Are Index Funds the Only Rational Choice?

|
Includes: EFA, IVV, IWM, IWV, QQQ, VT, VTI
by: Geoff Considine

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 (NASDAQ: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:

click to enlarge
Click to enlarge

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:

Click to enlarge

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:

Click to enlarge

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.