Tuesday, January 28, 2020

Is the Fama-French Model Dead?

When I was in graduate school at Northwestern in the early 90s the hot financial topics were all related to finding and estimating risk factors: Arbitrage Pricing Theory via latent factors  (Connor and Koraczyk 1986), Kalman filter state-space models (eg, Stock and Watson 1989), and method of moment estimators (Lars Hansen 1982). These appealed to central limit theorem proofs, which is the academic dream, as math proofs decisively prove objective meta-knowledge, how to know important things. Learning such methods involved intelligence and hard work, promising an instant barrier to entry, and certainly not from those boorish B-school students who had much better parties but didn't know statistics, let alone measure theory.

Around that same time, Eugene Fama and Ken French were looking at the returns of low and high dividend stocks by simply sorting them and looking at the basic statistics of these portfolios (see here). While Fama was well-respected for his theoretical work on defining efficient markets and his seminal 1973 paper confirming the capital asset pricing model (ie, the CAPM), he seemed like one of those antediluvian economists who typified the 1970s. Indeed, if you read those old papers, you will be amazed by how simple they were--you can understand them on one read--making the many inevitable false-positives glaringly obvious (with hindsight).

But then in 1992 Fama and French published their blockbuster 3-factor model documenting that if you sort stocks first by size and then by beta there is no correlation between beta and stocks. The previous finding was the product of an omitted variable, size. That is, one might look at humans and find hair length inversely correlated with height: longer hair correlates with shorter humans. But if you note women have longer hair than men and control for that, the correlation goes away; hair has nothing to do with height.

Size and value were identified in the late 70s, often in accounting journals. Fama and French's analysis was simple but the results were too strong to dismiss, especially as Fama was not some accounting noob, but rather, someone who understood risk and expected returns. Fama and French hypothesized size and value premiums implied they proxied risks that affect investors but academics can't measure, just as we can see the effects of dark matter but not the dark matter itself.

Still, many researchers were burned by false findings, and value and size were discovered in the same naive way of simply finding a strong pattern and presuming it's real as opposed to an order statistic (see here DeBondt and Thaler's list of anomalies circa 1989). While F-F said they were risk proxies, it seemed ad hoc. Economic theory implies risk premiums in that the sine qua non of economics, the utility function, implies a risk premium in an if and only if relation (which implies B ⇒ A and A ⇒ B). [my take: the error here is applying it to an individual's wealth, it works great for ice cream and shoes.] Add to this 20 years where economists learned that the CAPM model had been proven ('a peer-reviewed fact,' they would say today), and you have a strong bias that is not going to be discarded after some simple analysis. You can identify such researchers in the past--many still plying their trade--by how they would introduce their findings via moment conditions (see Harvey and Siddique, 1999), or factor models that identify loadings, factor returns, and the price of risk, λ (see Ang et al 2006).

Yet size and value investing became popular. Dimensional Fund Advisers created a highly successful and influential quant shop, and size and value became ubiquitous as either fund signatures or risk factors, depending on the application. There were dark times, such as when the size factor faltered in the late 80s and mid-90s, or when value stocks got clobbered in the tech bubble, but they always came back: they were risky! The rigorous methodology of latent factors models, Kalman filters, and GMM, meanwhile, produced nothing practical in finance.

Simple models win in the long run, but the short run is always dominated by the obfuscators. Socrates and Jesus criticized the sophists and Pharisees, respectively, because these official intellectuals were sanctimonious hair-splitters, and missed the forest for the trees. Christian apologists were the foremost Medieval scholars, and though now apologist is a derogatory term for a dogmatic thinker, the key is that sophisticated reasoning has always been used to mask dogmatic thinking. Sophisticates use their superior knowledge to out-argue, not find the truth. Complex arguments that are long and hard to follow, and have the support of the most other intellectuals are impossible to rebut. No one is going to spend a lot of time understanding such arguments if they think it's all a waste of time, so everyone who could argue with them was a fellow-believer (eg, I originally wanted to be a macroeconomist, but quickly discerned it was pointless and so today I cannot give a thorough critique of dominant macro models).

Simple models are better at finding the truth because they are easier for others to replicate and test, and this is the best evidence of something that is true and important, because things that work tend to be copied over time. They also expose dopey reasoning and overfitting, because readers can understand them. Complexity does not overcome overfitting, it just hides it better. GMM estimators are rarely criticized for overfitting because it's too hard to tell, and when no one is getting caught for the world's oldest statistical sin you can be sure it is rampant (eg, when the UFC had a steroid problem no one was getting caught).

More importantly, there just are not that many really profound financial ideas one would call complex. Off the top of my head, I think about how volatility is proportional to the square root of time, Black-Scholes, or the convexity adjustment in forwards vs. futures for interest-rates. Yet, these can all be communicated in one sitting to a person who understands basic statistics. That's not true for the fancy methods above.

While the Fama-French approach thrived due to its simplicity, we are now in another dark time. Specifically, the 5-factor model introduced by Fama-French in 2015 has reported the following  monthly return averages for their factors (excluding the uncontroversial market risk premium):

Since publication, however, the results look like this (note: they should be positive):

Unlike prior dark times, we now also have a boatload of factors in addition to Fama and French's 5.  Overfitting is a perennial problem. Unlike 'big data' used by Amazon and Netflix, factor data is orders of magnitude smaller and grows very slowly, all the while many thousands of full-time researchers are looking at the same data for new patterns. They are all highly motivated to find new, better factors, and we all know what happens when you torture the data long enough. The simplicity of the 3-factor Fama-French model was not an equilibrium, as this invited many to ignore some factors and create their own (even Fama and French joined in, adding 2 more). There is now just as much tendentious and disingenuous reasoning among the factor promoters as there was with those old opaque and complex methods, we have just gotten used to it.

This especially goes for equity factors applied at hedge funds, which number at least 20 and include orthogonally estimated style factors but also industry factors that no one thinks have a return premium. Argument by authority is ubiquitous among authorities of all stripes, only among scientists, this tactic is masked by having multiple subtle assumptions justified by references to various well-cited peer-reviewed articles, each of which itself does the same thing, making it impossible to refute because no one has that much time. I have never seen a good argument for how these factors help manage risk, but I understand how they are very useful in explaining why returns were down last month. Pretentious and parochial jargon makes it easier for the common (ie, dumb) risk manager, senior executive, fund advisor, etc., to feel valuable: they know something outsiders do not understand, and those outsiders can't prove it's not blather.

No financial researcher agrees on the canonical set of factors or how best to proxy them.  While no one is suggesting Kalman filters, everyone has some subtle twist for their value factor, how to time factors, or their own creation. Failure now has led many to reexamine their factors, worried that they either overfit their models in the past or would be doing so now by changing them. The risk of jumping off a factor just before it rebounds is symmetric to the risk of holding on to one that will join price, accruals, and inflation betas in the history dustbin.

Monday, January 20, 2020


I was interested in calculating what the portfolio volatility would be for a portfolio given various correlation assumptions, and also the number of assets. So I took two portfolio of the S&P500 in two very different years: 2008 and 2017. The VIX had one of its highest average levels in 2008, at 31.5, while its lowest in 2017, at 11.0.  Because I'm interested in low vol portfolios, I took the stocks with below-average volatility from the prior year.  The statistics on these 250 stocks were as follows:

Lowest 250 vol stocks in S&P500


Both total volatility and correlation were about 3 times higher in the crisis year of 2008. This is because the total market volatility was so much higher. One could say correlations rise in bad times, but one could also say that mathematically, given a 'one-factor' model (the market), if the market has higher volatility its assets will have a higher correlation.

The equation I presented last week calculates portfolio volatility as follows:
  • Volatility (n assets, correlation c)=sqrt(avgVol^2/n + (n-1)/n*c*avgVol^2)
Here c is the average correlation, so the average of the correlation matrix off the diagonal. Volatility and correlation are taken from the same period here, that in the years 2008 and 2017.

In the equation, most of this diversification benefit happens rather quickly, with 90% of it coming after n=15. Given many people look at multiple factors, not just the market factor, this could make this formula less relevant. So I took all those 250 stocks and created thousands random of sub-portfolios to get an estimate of the actual, or empirical, volatility. 

Comparing this to the formula generated the data in the above chart: they are basically identical. You only see two lines because there are two sets of lines that overlap. In both scenarios, the 10 asset portfolio had insignificantly higher volatility than the 250 asset portfolio. While the correlations are quite different, generating different levels of diversification as a function of the number of assets, they both almost perfectly matched the simple formula.  

Bottom line: 10 assets really is enough.  

Wednesday, January 15, 2020

Helmut Schoeck's Envy

Helmut Schoeck published Envy in 1966. It remains one of the few systematic treatises on the subject and highlights a profound aspect of human nature. Envy is of keen interest to me because ever since I wrote my dissertation on the low volatility effect back in 1994, I have been interested in why. In standard economic theory, individuals are assumed to maximize their utility, which is independent of other's wealth. With this assumption, you get a risk premium, and it should be ubiquitous. The risk premium is actually quite rare, limited to a couple of asset classes (though not within them). For more on envy in economics, see here.

Envy is eternal and ubiquitous, but also taboo. This is because envy is one of those few vices that is neither an excess or deficit of virtue, in that cowardice and recklessness are a deficit and excess of the virtue courage. The literature defending the rationality and value of emotions usually excludes envy as irredeemable.

Thus, no one candidly admits to being envious. We really do not even have a word for sincerely saying, 'I envy John,' in that one can only say this in a way that implies a benign, emulative, or admiring variety of envy, rather than the invidious form.  We do not even like to analyze it very deeply.  For example, Schoeck notes that Herman Melville's Billy Budd is about a good man who arouses the envy of the ship's master-at-arms, motivating many spiteful actions. The book's theme is clearly about envy, yet of the many written analyses of the novel they rarely mention envy, and never focus upon it, but rather highlight evil or injustice

Ordinary language tends to conflate envy and jealousy, yet they are distinct emotions. A man can be jealous of another man because of their mutual affection for a woman, and here the rival is fungible and the beloved is not fungible. In envy, it is the other way around, resenting a rival, not because of a specific woman, but rather, that he can obtain a woman of that type.

Most observers of envy, from Aristotle on, have noted it is felt toward those with whom the subject perceives himself as in competition. We only feel envious of our peers, or who we consider being our peers. Thus, we do not envy a world-class athlete, in that we know we are simply not in that class of people. In medieval times you had peasants, knights, lords, and a king, while in Ancient Greece you had slaves, freedmen, metics, and the upper class. Envy was restricted to one's class and perhaps those in the class above.

Essence of envy

Schoeck presents some theories for the origin of envy, not all convincing. First, from our competition for parental resources. As the runt of the litter gets fewer parental resources, or the weak bird is left to naked fratricide in the presence of the mother, all children wish to dominate their parent's attention out of self-preservation. Yet this is the definition of jealousy, in that the instinct presupposes a non-fungible desired object: parental attention. Another cause mentioned is in keeping society well-functioning. In his view, without envy, people with power would be haughty and overbearing. Yet, simple reciprocal altruism would seem to be at play, in that a successful alpha baboon realizes that if they are too overbearing, their underlings can and will kill him (see Frans de Waal).

Another interesting cause of envy is the ignorance of chance. The most envy-ridden tribes do not possess a concept of luck. Everything is determined by spirits, fortune, or the 'evil eye.' In primitive societies, the success of others is equated with the betrayal of the tribe, because it could have only have occurred by leveraging evil spirits or stealing from others. A certain degree of rationality, or at least a freedom from a magical view of things, is required before the envious man can fully realize that the man he envies does not possess something which, but for the possessor's existence, he, the envious man, might otherwise have.

I see envy as the result of our base, animalistic, status-seeking human nature. When we focus on life on this Earth, we want status, and what that implies, justification. Only a high status can prove, to ourselves and others, that we are good, important, and admired. Status, alas, is in fixed supply. While this constraint can be ameliorated by the concept of having many status silos--football, math, Fortnight--ultimately there are a limited number of positional goods: lakefront property, the 'best' cars or vacations, and most importantly, attractive mates.

Note that our greatest suffering is not caused by physical pain or privation, but rather when the will of another inflicts it. This is because random accidents do not reflect on us as individuals, as they happen by chance to everyone. But suffering caused by another implies inferiority, in that the tormentor had the ability to force their will against ours. Our status is diminished when a malefactor successfully torments us, as it highlights our impotence, and thus, lack of status.

Utopia and Envy

The completely just society where envy is absent is doomed because it is based on the false premise that once there is justice, there will be nothing left for anyone to envy. This situation can never occur because man inevitably discovers something new to envy. Further, by raising envy to the status of virtue (as righteous resentment over injustice), political entrepreneurs are motivated to reveal new inequalities that are to blame for people's impotence. Thus we now have the virtue of intersectionalism, where a transgendered black man is more righteous than a cis-black straight man.

There are so many ways to align individuals at some point we realize the ultimate minority is the individual. Yet, when envy is elevated it inverts all values that compete, resulting in the de-individualization of individuals in the name of equality. Simple utilitarianism implies that justice for many is more important than for any one person, and so what counts are the superficial categories we consider 'diverse.' The individual is unimportant.

Most utopias presume that reducing inequality will eradicate envy, though in fact, the opposite is more certain. Utopias are places where people are so equal that they will only have less than others by conscious choice, the way I have less strawberry ice cream than my neighbor because I prefer chocolate. A sad fact of life is that equality of opportunity comes to grief because individuals do not all have the same ability to make use of their opportunities with comparable success. This is a more bitter experience than one for which one can blame others rather than one's self.

The most egalitarian societies, hunter-gatherer societies, actually have more envy that less egalitarian ones. This isn't obvious because their lack of wealth seems to imply they are not greedy, and thus, selfish like Westerners, but this is just wishful naïve thinking. There is no tribe where social harmony prevails because each man has as little as the next. For primitive egalitarian societies, envy is both a cause and an effect. Schoeck notes that such communities tend to have no conception of luck, and so see any objective relative prosperity as a sign of theft or alignment with evil forces. Schoeck discusses Native American, African, and Polynesian tribes, and note the strong social pressure for anyone better off to be lavish in hospitality and generous with gifts. He knows that if he fails in this, 'the voice of envy will speak out in the whispers of witchcraft' which would make his life very unpleasant.

Envy prevents people from accumulating the wealth needed to create technology, and thus the free time needed to create art, science, literature, and philosophy. A lack of differentiation makes more apparent one's inadequacies, in that some will be more clever, athletic, or brave. When people are made equal in endowments, the only reason for not attaining a higher status is within us, our character, our essence.

In earlier times, the upper classes were different in many objective ways. An elite's risk of starvation was insignificant compared to the peasant, reflected in the fact that they were 10 centimeters taller than a commoner in 18th century England; they could read, sometimes in foreign languages, which implied a great deal of useful education. Today those barriers are gone. Almost everyone knows how to read and write, the basics of mathematics and history, the poor are fatter than the rich, and height disparities between individuals of the same race are absent.

 Equality Increases Envy

Our unprecedented wealth and comfort should have led to less envy, in that we all have access to the knowledge that brings self-actualization and self-esteem, but instead, it has lead to greater envy. The poorly paid op-ed writer of your local newspaper considers themselves not just equal to the rich, but better informed and more articulate, as proven by their many eloquent and insightful essays. Their lack of status motivates envy because they feel just as worthy, as competent, as those who are doing better. David Brooks highlighted this in his book Bobos in Paradise.

Consider our very best intellectuals. One might think they have acquired wisdom, and so a sense of self-actualization and self-esteem. Yet professors in the social sciences are an unhappy lot, reflected in Sayre's law: 'academic politics is the most vicious and bitter form of politics, because the stakes are so low.' This is because only those at the top of each specialty have the power to confer prestige and honor on favored individuals, subjects, and style of discourse. They influence taste, favor certain methodologies, and define the boundaries of their disciplines. To be chief consecrator is the intellectual’s dream, and it only can be apportioned to a few.

The idea that men are intrinsically equal in every admirable trait, combined with the idea that all we need is nourishment, warmth, and education, is simply wrong. Sure, to be engaged in a desperate struggle for food and shelter is to be wholly free from a sense of futility, but such environments are rare for anyone reading this blog. The desire for praise is more imperative than the desire for food and shelter. Praise from the praiseworthy is beyond all rewards, why we are more hurt by the lukewarm approval of men we respect than the contempt of fools.

Social justice justifies not having many things so that others may not have them either. In the politics of envy, all that is needed is to promise the envious the destruction or the confiscation of assets enjoyed by others; behind that, there is no need to promise anything constructive. Thus it really does not matter how the government spends punitive taxation. As shown in primitive societies, when creative ambition is punished, you get stasis, not just in economic productivity, but everything else: art, literature, science.

Resentment is held to be a potentially morally justifiable emotion, whereas envy former is not.  Resentment may come from real injustice, such as slavery. Yet good reasons for resentment are few, edge cases, while much resentment comes from a desire to blame others for our inadequacies. A passionate obsession with inequality is an attempt to compensate for a lack of meaning in one's own life, and you can never get enough of what you don't need to make you happy.

It is easy to lie to ourselves about our motivations, creating a bad equilibrium, as poor hunter-gatherer societies show. These are not idyllic communes free of self-interest, but rather, ignorant and envious cultures. Social flourishing is most fruitful when envious considerations unencumber man's creative faculties. Envy is something that should be discouraged. Pride is a sense of worth derived from the perceived appreciation of others, while self-esteem derives from the belief that we are profoundly appreciated, as a unique individual, by those we profoundly appreciate. Note that such a feeling comes out of a relationship of individuals, not some aggregate metric of status.

While there is nothing wrong with having wealth or wanting more, this should be of secondary importance, and wisdom is all about priorities. We should be encouraged to appreciate excellence in others to build excellence in ourselves. This takes faith, in that we have to believe our excellence in character, even if not reflected in the current status hierarchy, is appreciated by someone we admire, if not now, then in the future.