There are certain authors whom’s papers you just have to read when they publish one. This week’s AGNOSTIC Paper is one of those. Whenever AQR writes about systematic investing, it’s (in my opinion) time to listen. This one is a very good overview about factor investing. Given that this is the intellectual basis of many things I do here on the website, it perfectly fits to the series.
Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.
Setup and Idea
Let’s start with the question what factor investing actually is. The idea emerged over decades of research from both academics and quantitative investors. The (very) short story goes as follows. An important (and back then breakthrough) insight of academic finance is that movements of the aggregate stock market actually explain a large part of individual stocks’ returns. So when you observe a 1% return for Apple, it makes sense to check the US market to understand where it comes from. Most likely, the market will also be positive in this situation.
For quite some time, academics thus concluded that the only thing that matters to select and evaluate securities is their co-movement with the aggregate market (the famous beta). The stronger the correlation, the more risky the asset, and the higher the expected return (in theory!). Said differently, the beta to the market should reliably explain differences in expected returns of securities.
Now, as we probably all agree on, beta is a good starting point but there is certainly more. I mean, people like Ben Graham and Warren Buffett practiced what is now called Value Investing before the academics did their correlation analysis. So at some point, the academics opened their framework to other factors than just the aggregate market. Most prominently, Fama & French (1992) show how stocks that look cheap versus fundamentals tend to outperform those that look expensive (the famous value factor). In addition to that, they find that small stocks tend to outperform large ones (the much debated size factor). With that, fundamental valuation multiples and companies’ market capitalization were born as new factors to explain differences in expected stock returns.
More generally, a factor is simply a characteristic of stocks (or other securities) that reliably explains differences in expected returns. For example, if you believe in the analysis of Fama & French, you can build a portfolio of small cap stocks that look cheap versus fundamentals (nowadays known as Small Cap Value) because these characteristics reliably predicted higher returns in the past.
The more relevant question, of course, is how to come up with such factors. Since we have chosen finance as our field, we don’t have the luxury of constant laws of nature. There are countless variables that potentially impact security prices. News, fundamentals, macroeconomics, Tweets from overconfident CEOs, wars, pandemics, you name it. Unsurprisingly, academics and practitioners therefore came up with hundreds of factors that are somehow related to stock returns. A phenomenon that is now known as the factor zoo.1I also participated in this game and produced a master thesis about how copy-paste in annual reports historically correlates with stock returns…
I know, this sounds somewhat unsatisfying from an econometric perspective. Data mining, p-hacking, overfitting – all those bad words come to mind… However, as the first fiction will show, there are ways to test factors on their robustness. For the most part, there is also a consensus among academics and practitioners that there aren’t hundreds of relevant factors. Most of them are different variations of just four or five underlying themes. To finally answer the question, factor investing means to systematically overweight securities with desirable factor exposure that reliably correlate with higher returns.
Data and Methodology
There is not so much to say about specific data or methodology. The paper is an overview about factor investing and some misconceptions around it. That said, the authors use a lot of data to back up their arguments. However, they mainly source this material from other research.
Important Results and Takeaways
Fiction: Factor investing is just data-mining
As I mentioned in the introduction, there are no physical laws that dictate factors. Most of them come from a combination of economic theory and statistical analysis. Especially the latter part frequently attracts criticism. There are countless variables that potentially explain stock returns and if you try long enough, you will almost certainly find some significant correlations by chance.2It may sound strange to do that but remember that incentives matter. Suppose you a are a PhD student and need to come up with a paper. Nobody wants to read about how a novel variable does not predict stock returns… Opponents of factor investing therefore often argue that it works fine in hypothetical backtests but not much beyond that.
This critique is not entirely wrong. Many backtests don’t survive rigor scientific standards and can be easily abused for marketing purposes.3It is more difficult to run a robust backtest than most people think. For example, you need to consider securities that disappeared during the sample period (survivorship bias) and ensure that you don’t hypothetically act on information that wasn’t available at the simulated point in time (look-ahead bias). However, the authors show that academics (and serious practitioners) developed two reliable tools to address this problem.
The first one is the out-of-sample test. The idea is simple. You take whatever factor you have and test it across as many different settings as possible. Different time periods, different ways of measuring the underlying idea, different geographies, and different asset classes. If you find similar results out-of-sample, you can be reasonably sure that there is indeed a plausible mechanism behind the factor. You can also combine that with more rigorous statistical tests. For example, while most fields are happy with a t-statistic of 2, you can increase this threshold to 3 (or more) for considering a factor as statistically significant.
The other tool is economic theory. It is much easier to stick with something if you not only know that it worked historically, but if you also have a plausible idea why it did (and may continue to do so). With respect to factors, there are generally two explanations. Either the other side of the trade is not perfectly rational and don’t recognize that they give up returns (behavioral explanations). Or the factor proxies some type of risk for which the higher return compensates (rational or risk-based explanations). There is an ongoing (and probably never ending) debate about which explanation prevails. The reality, however, is most likely somewhere in between and both explanations are to some extent active at the same time.
As this post is more of a general overview, I will not go into details about each factor. What is more important at this point: there are plausible explanations (rational and behavioral) for the most important factors out there. In fact, the authors argue that just four or five broader themes summarize most of the factor zoo (see list below). For those, there exists strong empirical evidence (rigorous statistical tests and out-of-sample results) and plausible economic intuitions why people may take the other side of the strategy.4AQR subsumes Low-Risk and Quality under the theme Defensive. Other quantitative managers treat the two as separate factors. The idea is the same, just labeled differently.
- Momentum: buy/sell assets that went up/down recently
- Value: buy/sell assets that look cheap/expensive versus fundamentals
- Low Risk: buy/sell assets that look safe/risky by common risk measures
- Quality: buy/sell assets of high/low fundamental quality
- Carry: buy/sell assets with high/low “carry”
To sum up the first fiction: some factors are certainly data-mined but academics and serious practitioners mostly agree on four or five well-researched themes with strong empirical and theoretical evidence. These are very unlikely to be data-mined!
Fact: Factors are risky
Although attractive over the long-term, the authors highlight that factor investing is not arbitrage. As for almost all active strategies, factor investing bears the risk of underperformance and may produce long and painful drawdowns. The most recent example is the current value-drawdown which began around 2018 and, despite a meaningful recovery in 2021 and 2022, has still not ended.
If you remember the discussion about possible explanations for factor premiums, riskiness is a feature not a bug. One reason why factor strategies worked (and may continue to do so) is a compensation for some type of risk.5Momentum strategies, for example, sometimes suffer from painful crashes that are difficult to handle. Similar to the general equity risk premium, however, living through painful drawdowns is necessary to capture the premium over the long-term. Financial markets rarely offer excess returns without some pain…
Fiction: Factor diversification doesn’t work
What I didn’t mention so far is that although factors are already attractive individually, they tend to be even better in combination (so called multi-factor investing). The idea is to focus on securities that score well on all of the above factors (integrated approach) or to combine different factors in a portfolio (mixed approach). The beauty of multi-factor investing comes from positive expected returns for each factor individually, and low or sometimes even negative correlation of factors among each other.6For example, long-short value and momentum strategies were historically negatively correlated. The combination of the two was therefore much better than each one individually. Finding negatively correlated assets is not difficult (you can always short the stock market). But finding negative correlation among strategies where each has a positive expected return for itself is difficult. Historically, multi-factor investing achieved this.
However, and this is the origin of this fiction, diversification does not always work (else we would call it alpha). For example, since the start of the value-drawdown around 2018, many multi-factor strategies also suffered because other factors couldn’t balance the losses from value. While still unsatisfying for factor investors during this period, the authors remind readers about the difference between diversification and hedging. The latter is specifically designed to help you when most needed (but usually costly!), whereas the former helps to improve a portfolios risk-return profile over the long term. And in this respect, the case for multi-factor investing a.k.a. factor diversification is as strong as ever before.
Fact: Factors work in different market regimes
This fact is closely related to the importance of out-of-sample tests. The authors cite compelling evidence that successful factor investing doesn’t require specific market environments. The themes from above historically worked during different periods, in different geographies, and across asset classes. In addition to that, the authors also show that factor performance is not very sensitive to macroeconomic environments. Especially when implemented with state-of-the-art risk management procedures.
Fiction: Factors don’t work anymore
Is this time different? Probably one of the most dangerous questions in investing and finance. Usually this question arises when something new heavily outperforms and breaks with any historical norms. The authors name the mania around internet companies in the early 2000s but more recently, the strong run of the ARK Innovation ETF after COVID certainly also qualifies.
What needs to be fulfilled that the time is indeed different for factor investing? Well, the reasons why it historically worked must go away. That means either all investors suddenly become perfectly rational and behavioral explanations break down. Or alternatively, the factor stops compensating the risk for which factor investors collect the premium. Both are certainly possible and existing factor strategies must be continuously refined to keep track with changing markets. However, the authors argue that its quite unlikely that the underlying drivers of the four main factors suddenly disappeared. So no, this time is (most likely) not different for factor investing.
Fact: Factors were and are not crowded
The next fact also addresses a very common question around factor investing. When all people know that value, momentum, defensive, and carry historically worked, why aren’t those factors arbitraged away? The idea makes sense: as soon as people recognize that those strategies earn excess returns they should pile in until the strategies become so expensive that any return premium disappears. The factor thus becomes too crowded. Empirically, however, this was and is not the case. For example, although we all know that value historically earned a return premium, the factor is currently very cheap relative to its own history. This is quite the opposite of crowding! Actually, most investors currently seem to hate the factor.
Another reason why factors should continue to work in the future despite being well-known was already given by the second fact. Factors are not arbitrage. Everyone wants to have a risk-free profit and true alpha opportunities therefore tend to be quickly arbitraged away. Factors, in contrast, compensate for bearing a certain type of risk or exploiting the imperfect rationality of some investors.7Remember Keynes, “Markets can stay irrational longer than you can stay solvent.” It is therefore not so easy to collect those premiums (see last fact) and therefore, it is absolutely possible that they exist despite being well-known.8We also all know that we should walk 10,000 steps per day and yet most people (including myself) don’t do it.
Fiction: Everyone should (and can) invest in factors
This is an easy one. Factor investing is an active strategy, so by definition, you deviate from the market-cap weighted passive market portfolio. Someone must take the other side of this bet and thus underweight factor strategies. The previous facts and fictions showed that there are plausible reasons why people may do this. So by construction, not everyone can be a factor investing.9As mentioned above, this really applies to all active strategies. For every value investor there must be a growth investor, for every trend-follower there must be a contrarian, and so on. Otherwise, you have no one to trade with.
Fact: Factor discipline beats factor timing
In the fact about crowding, the authors show that factors also become cheap or expensive over time. As soon as you have such a measure it becomes tempting to engage in factor timing. For example, given how cheap the value factor currently appears, it may deserve an overweight within a multi-factor portfolio. The authors, however, advocate against too much excitement. There is broad consensus that it is very difficult to successfully time the aggregate stock market. If this is true (and it probably is!), they argue that it should be even more difficult to time factor strategies because their composition is much more dynamic.
In fact, the authors show that a disciplined multi-factor strategy without timing is a very tough benchmark to beat. When valuations were at truly extreme levels, the chance for successful timing was historically somewhat higher, but it remains quite difficult. In another fiction, which I haven’t summarized separately, the authors also show that it is similarly difficult to (successfully) cut or add factor exposure during drawdowns and recoveries. The bottom line remains the same. Timing is difficult and you shouldn’t do it in most cases. But if things get really extreme, it may pay off to sin a little.
Fact: Sticking with factors is often difficult
This last fact is, in my opinion, a brilliant summary of everything else. Despite tons of academic and practitioner research, strong empirical evidence, and decades of life track records from systematic investors, being a factor investor is still not easy. There are plausible reasons why factor strategies should generate excess returns but that doesn’t safe us from prolonged periods of painful underperformance. Once again, this a feature not a bug. Similar to the general equity risk premium, living through volatility and painful drawdowns is the price we pay for attractive long-term returns.
So even though Warren Buffett is not the typical factor investor, his insights are (as so often) still valid: Investing is simple, but not easy.10The addition “typical” is important. In Buffett’s Alpha, the authors show that Buffett also bets on profitable factors. This doesn’t question his genius. He discovered the factors much earlier than the rest of us and turned them into an outstanding track record.
- AgPa #74: Peer-Reviewed Research is Not Helpful to Predict Returns – Really?
- AgPa #73: Country and Industry Momentum
- AgPa #72: Machine-Reading of Private Equity Prospectuses
- AgPa #71: Go Where the Earnings (per Share) Are
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|I also participated in this game and produced a master thesis about how copy-paste in annual reports historically correlates with stock returns…
|It may sound strange to do that but remember that incentives matter. Suppose you a are a PhD student and need to come up with a paper. Nobody wants to read about how a novel variable does not predict stock returns…
|It is more difficult to run a robust backtest than most people think. For example, you need to consider securities that disappeared during the sample period (survivorship bias) and ensure that you don’t hypothetically act on information that wasn’t available at the simulated point in time (look-ahead bias).
|AQR subsumes Low-Risk and Quality under the theme Defensive. Other quantitative managers treat the two as separate factors. The idea is the same, just labeled differently.
|Momentum strategies, for example, sometimes suffer from painful crashes that are difficult to handle.
|For example, long-short value and momentum strategies were historically negatively correlated. The combination of the two was therefore much better than each one individually.
|Remember Keynes, “Markets can stay irrational longer than you can stay solvent.”
|We also all know that we should walk 10,000 steps per day and yet most people (including myself) don’t do it.
|As mentioned above, this really applies to all active strategies. For every value investor there must be a growth investor, for every trend-follower there must be a contrarian, and so on. Otherwise, you have no one to trade with.
|The addition “typical” is important. In Buffett’s Alpha, the authors show that Buffett also bets on profitable factors. This doesn’t question his genius. He discovered the factors much earlier than the rest of us and turned them into an outstanding track record.