The low-volatility anomaly and betting against beta

Advanced9 min read · 5 sources

The low-volatility anomaly contradicts a basic principle of financial theory: more risk should bring more return. Historically, however, stocks with low volatility and low beta have achieved similar or even higher returns than risky stocks, with considerably less fluctuation. Research explains this mainly by the fact that many investors cannot or will not borrow, and are measured against benchmark indices.

What theory expects

According to the CAPM, a stock's expected return rises linearly with its beta, i.e. with its sensitivity to the overall market. This line is called the security market line. With a market premium of 5%, a stock with a beta of 1.5 should return around 7.5% more than the money market, and a stock with a beta of 0.5 only 2.5%.

Even early tests found the line to be too flat: stocks with low beta earned more than the CAPM predicts, and stocks with high beta less. Black (1972) provided a theoretical explanation: if you cannot borrow without limit at the risk-free rate, the equilibrium shifts and the line becomes flatter than in the standard model.

What the data shows

This is how Baker et al. (2011) sum up the finding for US stocks, calling it a contradiction of fundamental principles of financial theory. Ang et al. (2006) found exceptionally low average returns for stocks with high idiosyncratic volatility (i.e. high fluctuation that cannot be explained by the Fama and French factors), which could not be explained by size, valuation, momentum or liquidity.

Frazzini and Pedersen (2014) extended the view far beyond US stocks: high betas went hand in hand with low alpha, in US equities, in 20 international equity markets, in government bonds, corporate bonds and futures. This makes the anomaly not a chance finding in one market but a broad pattern.

Betting against beta: the strategy behind it

To measure the anomaly as a factor, Frazzini and Pedersen (2014) construct the betting-against-beta portfolio (BAB): it buys low-beta assets with leverage and sells high-beta assets, each side scaled to a beta of 1. The overall portfolio is thus market-neutral; its return measures only whether low beta is rewarded better than high beta.

Why does the anomaly exist?

Leverage aversion and borrowing constraints

The most important explanation from Frazzini and Pedersen (2014) and Asness et al. (2012): many investors are not allowed to borrow or do not want to. Anyone who wants more return therefore buys risky stocks instead of safe ones with leverage. This demand drives up the prices of high-beta stocks and lowers their future returns. Consistent with this, Frazzini and Pedersen found that BAB has weak returns when funding conditions tighten.

Benchmarks and fund managers

Baker et al. (2011) emphasize the role of benchmark indices: a fund manager who is supposed to beat an index takes on high tracking error with a low-volatility stock, without this paying off in the competition. As a result, the anomaly is hardly arbitraged away. On top of this, many investors have a preference for lottery stocks with a small chance of very large gains.

Compounding: part of it is mathematics

Part of the effect only shows up in wealth growth. Two stocks with the same average annual return grow at different rates if they fluctuate differently. The geometric mean lies roughly half the variance below the arithmetic mean (volatility drag).

Volatility or beta?

The two characteristics are closely related but not the same. Volatility measures the total fluctuation of a stock, beta only the part related to the market. A stock can fluctuate strongly but correlate little with the market. Then its beta is low and its volatility high. Research finds the anomaly in both variants: Frazzini and Pedersen sort by beta, Ang et al. (2006) by idiosyncratic volatility, i.e. the part of the fluctuation that factors do not explain. For a portfolio that is meant to fluctuate less overall, the total volatility of the stocks is the more practical criterion; for a market-neutral strategy, beta is.

Advanced: implementation and variants

• Minimum variance portfolios: an optimizer searches many stocks for the mix with the lowest fluctuation, usually with limits per stock, sector and country. Many minimum volatility indices work this way.
• Low-volatility selection: the least volatile 20% or 30% of stocks are selected and weighted equally or by inverse volatility. Simpler, but often more concentrated in individual sectors.
• Betting against beta: market-neutral, with leverage on the long side. This is hardly feasible for private investors and is more of a tool for researchers and hedge funds.
• Without leverage: a pure low-volatility equity portfolio has a beta below 1. It often lags in rising markets and shows its strength mainly in downturns. A comparison with the market should therefore be risk-adjusted (Sharpe ratio, alpha).

The anomaly also shows up in the weighting of entire asset classes: overweighting low-volatility assets with leverage is essentially the same as risk parity. Both rest on the assumption that risk is rewarded better per unit in safe assets.

Low volatility in your own portfolio

For private investors, there are two typical ways to use it. The first replaces part of the equity allocation with a low-volatility strategy in order to fluctuate less with the same equity allocation. The second, thanks to the lower fluctuation, holds a somewhat higher equity allocation for the same overall risk. That is the leverage idea of betting against beta, only without borrowing.

If you take this approach, you should check three things. First, the sector and country structure: has the portfolio unintentionally turned into a utilities or consumer staples fund? Second, the interest rate sensitivity, for example by comparing years with sharply rising rates. Third, the yardstick: against the overall market, a low-vol strategy almost always looks weak in strong stock market years. A fair comparison looks at the Sharpe ratio, the maximum drawdown and the alpha from a regression on the market.

Factor strategies often complement each other because they lead at different times. How strongly a low-vol fund is related to value, profitability or momentum factors is shown by a factor regression. A mix of several factors can smooth out the long phases in which a single factor lags.

Limitations and risks

• Sector bets: low-volatility stocks often come from a few sectors such as utilities, consumer staples and healthcare. A low-vol portfolio therefore carries sector risks that the strategy does not intend.
• Interest rate sensitivity: many of these stocks behave like bonds because their earnings are stable and their payouts high. Rising rates can hurt them particularly badly.
• Valuation: if the strategy becomes popular, valuations of low-volatility stocks rise and future returns fall.
• Long dry spells: in strong bull markets driven by risky growth stocks, a low-vol strategy can lag the market significantly for years.
• Data and overfitting: as with every factor, the warning from backtest overfitting applies: many variants have been tested, and not every metric holds up out of sample.

How Portfolio Lab calculates

Under Asset classes, there is “Equities world minimum volatility” (ticker @FAKTOR_MINVOL): a chained time series made up of a global minimum volatility index fund, before that a US fund of this kind and, for the early years, the fifth of US stocks with the lowest variance according to the Fama and French methodology, going back to 1963. The early parts are approximations and are marked as such. You can compare the asset class with a broad global equity portfolio in the Backtest.

The factor regression uses market, size, value, profitability, investment and momentum; it does not include a separate betting-against-beta factor. It does, however, show how much of a low-vol fund's return can be explained by these factors and what beta it has. In Optimization, the “Min. variance” objective corresponds to the basic idea of minimum variance indices. More in the asset classes methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.