Towards An Optimized Portfolio Model - Part I: Is There A Case For A Better Index Fund?

by: EB Investor

As investors continue to pile into passive investment strategies, investors are not giving due consideration to the methodology used to construct their index fund.

For most investors, the assumption is that cap-weighted indexing is the best way to capture the returns of the market. I will explore the evidence.

For investors who are committed to the index philosophy, alternative methodology advocates will argue that the methodology of the index matters.

Whether non-traditional index methodologies add value is an open question; I will explore in this multi-part series on portfolio optimization.

Investors are moving to index funds at an alarming pace. Yet I have always wondered if there was a way to systematically analyze the alpha produced by the active managers I like and use, and explain their performance through factor exposures which can then be accessed at much lower cost.

In short, is there a case for a better index fund? One that mitigates the challenges with traditional index strategies and yet builds a bridge between active and passive managers, providing investors with the opportunity to outperform the index in a more structured way. In this piece, I want to go through and explore the evidence so you can make your own subjective conclusion on which methodology, if any, is best to manage your wealth.

The notion of beating the index is the goal of most market participants, but not index fund proponents. Index fund proponents are simply trying to match the index return for the least cost possible. But what if it was possible to create a better index by changing the methodology used to weight the companies in the index, while still keeping costs low? This is the subject of this piece: do fundamentally weighted strategies offer investors a better investment solution, or is it simply active management in disguise for a higher fee?

The Case For Passive Investing

It is primarily settled investment science that index funds beat the vast majority of active investors. The evidence clearly shows that, in the vast majority of cases, active managers fail to beat a passively managed benchmark. I do believe active managers can beat the index, and some do so over long periods as I have proven in past pieces, but the vast majority of active managers fail to beat the market, and this is a settled fact. This is due to a number of reasons. In some cases, active managers fail to embrace the principles of true investing, seeking instead to track an index at a higher cost. These are not active investors, they are closet indexers and should be avoided by investors. In some cases, research shows they are genuinely unskilled at picking securities. These funds should also be avoided by investors. In other cases, short-term thinking dominates the portfolio, as the managers engage in excessive trading, moving from one hot stock to the next. Investors should continue to avoid these funds as well.

Active managers on the whole have a horrible record against a passive benchmark, which explains, at least in part, why index funds have been so successful, especially in the recent past. Holding the power of corporate America in a passive vehicle with very low costs is a powerful way to create wealth over the long run, despite the many challenges I have brought up with index fund construction.

Holding securities for short time horizons or aiming to capitalize on events in the economy or the capital markets is not investing - it is speculating. Because active managers have failed so miserably, statistical analysis concludes that active management is an educated game of chance in the vast majority of cases. I maintain a balanced view on the role of active investing in the construction of portfolio models, but the data clearly will prove that in the vast majority of cases, holding corporate America in a passive vehicle is the best way to harness the returns of capitalism.

Active management is largely a game of chance: while you have no assurance of beating the market, what is guaranteed is the cost you will pay to try. Costs and underperformance compound on themselves, leaving an investor at a clear disadvantage to a passive index portfolio with low cost and no chance of underperforming its index before fees. When an investor engages an active manager at, say 1.05%, this investor is paying 1% more than a passive index fund. Because of this high hurdle rate, the active manager now must achieve returns that are 1% greater just to stay even with the additional costs of the fund. If they fail to do this, as over 90% of them do, then this underperformance begins to compound on itself, and over time, the active manager finds themselves drastically underperforming the index.

However, the active manager got paid a constant stream of income from the management fee, which is paid whether the manager performs well or not. Therefore, it is the investor who bears the cost and the risk, and it is the investor who fails to keep up with the index when the fund underperforms. Paying an investment manager a fee that is more than 20x the cost of a passive index will have a dramatically negative effect on your long-term wealth creation. Furthermore, the fact that a fund outperforms the index, even for an extended period of time, is mathematically a matter of luck in the vast majority of cases.

Even the father of active value investing, Benjamin Graham, became an index advocate later in life. With their low costs and passive ownership of stocks, it is easy to see why.

"I am no longer an advocate of elaborate techniques of security analysis in order to find superior value opportunities. This was a rewarding activity, say, 40 years ago, when our textbook "Graham and Dodd" was first published; but the situation has changed a great deal since then. In the old days any well-trained security analyst could do a good professional job of selecting undervalued issues through detailed studies; but in the light of the enormous amount of research now being carried on, I doubt whether in most cases such extensive efforts will generate sufficiently superior selections to justify their cost... I'm on the side of the "efficient market" school of thought now generally accepted by the professors."

- Benjamin Graham, Financial Analysts Journal, 1976

Even Warren Buffett has followed a passive approach, buying the shares of large corporations and holding them indefinitely. Buffett also advocates that the individual investor use passive index funds due to their passive ownership of corporate America and low costs.

1996 Chairman's Letter - "Most investors, both institutional and individual, will find that the best way to own common stocks (shares') is through an index fund that charges minimal fees. Those following this path are sure to beat the net results (after fees and expenses) of the great majority of investment professionals."

2007 Chairman's Letter - "Naturally, everyone expects to be above average. And those helpers - bless their hearts - will certainly encourage their clients in this belief. But, as a class, the helper-aided group must be below average. The reason is simple: 1) Investors, overall, will necessarily earn an average return, minus costs they incur; 2) Passive and index investors, through their very inactivity, will earn that average minus costs that are very low; 3) With that group earning average returns, so must the remaining group - the active investors. But this group will incur high transaction, management, and advisory costs. Therefore, the active investors will have their returns diminished by a far greater percentage than will their inactive brethren. That means that the passive group - the "know-nothings" - must win... The best way in my view is to just buy a low-cost index fund and keep buying it regularly over time, because you'll be buying into a wonderful industry, which in effect is all of American industry…People ought to sit back and relax and keep accumulating over time."

2008 Chairman's Letter- "The American economy is going to do fine. But it won't do fine every year and every week and every month. I mean, if you don't believe that, forget about buying stocks anyway… It's a positive-sum game, long term. And the only way an investor can get killed is by high fees or by trying to outsmart the market."

2014 Chairman's Letter- "What I advise here is essentially identical to certain instructions I've laid out in my will. One bequest provides that cash will be delivered to a trustee for my wife's benefit….My advice to the trustee could not be more simple: Put 10% of the cash in short-term government bonds and 90% in a very low-cost S&P 500 index fund. (I suggest Vanguard's.) I believe the trust's long-term results from this policy will be superior to those attained by most investors - whether pension funds, institutions or individuals - who employ high-fee managers...If not for their fear of meaningless price volatility, these investors could have assured themselves of a good income for life by simply buying a very low-cost index fund whose dividends would trend upward over the years and whose principal would grow as well."

The SPIVA Scorecard for mid-year 2017 has put together an excellent analysis showing that active funds do not beat the index. It states:

"Over the 15-year investment horizon, 93.18% of large-cap managers, 94.40% of mid-cap managers, and 94.43% of small-cap managers failed to outperform on a relative basis...Funds disappear at a meaningful rate. Over the 15-year period, more than 58% of domestic equity funds, 55% of international equity funds, and approximately 47% of all fixed income funds were merged or liquidated. This finding highlights the importance of addressing survivorship bias in mutual fund analysis.

It is important to note that in any period, the funds that do beat the index will likely not be the funds which beat the market in the next period. Not to mention the quotes reference to funds that simply disappear. Therefore, investors must come to grips with the reality that the house is gambling with your money if you engage in active management with an unskilled manager. You are simply playing a game of chance, and the odds aren't in your favor.

The Arguments Against Traditional Indexing

The arguments against indexing are many and largely revolve around the argument that the market is a double-edged sword of momentum. Because the index is unmanaged, the investor is given full exposure to the market factor in all environments, good and bad.

This full exposure to the market means that in bull super cycles like the one we are in, the investor captures the full market return, but is also increasingly concentrated in just a few stocks, as they continue to increase in market cap. The same investor will also be exposed to the losses when those same few stocks stop running higher and the index fund takes a dive.

The second issue with indexing is the fact that because they are cap-weighted, they may or may not be holding stocks in relation to their economic footprint. In other words, you may be holding highly overvalued stocks in a stock index, thus creating serious challenges over a full investment cycle as I noted above.

Third, and related to the second reason, is this concentration of wealth at the top of the index fund. If we take a standard index fund like the S&P 500 Index fund at Vanguard, the top 10 holdings represent nearly 20% of the value of the fund, even though they are only 2% of the holdings. The top 25 holdings represent one-third of the total value of the index, even though they are only 5% of the total holdings. Thus, it can be argued that what you really own with an index fund is a momentum fund where what is popular, rather than fundamental factors of value, will drive your holdings and your return.

So, the question then becomes is there a way for us to construct an index that allows us to mitigate the challenges with traditional index products, while also maintaining what is great about index funds, such as their broad diversification, low cost, and easy availability to all investors?

Towards the Construction of a Better Index: Insights From Academic Research

In order to analyze whether we can construct a better index, we must first understand the factors that drive investment returns, from academic research.

The One Factor Model

In seeking to understand the variability of stock returns, we must start at the beginning. The birth of capital asset pricing theory must begin with Harry Markowitz and the mean variance portfolio model (1952, 1959). Dr. Harry Markowitz's Portfolio Selection, written in 1952, is just as important today as it was then. Markowitz's work on the relationship of risk and return is truly one of the staggering intellectual achievements of modern economics and has a great practical impact on people's economic welfare.

This volume reiterates his argument that risk is what drives return, rather than being merely an unfortunate by-product of the search for higher returns. He concludes that the way to limit the risk for a given level of expected return is to minimize the co-variance of returns of the assets within that portfolio using a quadratic programming algorithm. This is a brilliant, seminal work, written with a liveliness usually lacking in economic texts. It is no wonder he won the Nobel Prize for Economic Sciences in 1990.

Markowitz advanced the theory that investors are conservative when it comes to taking on risk and are concerned only with whether the portfolio is mean-variance efficient, which assumes a control mechanism for risk and return. Markowitz advanced the notion of modern portfolio theory, which sought to view the risk and return characteristics of assets within the context of a given portfolio. MPT argued that investors can optimize a level of return for a given level of risk.

To build on this model, we move forward to the development of the Capital Asset Pricing Model (CAPM) of William Sharpe (1964) and John Lintner (1965). The CAPM which won Sharpe the Nobel Prize in 1990, sought to describe the relationship between systematic risk and expected return for assets, particularly equities. The CAPM single-factor model explains 70% of the variability of returns.

The CAPM advances a simplistic model, which sought to explain the returns of a given asset using beta. However, there are two major challenges with this one factor model. The first of the major challenges with this model has to do with regression variations, the other with the unpredictable nature of the beta of individual securities. Two solutions for this comes first from Friend and Blume (1970) and Black, Jensen, and Scholes (1972), and secondly from Fama and MacBeth (1973). Both introduced fixes to these challenges that were true advancements of knowledge that have become standard in future analyses:

The former by using portfolios rather than individual securities in regressions reduced the regression variation problem. The latter advanced the notion of using month-by-month regressions rather than single cross-section regressions. While these approaches are standard in a review of the literature going forward, there were still challenges in the usefulness of the CAPM, which required a new way of explaining asset returns.

The Two Factor Model

The size factor contends that small-cap stocks outperform large-cap stocks over long measurement periods. When we look at the past 25 years of data (1992-2018), we see that this factor holds true. As you can see in the data below, the Vanguard Small-Cap Index (NAESX) outperformed the Vanguard S&P 500 Index (VFINX) by 317.21%. DFA U.S. Small-Cap (DFSTX) produced an even better return by tilting the small-cap portfolio towards micro-cap stocks and incorporating the other factors, creating a factor premium of 328.95% over the S&P 500. Tilting deeper into small-cap value with the DFA U.S. Small Cap Value Fund (DFSVX) created 237.58% more return over the standard DFA U.S. Small-Cap fund over 26 years. The DFA funds outperformed the Vanguard fund due to a more complete exposure to the size factor, dipping deeper into the small cap universe. The Vanguard Funds portfolio ranks further up the capitalization spectrum. While its name is small-cap, its portfolio is decidedly mid-cap.

Small Cap Premium

Cumulative Return

Factor Premium (SMB)

Vanguard S&P 500 Index



Vanguard Small Cap Index



DFA US Small Cap



DFA US Small Cap Value



The Three Factor Model

The value factor contends that value stocks produce superior returns over time relative to growth stocks. While this can vary wildly and growth stocks can outperform for even long stretches of time, over the very long run, data leads to the conclusion that value stocks will outperform growth stocks. The evidence for the value premium is robust and diverse across geographical regions as demonstrated by (Fama/French, 1997).

"Value stocks have higher returns than growth stocks in markets around the world. For 1975-95, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.60% per year, and value stocks outperform growth stocks in 12 of 13 major markets. An international CAPM cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns." (Fama, French "Value Versus Growth: The International Evidence", 1997)

Over the last 25+ years (1992-2018), the Vanguard Value Index (VIVAX) outperformed the Vanguard Growth Index (VIGRX) by 11.09%, while the multi-factor DFA US Large Cap Value III Fund (DFUVX) outperformed the growth index by 137.56%. This is largely explained by a deeper exposure to value stocks, as well as the other premiums. While the Vanguard Value Fund's advantage has been eaten away by the recent run-up in growth stocks, the DFA fund continues to outperform due to its multi-factor strategy.

Value Premium

Cumulative Return

Factor Premium (HML)

Vanguard Growth Index



Vanguard Value Index



DFA US Large Cap Value III



The Four Factor Model

The quality factor measures the robust minus weak profitability measures. Some academics have identified the profitability factor as a quality factor, but ultimately, it is about capturing the premium between those stocks that exhibit high profitability from those that exhibit low profitability.

"Buying high quality assets without paying premium prices is just as much value investing as buying average quality assets at discount prices. Strategies that exploit the quality dimension of value can be profitable on their own, and accounting for both dimensions of value yields dramatic performance improvements over traditional value strategies. Gross profitability is particularly powerful among popular quality notions, especially among large cap stocks and for long-only investors." (Robert Novy-Marx, Quality Investing)

The Five Factor Model

"Firms that substantially increase capital investments subsequently achieve negative benchmark- adjusted returns. The negative abnormal capital investment/return relation is shown to be stronger for firms that have greater investment discretion, i.e., firms with higher cash flows and lower debt ratios, and is shown to be significant only in time periods when hostile takeovers were less prevalent. These observations are consistent with the hypothesis that investors tend to under react to the empire building implications of increased investment expenditures. Although firms that increase capital investments tend to have high past returns and often issue equity, the negative abnormal capital investment/return relation is independent of the previously documented long-term return reversal and secondary equity issue anomalies." (Titman, Wie, Xie, 2004)

"In 2004, researchers Titman, Wie and Xie controlled for the relevant variables and found that firms that significantly increase capital investment tend to achieve sub-par subsequent returns. In other words, given sufficient opportunity and proclivity, most managers become capital destroyers." Forbes

So, now that we have established that there is a sizable premium for investors who skew their portfolios towards small cap, value, profitability and positive investment factors, it naturally begs the question how do we construct a portfolio that captures these factors? Well, the solution is clearly through a portfolio that holds a majority of its assets in passive index products in order to maintain a constant exposure to the market factors. This is true even if you choose to include some active management as well. But the index methodology is important when accessing the factors. Let's explore the many types of index funds. For the purposes of this writing, I will focus on three main strategies for constructing an index.

Market Cap Weighting

Market Cap weighting is the traditional index fund. It ranks companies by their market capitalization, thus holding a representative sample of "the market". These funds generally produce returns that are commensurate with the market, with little or no tracking error. The exploration of new index methodologies is met by harsh criticisms from the founding fathers of the index movement, Jack Bogle, who started the first index fund at Vanguard in 1976, and Burton Malkiel a noted passive investor, and author of A Random Walk Down Wall Street. Both have spoken out against "alternative" index methodologies. Jack Bogle has referred to fundamental indexing as "witchcraft" and stated it is active management in disguise at a higher cost. Burton Malkiel has called it "a marketing ploy". I would advance a further question of whether we can access market factors through a much lower cost, which is a question I will look at in another piece. But market cap weighted indexes are the market, and thus, it can be argued that anything that is not market weighted is considered active management.

Fundamental Index

Fundamental index funds come in many shapes and sizes, but they generally attempt to weight companies by their fundamental factors. In this way, the index brings more of the value premium out of the index, as it is constantly selling what is expensive and buying what is undervalued. Tracking error can be meaningful. A recent article from The Globe and Mail in Canada explored the concept of whether it was worth it to switch to a fundamental index. The author states

"Fundamental indexers point out that a big market capitalization is no indicator that a company will perform well. In fact, the ten largest companies by market cap in the S&P 500 have typically underperformed the market. This trend has occurred during every rolling ten-year period, back to 1926.

A fundamental index, rather than emphasizing market size, weights its holdings based on cash flow, book value and dividends. Doing so, according to Mr. Arnott, ensures the index doesn't fall victim to fads, which can drive up a stock's price and therefore its market capitalization...

Back-tested studies of fundamental indexes, however, have been impressive. Between 1984 and 2004, a study of 23 different markets found fundamental indexes triumphed consistently over cap-weighted MSCI indexed benchmarks.

Equal Weighting

Equal weighting is just as it sounds, you hold each stock in an index in equal weight. This strategy tends to bring more of the small cap premium out of a total market index for example because small-cap stocks carry the same weight as large-cap stocks. Tracking error can be significant.

The Winner Is...

So, let's conduct a test of these three strategies using the large-cap blend market segment. In order to test these various index methodologies, I will be looking at the Schwab Fundamental Large Cap Index (SFLNX) vs. The Vanguard Total Stock Market Index (VTI), vs. the Guggenheim S&P 500 Equal Weight Index (RSP). I will look at the common period from 03/30/2007-03/30/2017.

Schwab Fundamental Large Company Index 0.25% 15% 112.19% 1.11 17.25 0.56
Vanguard Value Index 0.06% 7% 83.34% 1.01 15.46 0.53
Vanguard Total Stock Index 0.04% 4% 109.95% 1.03 15.58 0.59
Guggenheim S&P 500 Equal Weight Index 0.20% 21% 118.15% 1.15 17.7 0.59
Vanguard Mid-Cap Index 0.06% 15% 112.55% 1.13 17.7 0.55


What this period seems to show is rather interesting for anyone who believes in cap-weighted indexes, to the exclusion of all other methodologies. In terms of performance, the cap-weighted index produced the worst return during the period of our three options.

Yet, what I found most interesting is that one of the largest criticisms of fundamental indexing is that it will not hold up during a stretch when growth outperforms value. Yet, this is a test of one such time period, and yet, fundamental index and equal-weighted index strategies still were able to outperform traditional cap-weighted indexes.

An additional caveat to this test is the fact that many would contend that the proper comparison tool for the fundamental index would be a value-focused fund like the Vanguard Value Index (VTV), but the fundamental index outperforms this benchmark as well.

Similarly, a criticism may arise that the proper comparison tool for the equal weight index would be a mid-cap stock index, such as the Vanguard Mid Cap Index (VO). Yet again, the equal weighted index outperforms this benchmark as well.


So, it seems that whatever way you index, anything but cap weighting is ideal. Both of these alternative methodologies seem to mitigate the challenges to cap weighted index funds and provide investors with more exposure to the sources of outperformance from investment research.

Whether you believe the additional cost is worth it over the long run is up to you. In terms of arriving at a definitive objective conclusion, it remains an open question for researchers. There simply isn't enough data to form a definitive empirical conclusion.

But I believe alternative methodologies for indexation offer investors promise to capture more than their fair share of investment returns over the long run and, in the process, build a bridge between passive and active investors to form a more intelligent way of investing for the long run.

Criticisms to this approach, as well as evidence from Vanguard, will be explored in part II of this series.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: This article is for informational purposes only and is not an offer to buy or sell any security. It is not intended to be financial advice, and it is not financial advice. Before acting on any information contained herein, be sure to consult your own financial advisor. This article does not constitute tax advice. Every investor should consult their tax advisor or CPA before acting on any information contained herein.