Factor Evidence: Value, Quality, Momentum, Size

What each factor actually claims

A factor is a sorting rule — buy the cheapest stocks, or the most profitable, or those that have been rising — plus a claim about why the sorted group earns more than its risk warrants. Value says the ratio of price to fundamentals is too pessimistic: the evidence across countries and a century is that cheap portfolios beat expensive ones, and the argument for why is a mixture of distress risk (cheap companies are often cheap because they are levered and cyclical) and investors extrapolating recent bad news too far. Quality sorts on profitability, earnings stability, growth and payout, and its claim is the mirror image: good businesses are persistently cheap relative to what they earn, because the market prices their durability wrong. Momentum sorts on the last year of returns and claims that information diffuses slowly — underreaction to news, then eventual catch-up — which is the one factor whose risk story is the weakest and whose behavioural story is the strongest. Size says smaller companies earn more, and the honest summary is that the premium was clear in early samples, weaker since, and entangled with liquidity and illiquidity costs that a small investor pays more of than an institution does. Two shared caveats belong in the account. First, factors are defined with respect to a model: a portfolio of cheap stocks does not need to beat the index, it needs to beat what the index would have earned with the same sensitivity to value, growth, size and momentum. Much of the popular complaint that a factor "stopped working" is a comparison against the wrong benchmark. Second, the factors are correlated with each other in cycles — value and momentum are famously negatively correlated, which is why combining them produces a smoother result than holding either, and why a single-factor investor experiences the worst of both. The four claims, in one line each — Value: cheap beats expensive: risk of distress plus over-extrapolation of bad news · Quality: good businesses are mispriced: durability is underrated and shows up as a persistent premium ← · Momentum: winners keep winning: slow diffusion of news, then catch-up · Size: small beats large: weakest of the four, and net of liquidity costs often absent A factor result is only as strong as the number of independent tests it survived. Sorting the same fifty years of data thousands of ways will produce a premium with a convincing t-statistic by chance, which is why publication bias and multiple testing belong in the judgement.

Why a known premium is not arbitraged away

The strongest objection to factor investing is that it is public, and therefore should be gone. The answer has two parts. The first is that some premia are compensation for risk you cannot avoid: distress risk in value, crash risk in momentum, and liquidity risk in size are real exposures that a holding period imposes on you, and the premium is the price of holding them. That is why the returns are lumpy and cluster in bad times — a premium paid in recessions is not free money. The second part is that arbitrage requires capital, and capital is scarce exactly when the opportunity is largest. A manager who is down 20% on a value trade in month eight faces redemptions and margin, whatever the long-run arithmetic says, so the mispricing can widen rather than close. Add shorting costs, the fact that the cheapest stocks are often the hardest to borrow, and the career risk of being wrong in a distinctive way, and there is a real limit to how much the premium gets competed away. This is the argument in the limits-to-arbitrage literature, and it is also the practical argument for diversification across factors rather than concentration in one. The implication for a portfolio is mechanical: the decision to hold a factor is a decision to hold a specific risk, so it belongs in the same framework as any other position — what is the exposure, what is the expected premium, what is the drawdown you must fund, and how does it correlate with everything else you own. A factor sleeve with a 4% expected premium and a 12% tracking error is a long-horizon position that needs a written policy about how long the horizon is and what you will do in year four. • The premium has to be compensation for a risk you can name, or mispricing you can explain surviving arbitrage. • Benchmark it against a model with the same factor exposures, not against the raw index. • A 4% edge against 12% tracking error means the path, not the mean, decides whether you stay invested. • Correlation between factors — value against momentum especially — is why combining them beats picking one. Costs and taxes are paid by the patient investor too. A long-short factor portfolio financed at a spread pays for its financing, and a long-only tilt pays in tracking error. Both belong in the expected premium before the position is taken.

How to test a factor claim you have just read

Start with the specification: what is the sorting variable, what is the holding period, and what universe was excluded. Most factor enthusiasm dies on the universe question, because results computed on stocks above a size floor do not transfer to the microcaps where the effect is usually largest, and cannot be captured at all once spread and impact costs are applied. Then the regression: the premium should survive controlling for market, size, value and momentum, and should not be concentrated in the smallest, least liquid decile. Then the timing: does the effect exist out of sample, in other countries, and in the periods after publication? Post-publication shrinkage is the norm rather than the exception, and a premium that has never worked outside one market and one era is a description of an era. Finally, the mechanism: if nobody can state a risk or a behaviour that would keep the anomaly alive, treat the finding as provisional however clean the t-statistic. The practical conclusion is that factor investing is a bet on a set of risk premia you can name, sized for the possibility that any one of them has a decade of underperformance, and combined so that the noise of the portfolio as a whole is less than the noise of its parts. The evidence is strong enough to use and not strong enough to be certain — which is the ordinary condition of investing, and the reason the position has to be sized for being wrong. A checklist for a factor claim — Specification: what is sorted, held for how long, on which universe, with what costs · Robustness: does it survive controlling for the other factors, out of sample, in other markets · Mechanism: a nameable risk or behaviour, not just a historical return difference ← · Sizing: a written horizon and a drawdown you can fund, since the path is noisy by construction Post-publication shrinkage is the rule. A premium reported as 6% a year in a 1970–2000 sample is a much smaller number once it has been published, traded and financed — and the honest planning figure is the shrunk one.

How a factor is actually built

A factor’s premium is not a property of the market that somebody discovers; it is the output of a construction, and the construction choices can move the number as much as the signal does. The standard recipe is short. At each measurement date, rank a universe of stocks on the characteristic, sort them into groups, hold the groups for a period, and compare the returns of the top and bottom. Every clause in that sentence is a decision. The first decision is **weighting**. Equal-weighting gives the smallest companies in each group a weight equal to the largest, so the measured premium carries a small-cap tilt that a value-weighted version does not have — and that tilt is often the difference between a paper premium and an investable one, because the smallest names are where the spreads are widest and capacity is thinnest. A premium that exists under equal weights and disappears under value weights is a premium that lives in stocks you cannot trade in size. The second is the **universe and the breakpoints**: which stocks are eligible, where the cuts fall, and whether the cuts are recomputed every period or fixed. The third is the **rebalancing frequency**, which sets the turnover — momentum sorts churn heavily and pay real costs, while a slow value sort rebalances cheaply. That turnover has to come out of the gross premium before it can be compared with anything. The fourth decision is the one that most often turns a real effect into an impossible one: **the data lag**. If a factor is built using book value or earnings for a period and applied from the beginning of that period, it uses information that was not yet published, and the resulting return could not have been earned. Requiring the accounting data to be available at the measurement date — a lag of a quarter at least — routinely cuts a factor’s measured premium. And underneath all of it sits the multiple-testing problem. With a large universe of candidate characteristics, cheap computing and a literature that rewards novelty, a number of published premia will look strong by chance alone. The replication record is instructive: many of the smaller, more exotic published factors shrink sharply when tested on fresh data, and the ones that survive are usually the old ones with an explanation attached. The right prior for a factor you have just read about is that its measured premium is an upper bound. That yields a short list of checks before believing any of it: does the effect survive both weightings, does it survive excluding the smallest names, does it survive a lagged construction, is the magnitude plausible against the turnover it requires, and is there a reason it should exist — a risk it compensates or a behaviour it exploits? A factor that passes all five is worth a place in the analysis. One that fails the third is a claim about the past that nobody could have funded. • Equal versus value weighting decides whether the premium lives in tradable names. • Turnover is a cost the gross premium has to clear before it is real. • The data lag is the difference between an effect and a backtest artefact. • Many published premia are the winners of a large search; treat the size as an upper bound. When a factor is described to you, the useful question is not what its premium is but how the portfolio was formed: weighting, universe, rebalancing and lag. Those four facts tell you whether the number could have been earned by anyone.

Sources

• The cross-section of expected returns and the factor zooFama & French (1992, 2015); Harvey, Liu & Zhu (2016), “…and the Cross-Section of Expected Returns”
• Value, momentum and the long droughts a real premium containsAsness, Moskowitz & Pedersen (2013), “Value and Momentum Everywhere”
• Quality as profitability, growth and payoutNovy-Marx (2013), “The Other Side of Value”
• Limits to arbitrage and why mispricing can persistShleifer & Vishny (1997), “The Limits of Arbitrage”