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Some investors are prohibited from using leverage, and other investors’ leverage is limited by margin requirements. Therefore, they over-weigh risky assets instead of using leverage, which makes these assets more expensive. High-beta and risky assets should, therefore, deliver lower risk-adjusted returns than low-beta assets. Investors could exploit this inefficiency by using ETFs (or futures) by “betting against beta”, i.e., by going long on a portfolio of low-beta countries (leveraged to a beta of 1) and short on a portfolio of high-beta countries (de-leveraged to a beta of 1). Research also shows this effect isn’t limited to country equity indices and stocks but also works well in other asset classes (even between asset classes).

Fundamental reason

The reason for the anomaly functionality was already stated in the short description – a lot of the investors are prohibited from using leverage, and their only way to achieve higher returns is to buy more risky stocks, which is the main cause for their overvaluation. Investors not facing these constraints could earn above-average returns by exploiting this phenomenon.

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Financial instruments

ETFs, futures

Confidence in anomaly's validity

Strong

Backtest period from source paper

1980-2009

Notes to Confidence in Anomaly's Validity

Indicative Performance

9.77%

Period of Rebalancing

Monthly

Notes to Indicative Performance

per annum, annualized monthly return (geometrically) of 0.78% (from table IX – return for long short portfolio)

Notes to Period of Rebalancing

Estimated Volatility

18.46%

Number of Traded Instruments

13

Notes to Estimated Volatility

Notes to Number of Traded Instruments

data from source paper from table 2, it is up to investor how many countries he/she would like to use

Complexity Evaluation

Simple strategy

Notes to Maximum drawdown

Notes to Complexity Evaluation

Simple trading strategy

The investment universe consists of all country ETFs. The beta for each country is calculated with respect to the MSCI US Equity Index using a 1-year rolling window. ETFs are then ranked in ascending order based on their estimated beta. The ranked ETFs are assigned to one of two portfolios: low beta and high beta. Securities are weighted by the ranked betas, and the portfolios are rebalanced every calendar month. Both portfolios are rescaled to have a beta of one at portfolio formation. The “Betting-Against-Beta” is the zero-cost zero-beta portfolio that is long on the low-beta portfolio and that shorts the high-beta portfolio. There are a lot of simple modifications (like going long on the bottom beta decile and short on the top beta decile), which could probably improve the strategy’s performance.

Hedge for stocks during bear markets

Partially - Low beta stocks and countries are usually safer during turmoil, and Beta Factor in Country Equity Indexes in a long-short variant can be used as a portfolio hedge against equity risk. However, caution should be used as the popularity of betting-against-beta investing could move valuation (measured by common valuation ratios like P/E, P/B, P/CF, etc.) of low beta countries into excessive-high (compared to neutral market valuation). This popularity of betting-against-beta factor investing and the high valuation of low beta countries can be then detrimental to their performance during market stress.

Source paper

**Frazzini, Pedersen: Betting Against Beta**

**- Abstract**

We present a model in which some investors are prohibited from using leverage and other investors’ leverage is limited by margin requirements. The former investors bid up high-beta assets while the latter agents trade to profit from this, but must delever when they hit their margin constraints. We test the model’s predictions within U.S. equities, across 20 global equity markets, for Treasury bonds, corporate bonds, and futures. Consistent with the model, we find in each asset class that a betting-against-beta (BAB) factor which is long a leveraged portfolio of low-beta assets and short a portfolio of high-beta assets produces significant risk-adjusted returns. When funding constraints tighten, betas are compressed towards one, and the return of the BAB factor is low.

Strategy's implementation in QuantConnect's framework
(chart+statistics+code)

Other papers

**Berrada, Messikh, Oderda, Pictet: Beta-Arbitrage Strategies: When Do They Work, and Why?**

**- Abstract**

Contrary to what traditional asset pricing would imply, a strategy that bets against beta, i.e. long in low beta stocks and short in high beta stocks, tends to out-perform the market. This puzzling empirical fact can be explained through the concept of relative arbitrage. Considering a market in which diversity is maintained, i.e. no single stock can dominate the entire market, we show that beta-arbitrage strategies out-perform the market portfolio with unit probability in finite time. We use the theoretical decomposition of beta-arbitrage excess return to provide empirical support to our explanation on equity country indices, equity sectors and individual stocks. Finally we show how to construct optimal beta-arbitrage strategies that maximize the expected return relative to a given benchmark.

**Berrada, Messikh, Oderda, Pictet: Beta-Arbitrage Strategies: When Do They Work, and Why?**

**- Abstract**

Contrary to what traditional asset pricing would imply, a strategy that bets against beta, i.e. long in low beta stocks and short in high beta stocks, tends to out-perform the market. This puzzling empirical fact can be explained through the concept of relative arbitrage. Considering a market in which diversity is maintained, i.e. no single stock can dominate the entire market, we show that beta-arbitrage strategies out-perform the market portfolio with unit probability in finite time. We use the theoretical decomposition of beta-arbitrage excess return to provide empirical support to our explanation on equity country indices, equity sectors and individual stocks. Finally we show how to construct optimal beta-arbitrage strategies that maximize the expected return relative to a given benchmark.

**Frazzini, Pedersen: Embedded Leverage**

**- Abstract**

Many financial instruments are designed with embedded leverage such as options and leveraged exchange traded funds (ETFs). Embedded leverage alleviates investors’ leverage constraints and, therefore, we hypothesize that embedded leverage lowers required returns. Consistent with this hypothesis, we find that asset classes with embedded leverage offer low risk-adjusted returns and, in the cross-section, higher embedded leverage is associated with lower returns. A portfolio which is long low-embedded-leverage securities and short high-embedded-leverage securities earns large abnormal returns, with t-statistics of 8.6 for equity options, 6.3 for index options, and 2.5 for ETFs. We provide extensive robustness tests and discuss the broader implications of embedded leverage for financial economics.

**Andricopoulos: Leverage As A Weapon of Mass Shareholder-Value Destruction; Another Look at the Low-Beta Anomaly**

**- Abstract**

The ‘low-beta’ or ‘low-volatility anomaly’ is one of the most researched in the field of ‘alternative beta’. Despite strong published evidence going back to the 1970s that high beta/volatility stocks underperform relative to expectations generated by the Capital Asset Pricing Model (CAPM), the anomaly still persists. The explanations given for this are all behavioural; that investor biases lead to overpricing of high volatility stocks. This paper shows that investor biases cannot be the explanation for the anomaly. Instead, it is proposed that the anomaly stems from a destruction of shareholder value. The strong implication is that the more market leverage a firm has, the more shareholder value is destroyed. Although the prevailing view for a long time has been that adding debt is good for shareholders, making balance sheets more ‘efficient’, there is in fact a considerable volume of evidence that the opposite is true; evidence which has been incorrectly interpreted for many years. Some possible mechanisms for this shareholder-value destruction are proposed.

**Hedegaard: Time-Varying Leverage Demand and Predictability of Betting-Against-Beta**

**- Abstract**

The leverage aversion theory implies that returns to the betting-against-beta (BAB) strategy are predictable by past market returns: An outward shift in investors’ aggregate demand function simultaneously increases market prices and increases the expected future BAB return. I confirm the prediction empirically and find that the BAB strategy performs better in times when and in countries where past market returns have been high. I construct timing-strategies that are long BAB half the time and short BAB half the time, based on past market returns, and show that these timing strategies have realized strong historical performance.