The Case For Evidence-Based Investing, Part IV: The Multi-Factor Model And Portfolio Optimization

by: Nicholas P. Cheer


In this fourth piece in the series, I will explore the multi-factor model that emerges from the research.

I will explore how to apply this model to optimize your portfolio for varying levels of risk and return.

Finally, I will conclude with a quantitative analysis and review of the literature on why working with a qualified wealth manager could mean more wealth for your future.

This is a five part series aiming to make the case for evidence-based investing. In Part I of this series, I reviewed the problem with active management and why it is a loser's game for the vast majority of participants.

In Part II, I continued to make the case for evidence-based investing by exploring the extreme cost of active investing and the theoretical foundations of EBI.

In Part III, I explored a plethora of research supporting the underlying principles of EBI, and why investors should rely on centuries of academic research when building their investment portfolio, rather than the hunches or prognostications of an active manager.

In this fourth piece, I want to explore the multi-factor model that emerges from the research, discuss portfolio optimization, and quantify the advantage of working with a qualified wealth manager.

In Part V, I will review quantitative tools investors can use to assess their active manager and prove that, in the vast majority of cases, they have no skill and are simply lucky at the game of chance. This should also assist investors who are desiring some allocation to active strategies to select better options.

Developing a Multi-Factor Approach to Portfolio Construction

There has been a great deal of research that I reviewed in the previous piece. Markowitz made us aware of the importance of exposure to beta, but Fama and French included exposure to size and value in their Three Factor Asset Pricing Model. Investors tilting their portfolios towards value and small cap stocks can increase their overall return over the long run. Fama and French, through their work A Five Factor Asset Pricing Model, expanded the factors of risk further identifying five risk factors that investors can aim to capture when constructing an investment portfolio. These five factors, beta, size, value, profitability, and investment patterns, have been shown to lead to higher returns over the long run in academic studies. However, over long periods of time, they can go in and out of favor, so investors should not construct an investment portfolio that depends upon a single factor to achieve their goals.

The Research Based Factors of Outperformance

1. Beta

Harry Markowitz

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.

William Sharpe

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.

2. Size Factor

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 (1992-2017) 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 294.06%. 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 511.24% over the S&P 500. Tilting deeper into small cap value with the DFA U.S. Small Cap Value Fund (DFSVX) created 48.87% more return over the standard DFA U.S. Small-Cap fund over a full time period. 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



3. Value Factor

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 (1992-2017) the Vanguard Value Index (VIVAX) outperformed the Vanguard Growth Index (VIGRX) by 7.93%, while the multi-factor DFA US Large Cap Value III Fund (DFUVX) outperformed the growth index by 100.62%. 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. Further proving why DFA's structure is far superior to a standard index fund, and should act as the core of an investor's portfolio.

Value Premium

Cumulative Return

Factor Premium (HML)

Vanguard Growth Index



Vanguard Value Index



DFA US Large Cap Value III



4. Profitability (Quality) Factor

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)

5. Investment Factor

"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

Two Fixed Income Factors

There are two primary ways to increase the return on a fixed income portfolio. The first is to increase the term of the bond, and the second is to decrease the quality of the bond. This explains why junk bonds earn a higher yield than high quality U.S. Treasury securities, and 30-year bonds earn a higher yield than 3 year bonds. Lower quality opens an investor up to an increased chance of default, while longer maturity bonds expose an investor to greater duration risk. Duration is a bond's sensitivity to interest rates. An investor must make the decision about where they want their fixed income portfolio to be in order to achieve their goals.

Duration, Convexity, and Quality

Duration is a term used to describe the sensitivity of a bond portfolio to changes in interest rates by the Federal Reserve. If we take as an example the PIMCO 25+ Year Zero Coupon U.S. Treasury ETF (NYSEARCA:ZROZ), it currently has a duration of 27.39. This means that for every 1% increase in interest rates, the investment will fall by 27.39%.

Convexity on the other hand is a less popular concept, and one that is generally limited to discussions amongst professional bond investors. Convexity measures the degree of the curvature of the duration. Managing a portfolio of bonds for convexity means managing the overall market risk of the portfolio. As can be seen here:

Bond A, has more convexity than Bond B. Thus convexity is measuring the rate of change of change, or the second derivative of how the price of a bond changes with changes in interest rates, or the derivative of duration. As yields for a bond change, the change in the price of the bond is curved in a convex manner. Thus the graphing of a 30-year bond is far more convex, than the graphing of a 10-year bond or a 1-year bond. Thus the rate of change in the price for a 30-year bond is far more sensitive to changes in rates, or has more market risk than the 1-year bond, assuming bonds are not held to maturity. If bonds are held to maturity, then convexity and duration are far less applicable to the investment case, as interest will be capitalized and paid at maturity, regardless of what short-term swings in price may occur.

30-Year Bond Convexity

10-year Bond Convexity

1-year Bond Convexity

You can see that the convexity of the curve deepens as one goes up in maturity, with a 30-year bond demonstrating high convexity and a 1-year bond demonstrating no convexity. Thus bond pricing is sensitive to both maturity, changes in rates, and the degree to which the change in rates occurs.

For investors seeking to maximize long term portfolio returns, research shows that you are better off reducing duration risk, and holding a portfolio of short to intermediate term high quality bonds.

Is It Worth It to Extend Quality?

For investors intent on deriving income from their bond portfolio, one strategy some investors use is to extend the quality of the bonds. This could mean simply shifting from U.S. Treasury securities to investment grade corporate bonds, or for some it could mean extending quality to high-yield bonds.

In order to answer the question about whether it is worth it to extend quality, one must first decide what the role of bonds will be in the portfolio. High yield bonds tend to be more correlated to equities, while U.S. Treasury bonds have a negative correlation with equities. Investors with the need, and capacity to take risk may consider corporate bonds for their portfolio. For most investors research proves the best way to invest in fixed income for a long term diversified portfolio is through high quality U.S. Treasury securities. With yields at ultra low levels, currently investors are far better off holding increased levels of cash and CDs, or taking advantage of the market premium and owning dividend paying stocks, as I stated in my recent piece The Case Against Bonds. Current CD rates are higher than U.S. Treasury bonds out to 30 years.

Charles Ellis stated in a Money Magazine piece that investors should not own bonds, though he states there is no simple answer to the low rate environment. I agree, as I wrote in my recent piece about not owning bonds, each investor's allocation to fixed income should be based on time tested principles, and driven by their need and desire to take risk.

"The best piece of advice I could give long-term investors today is don't own bonds. And if you do own them, you probably ought to move out of them." - Charles Ellis

Building an Evidence-Based Investment Portfolio

Once an investor has dispelled with the notion that they can beat the market through active security selection, market timing, market forecasting, or any other speculative methodology, it is time for investors to move on to determining what is important to them. Discovering your own values and risk tolerance, is the key to being able to stick with your plan over the very long run. Once this process is completed it is time to actually build the portfolio.

We have explored that the evidence is clear that investors need to start with the market portfolio (beta factor) and then tilt the portfolio towards small caps (size factor) and then value stocks (value factor). As we begin to build the portfolio take notice that as we compound these factors the potential for outsized returns increases, as does tracking error from the standard market portfolio. Investors must choose whether they are willing to deviate from the market portfolio in order to capture the potential alpha that comes from tilting towards the sources of outperformance, or whether having tracking error is an undesirable outcome and they are happy with the market portfolio. Either way controlling costs and emotions are two of the most important factors in your ultimate investing results.

(All data is for the 25 year period 1992-2017.)

We start with the market portfolio, giving investors exposure to the beta factor. Some investors choose to hold the S&P 500, other investors prefer to hold a total stock market index. Because the total market index is more representative of the market portfolio, I am going to use the Vanguard Total Stock Market Index (VTSMX) to represent the market.

Let's begin by adding small caps to the portfolio.

We see that an investor has gained a meaningful advantage by including small caps versus just holding the market portfolio

Small Cap Premium

Cumulative Return

Factor Premium (SMB)

Vanguard Total Stock Market Index



DFA US Small Cap (DFSTX)



In addition to producing a nearly 412% premium return over the market portfolio, including small cap stocks also increases the benefits of diversification, spreading your dollars out more meaningfully between large and small cap stocks.

Next adding value has been proven to outperform growth stocks, as well as the market portfolio.

Value Premium

Cumulative Return

Factor Premium (HML)

Vanguard Total Stock Market Index



DFA US Large Cap Value (DFUVX)



DFA US Small Cap Value (DFSVX)



Including value produced a 36.67% premium over the period versus just holding the market portfolio. Additionally, you can see that combining factors with the Small Cap Value Fund produced an even higher return with a 505.47% premium.

Further diversification into commodities, real estate, U.S. and international bonds, international large caps, international small caps, and many other asset classes produces a better risk and return profile than a portfolio that is using just traditional stocks and bonds.

The traditional 70/30 index portfolio for an investor with the discipline to stay invested and avoid behavioral mistakes, produced an annual return of 9.3% over the past 42 years, with a standard deviation of 11.0%.

By adding additional asset classes and tilting the portfolio towards the sources of outperformance, an investor can achieve a better risk and return profile.

The portfolio produced an annual return of 11.4%, with a standard deviation of 10.2%, and a percentage increase in returns of 22.58%, while reducing risk by 7.2%. This is the power of diversification. For a long term investor, these small changes in portfolio allocation can have a large effect on the performance of your investments and thus your ending account value. A $10,000 investment in the standard portfolio grew to $452,686, or 4,427%, while the evidence-based portfolio fully diversified produced a portfolio worth $1,031,395, or 10,214%, which is $578,709 or 5,787% more wealth.

Controlling Investor Behavior Is Often the Most Important Factor

It is essential to understand investor behavior as we move forward in understanding the science of investing. In order to succeed long term investors need to keep their emotions in check. For investors who can't do this, a wealth manager who understands and follows the research on investing may be appropriate.

The cycle of wealth destruction is practiced by far too many investors. There was a great article from the Wall Street Journal that addressed this issue:

"Millions of Americans inadvertently made a classic investment mistake that contributed to today’s widening economic inequality: They bought high and sold low. Late in the stock-market booms of the 1990s and 2000s, more U.S. families clambered into stocks as indexes surged. Then, once markets tumbled, many households sold and took losses.Those that held on during the most recent collapses reaped the benefits as stocks nearly tripled between 2009 and today." Source

The cycle of wealth destruction involves investors buying at times of maximum euphoria, generally at market peaks, and selling at times of maximum pessimism, this leads to wealth destruction and ultimately financial ruin.

The most successful investors reverse the behavioral dynamics, buying at times of maximum pessimism, and selling at times of maximum euphoria when the fundamentals do not match the market price appreciation. Investors often cite the great Oracle of Omaha, Warren Buffett, as an investor they admire. They would do well at following his advice on investing.

“Be Fearful When Others Are Greedy and Greedy When Others Are Fearful”
― Warren Buffett

Can I Use Active Funds with This Model?

Many investors have questioned why an investor can not build an investment portfolio using the Fama/French model using active funds of their choice. While of course you can construct an active portfolio aimed at targeting the sources of outperformance, it is not optimal for two reasons.

1. Style Drift

Many active managers engage in style drift, which is when a portfolio manager will move the fund's portfolio out of its specified quadrant and drift towards a neighboring quadrant. For example, the widely used Dodge & Cox Stock Fund (DODGX), a traditionally large cap value fund, is currently labeled as a Large Cap Blend fund. This is because the portfolio managers have skewed the portfolio towards growth rather than value, resulting in a blend category placement. Therefore investors using this fund to target the value factor would be actually capturing the returns from largely growth oriented companies. The lack of consistency in style makes using active funds to target factors nearly impossible.

2. Cost

Even if an investor could target the factors using active managers, the cost to do so would likely erode the vast majority of your alpha. (See Part II for a deeper exploration of the effect of cost on investment returns.) This is simply not the optimal way to target factors. This does not mean that active management can not play a role in investor portfolios. In the next piece I will examine whether active management can become a winners game.

Quantifying the Value of Evidence-Based Wealth Management Counsel

Building an evidence-based investment model is best constructed by a financial planning professional, who understands the science of investing. Evidence supports the conclusion that investors should be working with financial advisors. A recent Forbes article articulated the many reasons why a financial advisor can add significant value to managing your wealth.

"An international HSBC study, The Future of Retirement, in 2011 showed that those with financial plans accumulated nearly 250% more retirement savings than those without a financial plan in place. Furthermore, nearly 44% of those who have a financial plan in place save more money each year for retirement."

"Research by David Blanchett and Paul Kaplan of Morningstar, Alpha, Beta, and Now . . . Gamma, has attempted to quantify into real numbers the value that financial planners can provide. Their research shows that financial planners help individuals generate roughly 1.82% excess return each year, creating roughly 29% higher retirement income wealth. This means even if an adviser is charging a 1% fee a year for the management of retirement assets, the financial advice still has a huge impact on generating additional retirement income."

A Vanguard study demonstrated that advisors could add 3% to returns for investors. That is significant over the long run.

Search for a Servant Leader to Manage Your Wealth

Not just any investment advisor will do. It is important for investors to search out quality wealth managers, who understand the best practices of investment management and can act in a client's best interest. Search out wealth management professionals that take a holistic approach to managing wealth, and seek out the best possible solution for a client's specific needs. Someone who can act as a servant leader in the process of wealth management, who can take the time to walk you through the specifics of your situation and answer all of your questions concerning investment products and strategies with your interest in mind, not their own. Someone who can truly advise you to achieve your financial goals. It is also important to get clear on your values, and investment goals. For example, many investors with significant wealth have aggressive philanthropic goals, others want to invest with strict social responsibility mandates. Having a detailed plan that includes your values is essential to accomplishing the goals you have with your wealth.

It is important that investors not be swayed simply by education, certifications, or because they are aligned with a specific fund family or investment firm. I have met quality financial professionals across the spectrum, from brokers to registered investment advisors, and I have met poor financial professionals across the spectrum including some who claim to be fiduciaries. Focus on the individual who will be advising you and their approach to wealth management. If they can not answer simple questions such as how they get paid, then in my view, it is time to find another individual to advise you.


In this piece I have discussed the merits of evidence-based investing, and why it is superior to speculating in stocks. I have reviewed the research, and established that following a passive approach to investing is superior to active management. I have also reviewed the research surrounding investment factors for investors who want to tilt their portfolio towards the sources of outperformance. Finally, I have reviewed the advantages of working with a financial professional, and attempted to quantify for investors the benefit of doing so. In my final piece I will provide quantitative tools for investors to analyze active managers for luck versus skill and see what role, if any, active management can play for investors.

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. 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.