与我们早先的研究推文不同的是，这个系列以类似期刊目录的形式为您介绍论文原文，但会分类呈现，且包含主要贡献和引用量等更多维度的信息。此外，对于知乎推文版本，点击文章题目，便可以直接进入文章官方主页。相比于横截面动量（大头来自 JF），低风险异象的核心论文来源更加均衡。此外，由于近年来备受关注，因而包括较多新文章，这些文章的引用量自然相对偏低。但早期的文献引用量则都非常可观。关于经典的低波动异象的梳理，可参见我们的系列推文（在公众号菜单栏选择“因子文献-低风险”即可）。此外，关于特质波动率异象的不对称性这类衍生研究，也未收录在本核心文献中（参见搞事情深度研究| 异质波动率之谜）。本文则包括广泛的低风险异象在内。
1. 异象的提出
[题目] The cross‐section of volatility and expected returns[作者] Andrew Ang, Robert J. Hodrick, Yuhang Xing, Xiaoyan Zhang[摘要] We examine the pricing of aggregate volatility risk in the cross‐section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book‐to‐market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.[核心贡献] 发现了低特质波动率异象。此研究正式拉开了低风险异象研究的序幕。[引用数] 3984（截至 2020/07/21）：21 世纪以来 JF 发表的最高引文章。作为 2006 年发表的文章，成为了 JF 史上最高引的 50 篇文章之一。[题目] Betting against beta[作者] Andrea Frazzini, Lasse H. Pedersen[期刊] Journal of Financial Economics[摘要] We present a model with leverage and margin constraints that vary across investors and time. We find evidence consistent with each of the model's five central predictions: (1) Because constrained investors bid up high-beta assets, high beta is associated with low alpha, as we find empirically for US equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures. (2) A betting against beta (BAB) factor, which is long leveraged low-beta assets and short high-beta assets, produces significant positive risk-adjusted returns. (3) When funding constraints tighten, the return of the BAB factor is low. (4) Increased funding liquidity risk compresses betas toward one. (5) More constrained investors hold riskier assets.此外，这篇文章在 beta 的估计、因子组合构造等方面都不同于经典方法（例如，采用不同时间的数据估计波动率和相关系数；构建因子组合时，采用 rank-weighted 而非通常的等权或市值加权；构造 beta 中性组合而非资金中性组合），也引发了后续不少争议。[引用数] 1566（截至 2020/07/21）
2. 其他风险指标
[题目] Stocks as lotteries: The implications of probability weighting for security prices[作者] Nicholas Barberis, Ming Huang[期刊] American Economic Review[摘要] We study the asset pricing implications of Tversky and Kahneman's (1992) cumulative prospect theory, with a particular focus on its probability weighting component. Our main result, derived from a novel equilibrium with nonunique global optima, is that, in contrast to the prediction of a standard expected utility model, a security's own skewness can be priced: a positively skewed security can be "overpriced" and can earn a negative average excess return. We argue that our analysis offers a unifying way of thinking about a number of seemingly unrelated financial phenomena.[引用数] 1286（截至 2020/07/21）[题目] Expected idiosyncratic skewness[作者] Bryan Boyer, Todd Mitton, Keith Vorkink[期刊] Review of Financial Studies[摘要] We test the prediction of recent theories that stocks with high idiosyncratic skewness should have low expected returns. Because lagged skewness alone does not adequately forecast skewness, we estimate a cross-sectional model of expected skewness that uses additional predictive variables. Consistent with recent theories, we find that expected idiosyncratic skewness and returns are negatively correlated. Specifically, the Fama-French alpha of a low-expected-skewness quintile exceeds the alpha of a high-expected-skewness quintile by 1.00% per month. Furthermore, the coefficients on expected skewness in Fama-MacBeth cross-sectional regressions are negative and significant. In addition, we find that expected skewness helps explain the phenomenon that stocks with high idiosyncratic volatility have low expected returns.[核心贡献] 指出预期特质偏度同股票未来收益显著负相关。[题目] Maxing out: Stocks as lotteries and the cross-section of expected returns[作者] Turan G. Bali, Nusret Cakici, Robert F. Whitelaw[期刊] Journal of Financial Economics[摘要] Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX reverses the puzzling negative relation between returns and idiosyncratic volatility recently shown in Ang et al., 2006, Ang et al., 2009.[核心贡献] 指出单日最大收益指标 MAX 同股票未来收益负相关且可以解释特质波动率效应。作者们将此称作“彩票需求”（lottery demand），并激发了随后的一系列讨论。[题目] Betting against correlation: Testing theories of the low-risk effect[作者] Cliff Asness, Andrea Frazzini, Niels J. Gormsen, Lasse H. Pedersen[期刊] Journal of Financial Economics[摘要] We test whether the low-risk effect is driven by leverage constraints and, thus, risk should be measured using beta versus behavioral effects and, thus, risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, with only volatility related to idiosyncratic risk. We introduce a new betting against correlation (BAC) factor that is particularly suited to differentiate between leverage constraints and behavioral explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment.[核心贡献] 将 BAB 因子拆分为了 BAC 和 BAV 以检验关于低 beta 异象的“杠杆约束”和“彩票需求”两类假说，并指出 BAC 因子主要与保证金负债有关，因而支持低 beta 异象的“杠杆约束”解释。[题目] Idiosyncratic risk and the cross-section of expected stock returns[期刊] Journal of Financial Economics[摘要] Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.[核心贡献] 指出 AHXZ (2006) 的发现并不能作为低特质波动率效应的证据。相反，基于指数 GARCH 模型估计预期的特质波动率，可以发现其同股票未来收益显著正相关。[引用数] 1158（截至 2020/07/21）[作者] Paul Schneider, Christian Wagner, Josef Zechner[年份/卷数] 2020, forthcoming[摘要] This paper shows that low‐risk anomalies in the capital asset pricing model and in traditional factor models arise when investors require compensation for coskewness risk. Empirically, we find that option‐implied ex ante skewness is strongly related to ex post residual coskewness, which allows us to construct coskewness factor‐mimicking portfolios. Controlling for skewness renders the alphas of betting‐against‐beta and betting‐against‐volatility insignificant. We also show that the returns of beta‐ and volatility‐sorted portfolios are driven largely by a single principal component, which in turn is explained largely by skewness.[核心贡献] 指出低风险异象源于投资者要求对协偏度风险的补偿，且期权隐含（事前）偏度可以很好地表征（事后的）剩余协偏度。当控制了偏度后，低风险异象不再显著。[题目] Cross-section of option returns and idiosyncratic stock volatility[期刊] Journal of Financial Economics[摘要] This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.[核心贡献] 发现特质波动率不仅对股票未来收益有显著负面的影响，还同 delta 对冲后的期权收益显著负相关。另外，本文一作 Jie Cao 就期权和特质波动率有不少研究，在其 2020 年的一篇最新 working paper 中还进一步指出，美股中特质波动率效应存在显著的日历效应（每月第三周最为显著，因第三个周五是期权到期日，实值期权的自动行权会诱发卖压，特质波动率高的股票相关卖压越大，从而加剧了特质波动率异象）。[题目] Left-tail momentum: Underreaction to bad news, costly arbitrage and equity returns[作者] Yigit Atilgan, Turan G. Bali, K. Ozgur Demirtas, A. Doruk Gunaydin[期刊] Journal of Financial Economics[摘要] This paper documents a significantly negative cross-sectional relation between left-tail risk and future returns on individual stocks trading in the US and international countries. We provide a behavioral explanation to this anomaly based on the idea that investors underestimate the persistence in left-tail risk and overprice stocks with large recent losses. Thus, low returns in the left-tail of the distribution persist into the future causing left-tail return momentum. We find that the left-tail risk anomaly is stronger for stocks that are more likely to be held by retail investors, that receive less investor attention, and that are costlier to arbitrage.[核心贡献] 指出以 VaR 为代表的尾部风险同股票未来收益显著负相关。3. 彩蛋
[题目] Betting against betting against beta[作者] Robert Novy-Marx, MIhail Velikov[年份/卷数] 2018. Available at SSRN.[摘要] Frazzini and Pedersen’s (2014) Betting Against Beta (BAB) factor is based on the same basic idea as Black’s (1972) beta-arbitrage, but its astonishing performance has generated academic interest and made it highly influential with practitioners. This performance is driven by non-standard procedures used in its construction that effectively, but non-transparently, equal weight stock returns. For each dollar invested in BAB, the strategy commits on average $1.05 to stocks in the bottom 1% of total market capitalization. BAB earns positive returns after accounting for transaction costs, but earns these by tilting toward profitability and investment, exposures for which it is fairly compensated. Predictable biases resulting from the paper’s non-standard beta estimation procedure drive results presented as evidence supporting its underlying theory.[核心贡献] 指出 BAB 因子的优异表现来自于其因子定义中的特殊处理。接下来两篇不是低风险异象。总体而言，他们的结论更接近“高风险高收益”的经典结论。[作者] Andrew Ang, Joseph Chen, Yuhang Xing[期刊] Review of Financial Studies[摘要] Economists have long recognized that investors care differently about downside losses versus upside gains. Agents who place greater weight on downside risk demand additional compensation for holding stocks with high sensitivities to downside market movements. We show that the cross section of stock returns reflects a downside risk premium of approximately 6% per annum. Stocks that covary strongly with the market during market declines have high average returns. The reward for beasring downside risk is not simply compensation for regular market beta, nor is it explained by coskewness or liquidity risk, or by size, value, and momentum characteristics.[核心贡献] 指出下行风险对股票未来收益有显著为正的预测力（严格来说，不算低风险异象）。[引用数] 1025（截至 2020/07/21）[题目] Tail risk and asset prices[作者] Bryan Kelly, Hao Jiang[期刊] Review of Financial Studies[摘要] We propose a new measure of time-varying tail risk that is directly estimable from the cross-section of returns. We exploit firm-level price crashes every month to identify common fluctuations in tail risk among individual stocks. Our tail measure is significantly correlated with tail risk measures extracted from S&P 500 index options and negatively predicts real economic activity. We show that tail risk has strong predictive power for aggregate market returns. Cross-sectionally, stocks with high loadings on past tail risk earn an annual three-factor alpha 5.4% higher than stocks with low tail risk loadings. We explore potential mechanisms giving rise to these asset pricing facts.
[核心贡献] 指出尾部风险同股票未来收益显著正相关。随后关于 tail risk 的研究多了很多，不同方法构造的 tail risk measures 同尾部风险的相关性不一。
[引用数] 452（截至 2020/07/21）
参见【044】More on Tail Risk: 风险越大，收益越低吗？