Can an ordinary investor profit from extensive academic research on factors that reliably boost portfolio returns, across multiple time-periods, markets, and countries? This article says yes, it's possible, and provides examples using low-fee funds from high-quality firms. The focus of the article is primarily on stocks. For those so inclined, there's also a technical appendix with step-by-step methods for crafting one's own portfolio with a free web application for factor-regression.

*Acknowledgment*: Many of the ideas in this article were inspired by Andrew Ang's fine book, Asset Management, and by academic studies cited below, notably by Clifford Asness, Andrea Frazzini, and their collaborators. The seminal work in this area was by economists Eugene Fama and Kenneth French. While this article tries to follow their advice and findings, the interpretations are those of able2pay.com and are presented for information only.

## Investment Factors for Stocks

A related article, Diversify!, introduces the concept of investment factors for bonds, using term structure (years to maturity) and credit risk (possibility of default) to construct diversified portfolios. The core idea is that by deciding how to weight these two factors, one might design a better portfolio of bonds than by simply investing in the total bond market. Academics and professional investors have pushed the idea further, devising additional factors for bond investments. However, for most retail investors, the two primary factors suffice.

Similar ideas apply to stocks, but the investment factors are different. This article divides them into two groups: standard factors that are well founded in academic research, and new factors that have fewer published studies but merit consideration. If you wish, you can skip this material and scroll ahead to Practical Options, which suggests ways to implement these factors, ranging from exceedingly simple to somewhat complex.

The classic investment factors for stocks typically have cute TLAs (three-letter abbreviations). One factor, momentum, even has multiple TLAs. Depending on the author, it masquerades as UMD (up-minus-down) or WML (winners-minus-losers) or even MOM. The connotations are endless, even amusing. Here they are, connotations notwithstanding:

Are these factors equally important? "No," is the clear answer from the academic research. Size, by itself, has the smallest effect, and when used alone its benefit may be nil, at least in some periods or regions. Value makes a positive contribution, particularly for smaller companies. Momentum makes an even bigger contribution, and, as noted above, its potency rises when combined with value. At the risk of over-simplification, one might summarize it this way:

Meyer and Mrozik made a similar point in a compelling fashion. They classified stocks in three groups: "

"What about growth?" you might ask. Your investment firm or retirement plan very likely has so-called value-funds and growth-funds. Unfortunately, these names can be misleading. Often, a purported "value" fund is positive on value but negative on momentum, while a "growth" fund may be weakly positive on momentum and quite negative on value. Digging beneath the name is necessary, if one's goal is to capture the combined effect of value plus momentum. (The technical appendix at the end of this article describes an online app that can do the necessary analysis.)

An impartial reading of the primary factors is that they are useful but incomplete. They leave important questions unanswered. What about a company's profitability? Or its safety, as measured by its debt-burden or by its resilience in the face of recessions and inflation? Is it possible to fold momentum, value, and other factors into a single metric of quality at a reasonable price? There are new factors that aim to answer such questions.

Compared to research on the standard factors, however, published studies of the new factors are less plentiful, and the implications, less compelling. To no one's surprise, that hasn't stopped investment firms from marketing mutual funds and ETFs based on the new factors. Nonetheless, they may, in some cases, with appropriate cautions, be worth considering.

How important might these new factors be? The evidence seems to imply that they add significantly to returns in portfolios that already have the benefits of value and momentum. Making the point another way, suppose your investments consist of exactly the right funds to capture all the best that the standard factors could possibly offer, including favorable portions of value and momentum. Should you try to add the new factors? Although the research is in its early stages, the likely answer is affirmative.

However, correlations among the factors make it challenging to find the right mix. Sometimes a mild negative correlation means that more benefit from one factor brings a penalty from another. Other times, a moderately positive correlation means that aiming to add modest benefits from two factors is more potent than striving to maximize either one of them in isolation. Thus, a revision of the simplified advice might be:

Similar ideas apply to stocks, but the investment factors are different. This article divides them into two groups: standard factors that are well founded in academic research, and new factors that have fewer published studies but merit consideration. If you wish, you can skip this material and scroll ahead to Practical Options, which suggests ways to implement these factors, ranging from exceedingly simple to somewhat complex.

**Standard Factors**The classic investment factors for stocks typically have cute TLAs (three-letter abbreviations). One factor, momentum, even has multiple TLAs. Depending on the author, it masquerades as UMD (up-minus-down) or WML (winners-minus-losers) or even MOM. The connotations are endless, even amusing. Here they are, connotations notwithstanding:

*Market exposure*measures the extent to which a stock portfolio moves in concert with the rest of the stock market. Typically called "beta," this measure is 1.0 if the stock portfolio moves up and down in lockstep with the rest of the market. (OK, "beta" is four letters. But read on, because it's going to re-appear as part of a genuine TLA.)*Size*(SMB or small-minus-big) measures the extent to which the stocks of smaller companies outperform bigger ones. Originally reported by Banz in 1981, the size factor is nicely reviewed in Ang's section 7.3.2.*Value*(HML or high-minus-low) depends on the book (or economic) value of a company, compared to its price in the stock market. It's better for the market price to be a low multiple of the book-value (the stock is on sale, thus high-value) than the reverse (it's over-priced). A timely review of the value factor is available in Fact, Fiction, and Value Investing by Asness et al. (2015).*Momentum*(UMD, WML or just MOM) captures the tendency of winners to keep rising and losers to keep falling, in the near term. Note that momentum and value can oppose each other. To become high-value (on sale) the stock must have had negative momentum (it was marked down as a loser), at least for a while. But the two factors are not total opposites. A stock can have high value after some time as a loser, yet acquire near-term momentum, as investors discover its value and bid up the price. Finding high-value stocks on their way back up would be lovely, would it not? For a good, very readable review, see Fact, Fiction, and Momentum Investing by Asness et al. (2014).*Other*is the term used in this article for "alpha," the statistical factor you'll find in formal research. It refers to anything that systematically affects stock prices but is not captured by the other factors. It could be the skill of the portfolio manager; or some investment factor that academics haven't discovered yet; or a collection of macro factors (large economic influences) that happened to occur for the historical period covered in a particular study. In short, it's what matters that we don't understand. (Maybe the TLA should be IDK, for "I don't know.") *

Are these factors equally important? "No," is the clear answer from the academic research. Size, by itself, has the smallest effect, and when used alone its benefit may be nil, at least in some periods or regions. Value makes a positive contribution, particularly for smaller companies. Momentum makes an even bigger contribution, and, as noted above, its potency rises when combined with value. At the risk of over-simplification, one might summarize it this way:

*Go for small-value and momentum everywhere*.Meyer and Mrozik made a similar point in a compelling fashion. They classified stocks in three groups: "

*Fast-Winners*are stocks that gain value immediately after an investment.*Late-Winners*are stocks that eventually see price increases, but only after longer periods of sideways movements.*Value-Traps*represent stocks that continue losing value, and eventually might become worthless. Evidently, investors want to invest in Fast-Winners, delay their investments in Late-Winners, and avoid Value-Traps altogether." Cautioning that "there is no silver bullet that reveals whether a certain stock is a Fast-Winner prior to an investment decision," they recommend a strategy of "buying cheap stocks that have garnered positive price momentum." In short, go for the combination of value and momentum, rather than either factor in isolation."What about growth?" you might ask. Your investment firm or retirement plan very likely has so-called value-funds and growth-funds. Unfortunately, these names can be misleading. Often, a purported "value" fund is positive on value but negative on momentum, while a "growth" fund may be weakly positive on momentum and quite negative on value. Digging beneath the name is necessary, if one's goal is to capture the combined effect of value plus momentum. (The technical appendix at the end of this article describes an online app that can do the necessary analysis.)

**New Factors**An impartial reading of the primary factors is that they are useful but incomplete. They leave important questions unanswered. What about a company's profitability? Or its safety, as measured by its debt-burden or by its resilience in the face of recessions and inflation? Is it possible to fold momentum, value, and other factors into a single metric of quality at a reasonable price? There are new factors that aim to answer such questions.

Compared to research on the standard factors, however, published studies of the new factors are less plentiful, and the implications, less compelling. To no one's surprise, that hasn't stopped investment firms from marketing mutual funds and ETFs based on the new factors. Nonetheless, they may, in some cases, with appropriate cautions, be worth considering.

*Low Risk*or*minimum volatility*is a factor that measures an anomaly without fulling explaining it. Over time, stocks that have a lower "beta" or less volatility than average tend to have better returns. Why this happens is a puzzle academics are keen to resolve. For an investor concerned about the drama of stock-prices, capturing this factor would be most helpful. It would reduce fluctuations in portfolio value while increasing overall returns. How nice! I'll take it, even if no-one can fully explain the mechanism. Frazzini and Pedersen (2013) developed BAB (betting against beta) to capture the low-risk factor; Ang's section 10.4 has a comprehensive review, including his own metric (VOL) which measure a stock's volatility in the market rather than it's statistical beta.-
*Quality* (QMJ, or quality-minus-junk) is one proposal for accumulating all the investable attributes of a company into a single number. As defined in a working paper by Asness, Frazzini, and Pedersen (2013), QMJ measures the combined effects of a company's profitability (profits per unit of book value), growth (5-year change in profitability), safety (low volatility, debt-ratio, and credit-risk), and payout (fraction of profits paid to shareholders, whether in dividends or share buy-back). Others have proposed narrower factors for profitability alone, or earnings-growth, or prudent use of debt and payouts. This article uses the QMJ factor because it includes the more specialized factors, and because the working paper evaluates it systematically against an extensive, multi-decade database of U.S. and foreign markets. It's a reasonable way to quantify what most investors might want when seeking investments in "quality" companies.

How important might these new factors be? The evidence seems to imply that they add significantly to returns in portfolios that already have the benefits of value and momentum. Making the point another way, suppose your investments consist of exactly the right funds to capture all the best that the standard factors could possibly offer, including favorable portions of value and momentum. Should you try to add the new factors? Although the research is in its early stages, the likely answer is affirmative.

However, correlations among the factors make it challenging to find the right mix. Sometimes a mild negative correlation means that more benefit from one factor brings a penalty from another. Other times, a moderately positive correlation means that aiming to add modest benefits from two factors is more potent than striving to maximize either one of them in isolation. Thus, a revision of the simplified advice might be:

*Go for small-value plus all the combined momentum, quality, and low-risk you can get*.## Practical Options

This section enumerates some suggested ways to incorporate these factors into your stock portfolio. The options are ordered from exceedingly simple (listed first) to more complex (if you survive to the very end).

For all the options, it's important to be keenly aware of a caveat. No investment factor is static. It will vary over time. The benefit of value, momentum, quality, or low risk may be strong in some periods but weak or even negative in others. Don't expect a steady or immediate payoff. Over time, the benefits should accumulate, but it may take years. Because the factors are imperfectly correlated with each other, some may thrive while others languish. Thus, it makes sense to diversify across factors.

A very simple strategy that captures the value factor in U.S. stocks is to invest at Betterment.com. They have done the work for you, in advance. That said, there are some limitations. In addition to the value factor, you will most likely get some limited benefits of quality and low risk, but no momentum.

Betterment's goal was to create a portfolio whose returns equal the worldwide stock and bond markets, but with a preference for value in U.S. companies. Focusing on the just the ETFs they use for U.S. stocks, their portfolio has the factor-profile shown in the chart below. Their strategy captures 20% of the U.S. value factor, which is quite good, and smaller portions of quality (10%) and low risk (7%). On theoretical grounds, in a portfolio like this where stocks cannot be sold short, the maximum possible is about 50%. The captured results are statistically significant, when applied backwards to the last five years. Overall, Betterment's U.S. portfolio almost perfectly mimics the pattern of the total U.S. stock market (beta = 1.02); exceeds the total market on value, quality, and low risk; and is completely neutral on momentum. Their international portfolio (not shown here) was designed to mimic the total international stock market for most investors, without capturing specific factors. (The estimates for this example, along with similar ones generated for other options, were computed by a regression model available from Portfolio Visualizer. Details are in a technical appendix at the end of this article.)

For all the options, it's important to be keenly aware of a caveat. No investment factor is static. It will vary over time. The benefit of value, momentum, quality, or low risk may be strong in some periods but weak or even negative in others. Don't expect a steady or immediate payoff. Over time, the benefits should accumulate, but it may take years. Because the factors are imperfectly correlated with each other, some may thrive while others languish. Thus, it makes sense to diversify across factors.

**1. Invest at Betterment.com**A very simple strategy that captures the value factor in U.S. stocks is to invest at Betterment.com. They have done the work for you, in advance. That said, there are some limitations. In addition to the value factor, you will most likely get some limited benefits of quality and low risk, but no momentum.

Betterment's goal was to create a portfolio whose returns equal the worldwide stock and bond markets, but with a preference for value in U.S. companies. Focusing on the just the ETFs they use for U.S. stocks, their portfolio has the factor-profile shown in the chart below. Their strategy captures 20% of the U.S. value factor, which is quite good, and smaller portions of quality (10%) and low risk (7%). On theoretical grounds, in a portfolio like this where stocks cannot be sold short, the maximum possible is about 50%. The captured results are statistically significant, when applied backwards to the last five years. Overall, Betterment's U.S. portfolio almost perfectly mimics the pattern of the total U.S. stock market (beta = 1.02); exceeds the total market on value, quality, and low risk; and is completely neutral on momentum. Their international portfolio (not shown here) was designed to mimic the total international stock market for most investors, without capturing specific factors. (The estimates for this example, along with similar ones generated for other options, were computed by a regression model available from Portfolio Visualizer. Details are in a technical appendix at the end of this article.)

**2. Combine a Large-Cap Index with Mid-to-Small Value**

For U.S. stocks, there's a simple strategy to implement the advice given above to "Go for small-value, plus all the combined momentum, quality, and low risk you can get." The strategy is simple enough to implement in most investment and retirement accounts. Here's how:

- Put half your U.S. stocks in a large-cap index, such as the S&P 500 or Russell 1000.
- Invest the other half in small-cap value and mid-cap value, preferably in indexed funds. If a fund is not indexed and has high fees (more than, say, 0.4%), its costs may wipe out any factor benefit.
- Optionally, substitute an index of REIT stocks instead of mid-cap value. The rationale for this substitution is explained in detail in the post on long-run inflation.

The next chart shows the factor profiles for four different examples of this strategy. One uses Vanguard index funds, with the S&P 500 for large caps and CRSP indexes for small-cap value and mid-cap value. Another uses SPDR ETFs, all based on S&P indexes. Yet another uses the iShares version of an S&P 500 ETF, plus their small-cap value and mid-cap value ETFs based on Russell indexes. The final example, from TIAA, may resemble many 401(k) and 403(b) plans, where the selection of funds is more limited. Here, half goes to a Russell 1000 large-cap index, and, with no fund available for small-cap value, the rest goes to a non-indexed mutual fund for mid-cap value.

Across the four examples in the chart, there are more similarities than differences. On the size factor, they all exceed the broad U.S. market. That's neither surprising nor terribly important. Size is the factor that has the least impact by itself; capturing 20% or 30% of this small-to-zero effect is truly trivial. More important is whether it enables the portfolio to capture more of the other factors. And it does! Compared to the broad market, the portfolios with small-to-mid value all capture more of the value factor; one, TIAA, captures a bit more momentum; and all except TIAA gain on the quality factor. On low-risk, they all resemble the broad market. Finally, it's good that none of them has any unexplained ("other") effects. Presuming the academic research to be correct, the findings in the chart imply that portfolios like these will have favorable returns compared to the broad U.S. stock market, if given enough time.

Using factors to construct a globally diversified portfolio is hard. Very few funds are available that meet the joint criteria of low fees, ready availability, and positive factor-weights. An example of the problem is Vanguard's International Value Fund. It is available only if you have a Vanguard account, and, despite its name, only captures 11% of the non-U.S. value factor. Even that slim effect is compromised by negative weights on momentum and low-risk. Better on all these points is the iShares MSCI EAFE Value ETF. An additional complication is that many of the most interesting funds, especially those claiming to offer low risk or high quality, such as Vanguard's promising Global Minimum Volatility fund, are very new. As a result, any estimate of their underlying factors is bound to be imprecise.

Because of these problems, we'll construct two portfolios as contrasting examples of using factors globally, and compare them to a simple benchmark. One example, the custom portfolio, is the result of an extensive search to find the best combination of a few, low-fee funds with positive factors overall, plus a trading history of at least three years. Being highly customized for stellar performance on recent data, this portfolio may be vulnerable to underwhelming results in the future (it may regress to the mean). In contrast, the standard portfolio is based on principles derived from the academic research, not on cherry-picking particular funds. This portfolio used option 2 above for the U.S., plus an international index for non-U.S. equities, and a global low-volatility fund to add the low-risk factor. An index of all investable equities worldwide was used as a benchmark for comparison. Here are the details:

**3. Select Globally Diversified Factors**Using factors to construct a globally diversified portfolio is hard. Very few funds are available that meet the joint criteria of low fees, ready availability, and positive factor-weights. An example of the problem is Vanguard's International Value Fund. It is available only if you have a Vanguard account, and, despite its name, only captures 11% of the non-U.S. value factor. Even that slim effect is compromised by negative weights on momentum and low-risk. Better on all these points is the iShares MSCI EAFE Value ETF. An additional complication is that many of the most interesting funds, especially those claiming to offer low risk or high quality, such as Vanguard's promising Global Minimum Volatility fund, are very new. As a result, any estimate of their underlying factors is bound to be imprecise.

Because of these problems, we'll construct two portfolios as contrasting examples of using factors globally, and compare them to a simple benchmark. One example, the custom portfolio, is the result of an extensive search to find the best combination of a few, low-fee funds with positive factors overall, plus a trading history of at least three years. Being highly customized for stellar performance on recent data, this portfolio may be vulnerable to underwhelming results in the future (it may regress to the mean). In contrast, the standard portfolio is based on principles derived from the academic research, not on cherry-picking particular funds. This portfolio used option 2 above for the U.S., plus an international index for non-U.S. equities, and a global low-volatility fund to add the low-risk factor. An index of all investable equities worldwide was used as a benchmark for comparison. Here are the details:

*Custom*: equal allocations to Vanguard U.S. Value, Vanguard Strategic Equity, Vanguard International Explorer, iShares MSCI EAFE Value, and iShares ACWI Minimum Volatility (50% U.S., 50% non-U.S.)*Standard*: equal allocations to Vanguard S&P 500, Vanguard Mid-Cap Value, Vanguard Small-Cap Value, Vanguard Total International Stock Index, and iShares ACWI Minimum Volatility (70% U.S., 30% non-U.S.)*Benchmark*: Vanguard Total World Stock Index (52% U.S., 48% non-U.S.)

The chart above summarizes the results. The custom portfolio exhibited consistent, positive weights on all factors, and was stronger than the global benchmark on all except quality. The standard portfolio exceeded the global benchmark on every factor but retained some of the benchmark's exposure to riskier stocks. Though not obvious from the chart, the custom and standard portfolios both outperformed the benchmark during the four-year period on which data was available for the underlying funds. The margin of outperformance was similar, almost 3% more in compound annual returns plus a modest reduction in risk of loss. That's impressive!

In sum, it appears to be possible to construct simple portfolios, with just a few funds, that diversify across investment factors and, by doing so, deliver better returns with reduced risk. Despite the silliness of their TLAs, the academics may be onto something.

In sum, it appears to be possible to construct simple portfolios, with just a few funds, that diversify across investment factors and, by doing so, deliver better returns with reduced risk. Despite the silliness of their TLAs, the academics may be onto something.

## Technical Appendix

Portfolio Visualizer is a fine set of free, online tools with many strong points. But there are also some weaknesses. This section explains step-by-step how the tools were used for the findings reported above. You may be able to use them in a similar manner to customize your own portfolio.

Under the “Factor Analysis” menu at www.portfoliovisualizer.com, several options are listed. The most useful one is "Factor Regression." (On some pages, it's called “Fama-French Factor Regression,” which is a misnomer because, in addition to datasets from Eugene Fama and Kenneth French, it also uses one from Andrea Frazzini and Lasse Heje Pedersen.) The menu choices generally used for this article were these:

These choices enable one to estimate the factor-weights of a mutual fund or ETF, or an entire portfolio, by regressing their monthly returns against a dataset of the benchmark factor-returns. If you know what that means, great! Read on. If not, you should probably do some homework on this type of analysis before attempting to use Portfolio Visualizer.

A few other choices must be entered, and they deserve some comments:

On the site's home page, you’ll find an option to “Backtest Portfolio.” It may be useful for exploratory analysis on the long-run returns of various combinations of mutual funds and ETFs. But, be honest, this is data-mining and cherry-picking at its worst. What’s more, many of the funds and ETFs have a skimpy history, which makes optimization a charade. That said, it’s a quick, simple tool that generates useful tabular and graphical output.

The site also has a tool to “Backtest Asset Class Correlation.” Read the FAQs carefully, to be sure you know what’s used as historical data for an “asset class.” A number of the choices seem questionable, and none of them go back farther than the early 1970’s, even when such data would have been readily available from sources such as FRED or Shiller.

**Investment Factors**Under the “Factor Analysis” menu at www.portfoliovisualizer.com, several options are listed. The most useful one is "Factor Regression." (On some pages, it's called “Fama-French Factor Regression,” which is a misnomer because, in addition to datasets from Eugene Fama and Kenneth French, it also uses one from Andrea Frazzini and Lasse Heje Pedersen.) The menu choices generally used for this article were these:

- Tools
- Factor Regression
- Factor-Returns = Frazzini-Pedersen Factors
- Equity Factor Model = Four-Factor Model
- Include Quality Factor (QMJ) = Yes
- Include Low-Beta (BAB) Factor = Yes

- Factor Regression

These choices enable one to estimate the factor-weights of a mutual fund or ETF, or an entire portfolio, by regressing their monthly returns against a dataset of the benchmark factor-returns. If you know what that means, great! Read on. If not, you should probably do some homework on this type of analysis before attempting to use Portfolio Visualizer.

A few other choices must be entered, and they deserve some comments:

- Tools
- Factor Regression
- Regression Type
- Individual Assets, if you want factor-weights for each of several mutual funds or ETFs
- Portfolio, if you want a single set of factor-weights for the entire portfolio. This is the option used for this article.

- Start-Date & End-Date: Pay close attention to the dates on your output. You may get a default based on the newest fund or ETF in your portfolio. A short time-span will generate unreliable estimates. You will need many more months of data than the number of regression coefficients being estimated; 36 months is probably a minimum. On the other hand, funds and ETFs change, so recent data is better. Five years or 60 months of data would be a good standard.
- Stock Market: Of many options, the most useful are these: (a) use a portfolio of exclusively U.S. funds and select “United States,” or (b) use a portfolio of exclusively non-U.S. funds and select “Global x U.S.,” or (c) use an international mix of U.S. and non-U.S. stocks and select “Global.”
- Fixed Income Model: Leave it at “None” and omit all-in-one and bond funds from the analysis. Other settings rarely generate useful information in our analyses.

- Regression Type

- Factor Regression

**Mutual Fund and ETF Portfolios**On the site's home page, you’ll find an option to “Backtest Portfolio.” It may be useful for exploratory analysis on the long-run returns of various combinations of mutual funds and ETFs. But, be honest, this is data-mining and cherry-picking at its worst. What’s more, many of the funds and ETFs have a skimpy history, which makes optimization a charade. That said, it’s a quick, simple tool that generates useful tabular and graphical output.

The site also has a tool to “Backtest Asset Class Correlation.” Read the FAQs carefully, to be sure you know what’s used as historical data for an “asset class.” A number of the choices seem questionable, and none of them go back farther than the early 1970’s, even when such data would have been readily available from sources such as FRED or Shiller.

*Disclaimer*: Historical data cannot guarantee future results. Although a mixture of bonds, stocks, and other investments may be safer than investing exclusively in one class of assets, diversification cannot guarantee a positive return. Losses are always possible with any investment strategy. Nothing here is intended as an endorsement, offer, or solicitation for any particular investment, security, firm, or type of insurance. You are responsible for your own investment decisions. Please read our full disclosures and Fiduciary Oath.

* Sometimes, researchers formulate a statistical analysis in a way that leads to a different interpretation of alpha. It becomes a metric for the incremental value of an additional, new factor on the "left hand side" of a regression, after removing the covarying effects of other factors on the "right hand side." For example, the model might ask, "Can momentum and value explain the apparent effects of low volatility? Or is there something more?" If there's indeed something more, it shows up in the alpha (or intercept) of the regression model.