**The most of the risk premiums are better explained by tail-risk skewness (compared to volatility)… Related to multiple strategies.**

**Authors: **Lemperiere, Deremble, Nguyen, Seager, Potters, Bouchaud

**Title: **Risk Premia: Asymmetric Tail Risks and Excess Returns

**Link:** http://arxiv.org/pdf/1409.7720v3.pdf

**Abstract:**

We present extensive evidence that “risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry, Short Vol, Bonds, Credit) and their negative skewness. We find a clear exception to this rule: trend following has both positive skewness and positive excess returns. This is also true, albeit less markedly, of the Fama-French “Value'' factor and of the “Low Volatility'' strategy. This suggests that some strategies are not risk premia but genuine market anomalies. Based on our results, we propose an objective criterion to assess the quality of a risk-premium portfolio.

**Notable quotations from the academic research paper:**

"Classical theories identify risk with volatility σ. This (partly) comes from the standard assumption of a Gaussian distribution for asset returns, which is entirely characterised by its first two moments: mean μ and variance σ^2. But in fact fluctuations are known to be strongly non Gaussian, and investors are arguably not much concerned by small fluctuations around the mean. Rather, they fear large negative drops of their wealth, induced by rare, but plausible crashes. These negative events are not captured by the r.m.s. σ but rather contribute to the negative skewness of the distribution. Therefore, an alternative idea that has progressively emerged in the literature is that a large contribution to the “risk premium” is in fact a compensation for holding an asset that provides positive average returns but may occasionally erase a large fraction of the accumulated gains.

Our work is clearly in the wake of the above mentioned literature on skewness preferences and tail-risk aversion. We will present extensive evidence that “risk premium” is indeed strongly correlated with the skewness of a strategy but very little with its volatility, not only in the equity world – as was emphasised by previous authors – but in other sectors as well. We will investigate in detail many classical so-called “risk premium” strategies (in equities, bonds, currencies, options and credit) and elicit a linear relation between the Sharpe ratio of these strategies and their negative skewness. We will find however that some well-known strategies, such as trend following and to a lesser extent the Fama-French “High minus Low” factor and the “Low Vol” strategy, are clearly not following this rule, suggesting that these strategies are not risk premia but genuine market anomalies.

Compared to the previous abundant literature, the present results are new in different respects. First, at variance with most previous investigations (that mostly focusses on stock markets), we do not attempt to frame our empirical analysis within the constraining framework of asset pricing and portfolio theory, but rather let the data speak for itself. This is specially important when studying, as we do here, risk premia across a much larger universe of assets, where the notion of a global “risk factor” (generalizing the market factor in the equity space) is far from clear. Second, we introduce a simple way to plot the returns of a portfolio that reveals its skewness to the “naked eye” and suggests an intuitive and robust definition of skewness that is much less sensitive to extreme events. Third, our empirical conclusion that for a wide spectrum of “risk premia” strategies, skewness rather than volatility is a determinant of returns is, to the best of our knowledge, new, as is the finding that some investment strategies – like trend following – seem to behave quite differently.

We first start in Sect. 2 with the equity market as a whole and revisit the equity risk premium world-wide, and its (negative) correlation with the volatility. We then introduce our new, intuitive definition of skewness that we use throughout the paper and that we justify in the Appendix. We focus on the Fama-French factors in Sect. 3 and study the statistics of market neutral portfolios, including a “Low Volatility” portfolio. We move on to the fixed income world (Sect. 4), where we again build neutral portfolios. Sect. 5 is devoted to an account of risk premia on currencies (the so-called “Carry Trade”), and finally, in Sect. 6, to the paradigmatic case of selling options. We summarise our findings in Sect. 7 with a suggestive linear relation between the Sharpe ratio and the skewness of all the Risk Premium strategies investigated in the paper, and discuss some exceptions to the rule – i.e. positive Sharpe strategies with zero or positive skewness – that we define as “pure α strategies". "

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