AQR, a large hedge fund founded by famed investor Cliff Asness, uses a strategy of statistical arbitrage by taking a short position in stocks with high beta and a long position in stocks with a low beta. This strategy is known as a bet against beta. The theory is based on alleged inefficiencies with the capital asset pricing model, or CAPM, due to large funds being constrained in the type of leverage they can utilize and the risk they can take. Beta is a statistical measure of the risk of an individual stock or portfolio against the market as a whole. The phrase bet against beta was coined from a few economics papers written by the creators of the strategy.

## Beta

Beta is a measure of the risk that cannot be reduced by diversification. A beta of one means a stock or portfolio moves exactly in step with the larger market. A beta greater than one indicates an asset with higher volatility tends to move up and down with the market. A beta of less than one indicates an asset less volatile than the market or a higher volatility asset not correlated with the larger market. A negative beta shows an asset moves inversely to the overall market. Some derivatives such as put options have consistently negative betas.

## CAPM

CAPM is a model that calculates the expected return on an asset or portfolio. The formula determines the expected return as the prevailing risk-free rate plus the return of the market minus the risk-free rate times the beta of the stock. The security market line, or SML, is a result of CAPM. It shows an expected rate of return as a function of non-diversifiable risk. The SML is a straight line that shows the risk-return tradeoff for an asset. The slope of the SML is equal to the market risk premium. The market risk premium is the difference between the expected return on a market portfolio and the risk-free rate.

## Bet Against Beta Strategy

The basic bet against beta strategy is to find assets with higher betas and take a short position in them. At the same time, a leveraged long position is taken in assets with lower betas. The idea is the higher beta assets are overpriced and the lower beta assets are underpriced. The theory posits the prices of the stocks eventually come back into line with each other. This is essentially a statistical arbitrage strategy with the prices of the assets coming back to the median price versus risk. This median is defined as the SML.

A main tenet of CAPM is all reasonable investors invest their money in a portfolio with the highest expected excess return per unit of risk. The expected excess return per unit of risk is known as the Sharpe ratio. The investor can then leverage or reduce this leverage based on his individual risk preferences. However, many large mutual funds and individual investors are constrained in the amount of leverage they can use. As a result, they have a tendency to overweight their portfolios toward higher beta assets to improve returns.

This tilting toward higher beta stocks indicates these assets require lower risk-adjusted returns versus lower beta assets. Essentially, some experts believe the slope of the SML line is too flat for the U.S. market versus CAPM. This allegedly creates a pricing anomaly in the market in which some attempt to profit. Some economic papers doing historical backtesting have shown superior Sharpe ratios versus the market as a whole.

In examining this phenomenon, AQR has constructed market-neutral betting against beta factors that can be used to measure this idea. As a practical matter, the performance of this strategy suffers due to commissions and other trading expenses. As such, it may not be useful for individual investors. The strategy likely requires a large amount of capital and access to low trading costs to be successful.