Factor investing: value, momentum, quality, size and low volatility

Key takeaways

• A factor return is the return of a long-short portfolio: long the securities with the most of a characteristic, short those with the least, so the market's direction largely cancels out.
• The Fama French three factor model explains stock returns with the market, size (SMB) and value (HML); the five factor model adds profitability (RMW) and investment (CMA), and Carhart's four factor model adds momentum.
• Momentum is usually built as 12-1: the return from twelve months ago to one month ago, skipping the latest month because very short horizon returns tend to reverse.
• Regressing a fund's excess returns on factor returns gives its exposures (betas) and an intercept (alpha); alpha is only evidence of skill if it is statistically distinguishable from zero.
• Factor premia are rewards for bearing risk or behavioural error, and they come with drawdowns that can last years; crowded factors can also crash quickly when many holders unwind at once.

What a factor is

The capital asset pricing model (CAPM) says one thing should explain expected stock returns: exposure to the market, measured by beta. Decades of data rejected the strong form of that claim. Stocks with low prices relative to book value earned more than CAPM predicted, small companies earned more than large ones over long samples, and stocks that had risen over the past year kept rising for a while. Each of these patterns is a candidate factor.

A characteristic earns the name factor when it does two things. It must explain co-movement: stocks that share it tend to rise and fall together, which makes it a source of risk a portfolio can be exposed to. And, for the factors investors pay attention to, it must carry a premium: a long-run average return that is positive after accounting for the market. The debate about why premia exist splits into two camps. The risk view says value stocks are cheap because they are genuinely riskier in bad times, so the premium is compensation. The behavioural view says investors systematically overreact or underreact, and the premium is the reward for taking the other side.

The two views lead to different expectations. A risk premium should persist, because the risk does not go away. A behavioural premium may shrink once it is widely known and traded, because the mispricing gets arbitraged. The honest answer for most factors is some of each, which is why published premia tend to be smaller after publication than in the original papers.

Building a long-short factor portfolio

A factor return is measured with a long-short portfolio. Rank the investable universe on the characteristic, buy the top group, sell the bottom group short in equal dollar amounts, and record the return of the combination each month. Because the long and short legs are both full of stocks, the market's overall move largely cancels. What is left is the return to the characteristic itself. If cheap stocks rose 1.2 percent in a month and expensive stocks rose 0.5 percent, the value factor returned 0.7 percent, whether the market rose or fell.

Design choices drive results. The universe (all US listed stocks, or only the largest thousand), the breakpoints (top and bottom 30 percent, or deciles), the weighting (equal or by market capitalisation), the rebalancing frequency and the treatment of the smallest, least liquid stocks all change the return. Academic factors are usually value weighted and use breakpoints from NYSE stocks only, so that thousands of tiny companies do not dominate. Commercial indices often add sector neutrality, turnover limits and capacity screens.

A long-only investor cannot hold the short leg, so a smart beta fund is not the factor itself. It is the market plus a tilt toward the long side. That tilt captures only part of the premium, and in the factors where most of the premium historically came from the short side (shorting the most expensive or most distressed stocks), the long-only version captures less still.

The Fama French models and momentum

Eugene Fama and Kenneth French published the three factor model in 1993. It explains a portfolio's excess return over the risk-free rate with three factor returns: the market's excess return (MKT minus RF), small minus big (SMB) and high minus low book to market (HML). It absorbed most of the anomalies known at the time and became the standard benchmark in academic finance. In 2015 they added two more: robust minus weak profitability (RMW) and conservative minus aggressive investment (CMA), which together capture much of what practitioners call quality.

Momentum sits awkwardly in the Fama French framework, which does not include it, so most practitioners use Mark Carhart's 1997 four factor model: the three Fama French factors plus a momentum factor, often labelled UMD (up minus down) or WML (winners minus losers). The documentation of momentum itself is usually credited to Narasimhan Jegadeesh and Sheridan Titman in 1993.

The standard momentum signal is 12-1. For each stock, measure the return from the end of month t minus 12 to the end of month t minus 1, and ignore the most recent month. The skip exists because returns over one month tend to reverse, partly from liquidity and bid-ask effects, so including the latest month would mix a reversal signal into a continuation signal. Kenneth French's online data library publishes monthly returns for all of these factors for US and international markets, which is what most regressions use.

Measuring exposures with a regression

To see what a fund really holds, regress its monthly excess returns on the monthly factor returns over the same dates, usually 36 to 60 months. The slopes are the fund's factor loadings. A market beta of 1.05 means the fund moves about 5 percent more than the market. A positive SMB loading means a small cap tilt; a negative HML loading means a growth tilt; a positive MOM loading means it tends to hold recent winners. R squared says how much of the fund's month to month variation the factors explain.

The intercept, alpha, is the average monthly return left after subtracting what the loadings and factor returns predict. Alpha is the number managers want to talk about, and it is the number that is hardest to estimate. Its standard error depends on the residual volatility and the number of months. A rule of thumb: a t statistic (alpha divided by its standard error) below about 2 means the data cannot distinguish the alpha from zero at the usual 5 percent level.

Regressions describe the past, and loadings drift. A manager whose style changed, or whose leverage moved, will show unstable betas. Rolling regressions (for example 36 months, moved forward one month at a time) show whether the exposures are steady. They also catch a common fact pattern in due diligence: a fund that markets itself as a stock picker but whose alpha vanishes once momentum or quality is added to the model.

Crowding and factor drawdowns

Factor premia are averages over decades, and the path is rough. US value, measured by HML, underperformed growth for most of the period from the global financial crisis to 2020, a stretch long enough to end careers and close funds. Low volatility can lag badly in sharp rallies led by risky stocks. Size has spent long periods with no premium at all. An allocator who buys a factor should expect to sit through multi-year stretches of underperformance, and should decide in advance what evidence would mean the premium is gone rather than merely resting.

Momentum has a different failure mode: crashes. When markets rebound sharply after a fall, the stocks that fell most (the momentum short leg) rally hardest, and a long-short momentum portfolio can lose a large share of its value in weeks. The spring of 2009 is the textbook case, documented by Kent Daniel and Tobias Moskowitz. Their work shows momentum crashes cluster in high volatility rebounds, which is useful because it means the risk is partly predictable.

Crowding is the risk that too much capital holds the same positions. In August 2007, several large quantitative equity funds that held similar long-short books began deleveraging at the same time, and the selling hit everyone with similar holdings within days: the episode known as the quant quake. Signs of crowding include factor valuations far from their history (the spread between cheap and expensive stocks), rising short interest in the short leg, and high correlation between unrelated managers' returns.

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• NotebookFactor regression notebookA fund's excess returns on market, size, value and momentum: betas, alpha, t statistics, R squared and the attribution.Download