Size and Low Volatility
Two of the original documented effects. One has weakened substantially since publication; the other contradicts the basic risk-return relationship and has persisted.
MadStockAlerts Research · Updated August 29, 2026
What to take away
- The size effect held that small companies outperform large ones, adjusting for risk.
- It has weakened considerably since it was published in 1981.
- The low volatility anomaly is that low-beta securities have outperformed on a risk-adjusted basis.
- That directly contradicts what the basic asset pricing model predicts.
- The leading explanation is a constraint on the use of leverage.
MAD Academy Training Video · 0:45
Two Factors That Argue With Each Other
The size premium says riskier small companies pay more; the low-volatility anomaly says calmer stocks do. Both cannot be a pure risk story.
This lesson is part of a Stock Alerts + Tools plan.
The size effect and what happened to it
Research published in 1981 found that small companies had outperformed large ones by more than their higher risk explained. It became one of the original documented factors and is embedded in the standard three-factor model.
The effect weakened substantially in the decades afterwards. Explanations offered include arbitrage following publication, the growth of small-cap funds, and methodological issues in the original work including the treatment of very small and illiquid securities.
The last of these is worth stating carefully. The original samples included securities so small and thinly traded that the returns were difficult to realise after transaction costs, which is a recurring problem in factor research and is addressed in the transaction cost article.
Where size still appears to matter
- Interacted with quality: small and profitable has held up better than small alone.
- In markets other than the largest, where coverage and liquidity differ.
- As an explanatory variable in models rather than as a standalone strategy.
- In the very smallest deciles, where the returns are also hardest to capture.
The first item is the most substantive. Research finding that the size premium is concentrated among profitable small companies suggests the raw effect was partly a mixture of a genuine premium and a large number of unprofitable small companies dragging it down.
The low volatility anomaly
The capital asset pricing model predicts that higher beta earns higher expected return. Empirically the relationship has been flat or inverted: portfolios of low-beta, low-volatility securities have delivered similar or better returns with substantially less variability.
This is a direct contradiction of the model's central prediction, it has been documented across markets and across long periods, and it is among the more robust findings in the literature.
It is also the anomaly whose explanation is most widely agreed. Investors seeking higher returns who cannot or will not use leverage bid up high-beta securities instead, which raises their prices and lowers their subsequent returns.
Scroll the chart sideways to see all of it.
- Predicted by the model
- Observed
The leverage constraint explanation
- 1A investor wants a return above the marketThe textbook answer is to hold the market with leverage.
- 2Leverage is constrainedBy mandate, by regulation, by margin rules or by preference.
- 3High-beta securities substitute for itThey provide the desired exposure without borrowing.
- 4Demand raises their priceWhich lowers their expected return, and the reverse for low-beta ones.
The explanation predicts that the effect should persist even though it is known, because the constraint that causes it does not go away. That is a substantive difference from an anomaly attributed to an error, and it is consistent with what has been observed.
Capturing them, and what gets in the way
Both effects are documented in data and both are harder to capture than the data suggests, for reasons specific to each.
| Factor | The obstacle |
|---|---|
| Size | The premium is concentrated in the smallest and least liquid securities, where costs are highest |
| Size | Capacity is limited: a large allocation moves the prices it is buying |
| Low volatility | The strategy is crowded, since it is widely offered in fund form |
| Low volatility | It concentrates in a few defensive sectors, which is a sector bet as much as a factor one |
| Both | Long periods of underperformance, which is where the evaluation problem applies |
The fourth row is a real and current caveat. A low-volatility portfolio is frequently heavily weighted to utilities, staples and similar sectors, which makes it sensitive to interest rates in a way the factor description does not mention.
This is the general shape of the gap between a documented factor and a portfolio: the documentation describes a sorted long-short construction, and the implementable version is a long-only portfolio with constraints, costs and sector concentration.