfolios that were built on a risk tolerance.
>
> He started a fund company and offered these funds.
>
> His funds massively underperformed, even before 2000. He closed the
> funds.
>
> His analysis is superb in the book. To this day, i don't have a rational
> explanation for why it failed Others will use their 20/20 hindsight
> to tell me why O'Shaughnessy's analysis and portfolios didn't work.
> But his approach is the same presented by Mr. Considine.
> The book is well worth your time.
"Remember when you buy SPY for every DELL, MSFT, and other star performer you also get stuck with overleveraged stinking corpses like AIG, F, GM, Enron, and WorldCom."
Precisely!
I think you made some excellent points. How does this line of reasoning apply to ETF's?
For investors that don't want to restrict themselves to 15 stocks, but buy into a weak version of your theory--could the analogy be to apply your thinking to low volatility ETF's with negative or low correlations?
This year, by simply buying a Treasury ETF, a Gold ETF, a biotech ETF, and a health Care ETF---one could have a low correlation portfolio--and be considerably ahead (in relative terms) this year.
I know this misses your point about volatility--but can one pick ETFs based on weak correlation, and lower than average volatility, and apply a weak version of your theory?
Does QPP work with ETFs?
Thank you for an excellent article that gives much to think about,
Eric
They'd rather be fishing.
And I think that's perfectly fine.
Stock picking is for the little guy, and for the professionals.
Why are some underperforming stocks a drag on randomly assembled portfolios? There's a good topic for further quant research, starting with earnings quality.
There is a reason why many people are conservative and prefer bonds and gold and other hard assets. Then there are others who invest in one or two established divy paying businesses (risky of course, e.g Enron). But still this a well researched issue and your article is not contributing too much new information, imho. Your article starts off being addressed toward "investors" which makes me think you are addressing the average investor. But towards the end you change your tune and say that the sophisticated investor should own stocks. New Flash: An investor becomes sophisticated when he/she chooses individual businesses to invest in- thereby picking stocks. So category A is not your audience, Category B, is way ahead of the curve to be reading your articles. I hope you don't have any connection to penn state..[random remark based on last name]
On Dec 15 07:30 PM Nikola wrote:
> I think the reason why most people buy index funds is so they don't
> have to spend the time learning and analyzing the fundamentals, and
> watching the market to make sure they made the right choices.
>
> They'd rather be fishing. OR Playing golf or Bridge.
>
> And I think that's perfectly fine.
>
> Stock picking is for the little guy, and for the professionals.
I understand and agree that you can get highly effective asset allocation with a small number of holdings. I don't believe that the statement you make: "the conventional wisdom [is] that investors must buy the entire market index (i.e. owning all 500 stocks in the S&P 500) or end up with disproportionate risk in their portfolios" is the conventional wisdom at all, nor is it the reason people buy index funds.
However, that being said, the average investor cannot build a diversified stock portfolio with only 15 stocks. He doesn't have the statistical or market knowledge to do so. So he buys an index fund, gets better diversification than he would otherwise have in a self-constructed 15 stock portfolio, and gets probably better performance than a managed portfolio.
On Dec 15 04:09 PM Geoff Considine wrote:
> Kinabalu:
>
> The statistical 'straw man' that I set up has been proposed by a
> range of experts and you can read this argument in many books and
> articles. Bernstein is no pushover. I am not talking about active
> management--I am talking about strategic asset allocation without
> needing to have hundreds of holdings. If this is correct--and obviously
> I believe it is--this has important implications for how people invest.
>
>
> You can do Strategic Asset Allocation without investing in 500 stocks
> in the S&P500 to get exposure to large cap domestic equities,
> for example. This can be done as a passive investment strategy--not
> active.
I recommend reading Fama & French's 2007 paper "migration" and his related 2008 paper that investigates the source of the value and size premiums.
Thanks,
Tristan Yates
Author: Enhanced Indexing Strategies
Sadly, you are correct. I have cited this very body of research myself in my article called The Humble Arithmetic of Portfolio Management. The majority of investors under-perform the basic indexes--so the first thing to do is to improve a portfolio so it has good odds of at least matching the index. Second, you want to diversify properly to exploit diversification benefits. And yes, in a market panic, correlations seem to go to one. You are making Bogle's argument and the world would be better for most investors if they followed Bogle. This article is looking at a topic to be considered late in the process of portfolio strategy.
There are some issues with "agency" problems with mutual fund managers which I have written about elsewhere. Many are afraid to stray much from the index. See the research on Active Share, for example.
Anyone without the time, and this is why I think the author is misguided, is not doing either - index funds or stock picking. They are in mutual funds, which is the real comparison to make - mutual funds, or index funds? And there, IMHO, is where index funds shine. If you don't have the time to pick stocks yourself, you probably don't have the time to do due diligence on your fund manager to ensure (s)he's doing what you think (s)he's doing. So, unless you have Bill Gross or Warren Buffett as your golfing buddies, this type of investor should stick to index funds, which have almost 0 expenses, and require no active management. Lastly, index funds in nearly every 10 year inconclusive study published (they're all inconclusive for some reason) beat mutual funds the majority of the time, once fees are included.
Lastly, people that should be in index funds are probably not subscribers to a site called "seeking ALPHA" - most would have no idea what the hell ALPHA is.
Note that mutual fund managers, unlike baseball players, show no sign of systematic skill. Take managers that do well over a five year period and track them for the succeeding five year period--they will not do any better than random (The opposite is not true--the poorest 20% of managers will, in general do more poorly over the second five year period. Talent is not well-demonstrated in financial markets, but mediocrity is).
I'm sympathetic to the fundamentalist argument myself, but that requires a substantial investment of time and energy and talent. The typical portfolio can be improved quite simply by being invested in the market portfolio, and any improvements that you make should move from there.
They have done studies and seems like most demonstrate alpha (Even in passive mode) against S&P Index.
The widsomtree index uses high Div, High earning yields (which most times is accompanied by low p/e or p/b) and is one of the criteria I would love when picking stock.
I'm now wondering whether I should go into wisdomtree indexes instead of picking stocks myself. I've been doing fine but it really takes too much work and affecting my social life after work.