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The first references to a low-risk anomaly in financial markets date back to the report by Haugen and Heins [1972] and the paper by Black, Jensen, and Scholes [1972], In the first, the authors found empirically that the relationship between return and risk for U.S. equities between 1926 and 1969 had been much flatter than predicted by the capital asset pricing model (CAPM) with returns to portfolios invested in the lowest-risk stocks much higher than predicted by CAPM. Conversely, portfolios invested in riskier stocks had much lower returns than predicted by CAPM. In the second paper, the authors proved theoretically that in a world where leverage costs more than the risk-free rate, the relationship between return and risk must be flatter than predicted by CAPM. Since then, the evidence of the low-risk anomaly in equity markets has grown, with a vast number of papers documenting it both empirically and theoretically.
Recently, Baker and Haugen [2012] confirmed that the lowest-risk stocks outperformed in all observable markets in the world. For the U.S., the evidence spans 86 years of history and for most other markets there is evidence at least since the seventies. It has also been shown in a number of studies that neither the three-factor Fama and French [1992] model nor the four-factor Carhart [1997] model succeeds in explaining the positive alpha in low-risk stocks. Blitz, Falkenstein, and van Vilet [2013] reviewed the literature on the low-volatility anomaly. They listed the possible explanations put forward so far for the anomalous behavior of stocks, which CAPM did not predict.
Not all evidence is empirical. Theoretical evidence has been produced simply by analyzing the consequences of replacing some of the hypothesis behind CAPM with more realistic ones. The first example was the Black, Jensen, and Scholes [1972] paper mentioned earlier, looking at the impact of increasing the cost of leverage beyond the risk-free rate. Frazzini and Pedersen [2011] demonstrated that if agents have a constrained access to leverage limited to some multiple of their wealth, then stocks with the lowest risk, as measured by beta, must have positive alpha and stocks with the highest risk must have negative alpha. Blitz [2012] demonstrated that in a world with peereddelegated portfolio management, where...