Financial theory assumes that higher risk is compensated on average by higher returns. However, the outperformance of low volatility stocks during the last 50 years has been among the most puzzling anomalies in equity markets. At the same time, low risk investing has recently gained a remarkable interest, due to its documented performance coupled with the unprecedented volatility experienced during the last global financial crisis. In our work we show how researchers have been documenting such anomaly since the early nineties: Fama and French (1992) show a rather negative relationship between risk and returns, and Baker and Haugen (1991) find significant reduction in volatility with no reduction in returns, for US minimum variance portfolios. We find that most of the relevant empirical studies focus on total or systematic volatility; some of them state that the low risk anomaly holds regardless of which of the two measures is used for stock selection. Only few exceptions instead (Ang et al, 2006) rather refer to idiosyncratic volatility. After reviewing empirical evidence, we discuss how literature has so far explained such an anomaly. Among others, theories referring to leverage constraints are well represented: the idea behind is that investors willing to leverage and facing leverage constraints buy high beta stocks, thus lowering subsequent returns. In some other works where the mispricing belongs rather to behavioral bias, leverage constraints still prevent the anomaly from being arbitraged away. Other theories refer to delegated portfolio, benchmarking, and fund managers’ utility function. We also investigate explanations related to distribution of equity returns: skewness and convexity in particular. The intuition here is that returns of high beta stocks are usually characterized by positive skewness and by a convex relationship with market returns. These features inflate the price paid for those stocks, thus lowering subsequent returns. In the last section of our research, we annex a formal description of two Amundi investment processes (belonging to NextGen Equity Strategies) that successfully exploit this low risk anomaly: the Global Minimum Variance and the Global Smart Beta (risk parity).
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