You've worked hard, saved like mad, and invested your life savings in the stock market. Sure, you've earned pretty good returns thanks to the long bull market, but not without enduring gut-wrenching volatility.

Chances are, you've questioned whether the returns you've earned are enough to justify the risk more than once over the last several years. Could there be a better way? A way to earn better returns with less risk using the power of math and mountains of empirical data? Well, maybe. There are no guarantees, of course, but a factor investing strategy holds the promise of squeezing incremental returns out of your portfolio for the same (or less) risk.

### Basic Factor Investing Series

__Introduction to Factor Investing__- Popular Multi-Factor Models (3, 4, and 5 factor models)
- How to Tell Good Factors From Bad: Taming the Factor Zoo
- How Do We Know Factor Premiums Will Persist?
- In Depth: Beta
- In Depth: Size Factor
- In Depth: Value Factor
- In Depth: Momentum Factor
- In Depth: Quality Factor
- In Depth: Low Volatility Factor
- Other Factors You Can Probably Ignore
- Fundamentals of Factor Portfolio Construction
- How to Calculate Your Portfolio's Factor Loadings (Exposure)
- Best in Class Factor Funds and ETFs
- Four Sample Factor Portfolios

### What is Factor Investing?

The core tenant of factor investing is that there are multiple **independent **sources of risk and return for stocks above and beyond *market beta*, which is defined as the risk and return attributable to investing in the stock market as a whole. This implies you can, in fact, beat the market. The bolded word *"independent"* above is important for diversification purposes, and we'll get more into why later.

In years past, the prevailing logic has gone something like this:

- Investing in the stock market is risky.
- People will not risk their money unless they are likely to be compensated with higher returns for taking that risk.
- Stocks must be priced low enough so that future returns are likely to offer a significant premium over the alternative, which is to invest in risk-free assets such as Treasury Bills.
- If the price of stocks are too high relative to risk-free alternatives, prices will fall (i.e. a market crash will occur). If they are priced too low, prices will increase (i.e. an extended bull market will occur). In this way, stocks should always be more or less priced to deliver better long-term returns than bonds.

This logic has proven to be correct. While there have been extended periods where bonds have out-performed stocks, in the long run stocks in this country have always won. But the above logic doesn't tell the whole story. It turns out there are other sources of risk and return beyond just the generic risk and return of investing in equities, and investors can tap into them. Some of them are probably familiar to you and have been around for ages, like *Size *(small companies as a group tend to outperform large companies as a group) and *Value *(cheap stocks as a group tend to outperform expensive stocks as a group). Others, like *Quality *and *Low-Volatility*, may be new to you.

In their excellent book on the subject Your Complete Guide To Factor Based Investing: The Way Smart Money Invests Today by Andrew L. Berkin and Larry E. Swedroe, the authors describe factors as the *"secret sauce"* of legendary investors like Warren Buffett and Peter Lynch, *"...the characteristics of stocks...that both explain performance and provide premiums...above market returns."* They are, in essence, *"a quantitative way of expressing a qualitative theme."*

### Why Factor Investing?

Why factor investing? Simply put, the prospect of higher returns and/or lower risk. A portfolio with a high **factor loading** on one of the mainstream factors mentioned below in addition to market beta can be expected to earn a higher return than a portfolio with exposure to market beta alone. And because these factors are generally **independent **from and uncorrelated with one another, combining exposure to multiple factors can decrease the volatility of a portfolio even while increasing the return. Let's take a look at the correlation between the most popular factors over a 15 year period.

**Fig 1: Global Factor Correlations, 2002-2017**

Size | Value | Quality | Momentum | Low Volatility | Beta | |
---|---|---|---|---|---|---|

Size | 1 | 0.17 | -0.13 | -0.13 | -0.09 | 0.02 |

Value | 0.17 | 1 | -0.49 | -0.49 | 0.20 | 0.16 |

Quality | -0.13 | -0.49 | 1 | 0.24 | -0.05 | -0.03 |

Momentum | -0.13 | -0.49 | 0.24 | 1 | 0.38 | -0.03 |

Low Volatility | -0.09 | 0.20 | -0.05 | 0.38 | 1 | 0.12 |

Beta | 0.02 | 0.16 | -0.03 | -0.03 | 0.12 | 1 |

_{Source: ResearchFactor}

The correlation coefficients in the chart above are a thing of beauty, a finance nerds dream! All of the factors have been uncorrelated with market beta as well as each other. And a few of the factors, like Value and Quality/Momentum, are negatively correlated with each other. *Factors represent the holy grail of portfolio diversification.* But a portfolio of uncorrelated assets that perform poorly isn't worth much. So how have they performed over time? The chart below lists the excess annual returns earned by a selection of popular factors over and above that attributable by market beta.

**Fig 2: Excess Annual Returns by Factor, US 1927-2015**

Premium | |
---|---|

Size | 3.3% |

Value | 4.8% |

Quality | 3.8% |

Momentum | 9.6% |

_{Source: Your Complete Guide to Factor-Based Investing: The Way Smart Money Invests Today by Andrew L. Berkin and Larry E. Swedroe}

Past data clearly shows it **has been** possible to construct a portfolio with both higher returns and less risk than the market. But as the saying goes, past returns are no guarantee of future results. And since these factor premiums reflect cost-less long-short portfolios you can't actually invest in (because investing in the real world entails cost), they significantly over-state the excess returns you can expect to actually earn from a multi-factor strategy. But still, if you can capture even just a fraction of the historical factor premiums over time, it could add hundreds of thousands of extra dollars to your portfolio by retirement.

So how do we know these excess returns will persist? How do we know the factors aren't just the result of data mining, ghosts in the data? This is a good question, and there's been a great deal of research on the topic. We'll dig deep into why it's likely the most popular factors are real and can be expected to continue earning excess returns in a future post. For now, we will use the logic of the Capital Asset Pricing Model (CAPM) and assert that since these factors represent real and unique economic risks to investors, you would expect them to earn a return premium to compensate for that risk. After all, the central tenant of the CAPM is that risk and return are intrinsically linked.

### What Are The Factors We Should Care About?

In 2011, John H. Cochrane coined the term "factor zoo" in a paper published in the Journal of Finance (pdf), referring to the constant stream of new investment factors discovered on an annual basis. Over the last two decades there have been hundreds of potential factors "discovered" and many subsequent attempts to sort the good from the bad. Which factors describe real sources of return premiums and which are the result of torturing the data into submission, members of Cochrane's so-called factor zoo? Check out *Taming the Factor Zoo: A Test of New Factors *by Feng, Giglio, and Xiu, June 2019 (pdf) for a detailed analysis of the technicals, but I prefer the intuitive framework put forth by Swedroe and Berkin in their book. In order for a factor to warrant your investment dollars, it must meet **all **of the following criteria:

**Provides additional explanatory power to the cross section of returns**- The factor must provide statistically significant explanatory power independent from and in addition to previously published factors. In other words, it must represent a unique source of risk and return over and above the current model, i.e. if the current model successfully explains 95% of the cross section of stock returns, this new proposed factor should push it to, say, 97%.**Provides a positive return premium**- A factor with explanatory power that doesn't help you achieve higher returns probably isn't valuable to your portfolio.**Persistent**- The factor premium has persisted across a long period of time in both bull and bear markets. The probability of a negative return premium should approach zero over long periods. Framing this in terms of the S&P 500 index (i.e. market beta), while the odds of a negative return in any given year are not particularly low, there are very few 20-year periods where stocks haven't earned a positive return. Thus, market beta is persistent.**Pervasive**- A factor that only exists in one country, or one specific type of asset, is much more likely to be an artifact of data mining than one that exists in all countries and in all or substantially all types of assets (i.e. bonds, commodities, sports betting, etc). If a factor exists across a broad swath of asset classes and markets, chances are it reflects something fundamental about the relationship between risk and return, human behavior, of both.**Robust to different formulations**- The factor should not be overly sensitive to how you define it. The value factor premium, for example, exists whether you define it as low price-to-earnings (PE), low price-to-book (PB), low price-to-sales (PS), or low price-to-cashflow (PCF). If a factor premium shows up under many reasonable formulations, it's more convincing than if it only shows up under one very specific formulation.**Investible**- A premium that can't be captured in the real world, be it because of transaction costs, taxes, etc, is not worth pursuing. Ideally, there should be a retail mutual fund or ETF available with significant exposure.**Intuitive**- There should be a logical reason you would expect the factor premium to exist. For example, the stocks of very small companies tend to be riskier than the stocks of large, established companies and you'd intuitively expect them to hold out the promise of higher returns to compensate for that risk. Otherwise, nobody would buy them. In this framework, the Size premium is not a free lunch but rather compensation for taking on additional risk.

There are 5 factors that unambiguously meet these criteria: **Value **(HML), **Size **(SMB), **Momentum **(MOM), **Quality **(QMJ), and of course **Beta **(Rm-Rf).

**Value**- Stocks with low prices relative to their earnings, book value, cash flow, etc tend to outperform stocks with high prices relative to those same metrics.**Size**- Stocks of very small companies tend to outperform stocks of very large companies over time.**Momentum**- Stocks that have performed well recently tend to continue performing well in the short term, and stocks that have performed poorly tend to continue performing poorly.**Quality**- Stocks of companies with strong profitability, that are growing, and are well managed tend to outperform the stocks of companies that lack one or more of those characteristics.**Beta**- Beta is simply the risk and return associated with owning the entire stock market. It is what you earn when you own a total stock market index fund.

### Can I Really Outperform the Market by 3-9% Annually By Investing In These Factors?

Unfortunately no, you can't. Factor premia are expressed in terms of cost-less long-short portfolios. A long-short factor portfolio "buys" stocks meeting the criteria under consideration and "shorts" stocks not meeting it. In that way, we can isolate the excess return due to the factor being measured from the return of the overall stock market, or beta.

Let's look at an example to understand how factor premiums are calculated. In their seminal 1992 paper in the Journal of Finance, Fama and French define the Value factor (HML) as the returns of stocks with high book-to-market ratios minus the returns of stocks with low book-to-market ratios. They do this by dividing the market into 3 segments. The 30% of stocks with the highest book-to-market ratios (that is, the stocks with the lowest price relative to accounting book value) are defined as value stocks and form the "long" portion of the portfolio. The 30% of stocks with the lowest book-to-market ratios (or, the stocks with the highest price relative to book value) are defined as growth stocks and form the "short" portion of the portfolio. The 40% of stocks between these two extremes are ignored. The value premium is calculated by subtracting the return of the second group from the first (return of cheap stocks - return of expensive stocks).

Because factors are expressed in terms of long-short portfolios, they are impossible to reproduce exactly because buying stocks incurs transaction costs and shorting stocks incurs interest expense. The best we small investors can hope for is to capture a fraction of the pure long-short factor premiums in our long-only portfolios.

### So What Kind of Factor Return Premium Can I Expect?

A factor loading of 0.20 on the non-beta factors would be considered a fairly strong tilt, meaning you could expect to capture roughly 20% of the full premium for each factor you target. But as you'll see in a future article in this series, even this moderate factor loading can be difficult to achieve across all the factors because some of the are negatively correlated with each other (see fig 1 above). For example, because the Value and Momentum factors are negatively correlated, it can be difficult to construct a portfolio that has large loadings on both at the same time. This is because stocks with strong Momentum characteristics tend to have negative Value characteristics, and vice versa. Thus, while it's relatively easy to obtain a 0.20 loading on two or maybe three factors, you probably won't be able to get deep exposure to four or five. Most investors end up constructing portfolios with significant exposure to one or two factors in addition to Beta (Size and Value are by far the easiest factors to tilt towards) and minor exposure to the others (Momentum and Quality, usually).

Beyond the practical portfolio construction issues, it's important to have conservative expectations about future returns. If all goes well and returns are higher than expected, great! But if the factor premiums turn out to be lower than they have been in the past, you don't want to have your financial plan dependent on earning large excess returns. To that end, I assume each of the historical factor premiums will be half as large going forward. Let's see what that looks like for a portfolio with realistic factor loadings that can be achieved using real ETFs.

Pure Annual Premium | Factor Loading | Excess Return | |
---|---|---|---|

Size | 3.3% / 2 = 1.65% | 0.20 | 0.33% |

Value | 4.8% / 2 = 2.4% | 0.20 | 0.48% |

Quality | 3.8% / 2 = 1.9% | 0.10 | 0.19% |

Momentum | 9.6% / 2 = 4.8% | 0.10 | 0.48% |

Total |
1.48% |

As you can see, a 1.48% return premium is a far cry from the 3-9% premiums advertised in the financial media. Still, 1.48% compounded over 20 or 30 years can mean hundreds of thousands of extra dollars in retirement. But nobody can predict the future, and the 1.48% figure is just a back-of-the-envelope estimate. The real premium could turn out to be 0.01%, or 5%, or any number in between. There are no guarantees here, just a reasonable likelihood of out-performance.

### What Are the Risks of Factor Investing?

There are two primary risks for factor investors. The first is tracking error regret. Like everything else in investing, there are no free lunches and no smooth rides. While these factor premiums are persistent and have a high probability of delivering excess returns over the long term, there **will be** long periods of under-performance for each of these factors, both individually and collectively. Will you be able to stay the course if your multi factor portfolio under-performs the market for a decade at a time? Years of missing out on big gains can beat even the best of us into submission. Warren Buffett himself was repeatedly accused of losing his touch in the late 90s when Berkshire Hathaway under-performed for just a few years during the tech boom. He stayed the course, but you and I are decidedly not Warren Buffett.

The second risk is the risk that the factor premiums themselves will decrease substantially or disappear over time. There is some risk here, to be sure. As these strategies become cheaper to implement and more and more money pours into them, it is likely the magnitude of excess returns will decrease over time. That's why I insist on cutting the historical premiums in half for the purposes of estimating future return premiums. However, since these factors reflect real economic risks, investors will continue to demand a risk premium to invest in them. We may end up getting 1% rather than 3%, but the premium should show up if we stay the course.

### Okay, I'm Convinced. Where Do I Go From Here?

Ready to get started building your own factor portfolio? Check out the rest of our factor investing series as we step you through the fundamentals of theory and practice. If you're feeling impatient, skip straight to our list of best-in-class factor ETFs and Sample Factor Portfolios (coming soon).

### Basic Factor Investing Series

__Introduction to Factor Investing__- Popular Multi-Factor Models (3, 4, and 5 factor models)
- How to Tell Good Factors From Bad: Taming the Factor Zoo
- How Do We Know Factor Premiums Will Persist?
- In Depth: Beta
- In Depth: Size Factor
- In Depth: Value Factor
- In Depth: Momentum Factor
- In Depth: Quality Factor
- In Depth: Low Volatility Factor
- Other Factors You Can Probably Ignore
- Fundamentals of Factor Portfolio Construction
- How to Calculate Your Portfolio's Factor Loadings (Exposure)
- Best in Class Factor Funds and ETFs
- Four Sample Factor Portfolios