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[原创] 对于目前流行的量化投资与smart beta策略的一些看法
恭喜行为经济学大牛Thaler教授荣获2017年诺贝尔经济学奖！他在行为金融学方面的贡献之一，就是和De Bondt教授发现了投资者倾向于过度反应的行为偏差（Does the Stock Market Overreact? 1985）。接着，Jegadeesh和Titman两位教授由于怀疑“过度反应”这种行为偏差的存在，“一不小心”发现了“动量因子”。历史就是如此的有趣！(Jegadeeshand Titman, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, 1993)。由于“动量因子”显著的超额回报率，数十年来一直是学术界经久不衰的研究课题之一，并经常与“反转因子”一起研究（下文会提到），两者共同构成了如今蓬勃发展的因子交易策略的基石。
让我们先来看看“动量因子”，其范围涉及各种资本市场，各种资产类型，各种时间跨度。例如：
- 关于S&P的: Style Momentum Within the S&P 500 Index (Chen and De Bondt, 2004) 和 Cross-Asset Style Momentum (Kim,2010)
- 美国行业/板块: Do Industries Explain Momentum? (Moskowitz and Grinblatt, 1999), Understanding the Nature of the Risks and Sources of Rewards to Momentum Investing (Grundy andMartin, 1998)
- 美国小盘股: Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies (Hong et al, 1999)
- 欧洲股票市场: International Momentum Strategies,(Rouwenhorst, 1997)
- 英国股票市场: The Profitability of Momentum Investing, (Lui et al, 1999), Momentum in the UK Stock Market (Hon and Tonks,2001)
- 中国股票市场: Contrarian and Momentum Strategiesin the China Stock Market: 1993-2000 (Kang et al, 2002), The “Value” Effect and the Market for Chinese Stocks (Malkiel and Jun, 2009), Momentum and Seasonality in Chinese Stock Markets (Li, Qiu, and Wu, 2010) 和 Momentum Phenomenon in the Chinese Class A and B Share Markets (Choudhry and Wu, 2009)
- 日本股票市场: Eureka! A Momentum Strategy that Also Works in Japan (Chaves , 2012)
- 澳洲股票市场: Do Momentum Strategies Work?: Australia Evidence, (Drew, Veeraraghavan, and Ye, 2004)
- 瑞士股票市场: Momentum and Industry Dependence (Herberger, Kohlert, and Oehler, 2009)
- 新兴股票市场: Local Return Factors and Turnover in Emerging Stock Markets, (Rouwenhorst, 1999)
- 前沿新兴股票市场: The Cross-Section of Stock Returns in Frontier Emerging Markets (Groot, Pang, and Swinkels, 2012)
- 全球股票市场: Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole, (Griffin et al, 2002), International Momentum Strategies (Rouwenhoust, 1998), The Case for Momentum (Berger, Isael, Moskowitz, 2009)
- 外汇市场: Do Momentum Based Strategies Still Work In Foreign Currency Markets? (Okunev and White, 2003), Interaction between Technical Currency Trading and Exchange Rate Fluctuations (Schulmeister, 2006), Momentum in Stock Market Returns: Implications for Risk Premia on Foreign Currencies (Nitschka, 2010), 和 Currency Momentum Strategies (Menkhoff et al, 2011)
- 大宗商品市场: Momentum Strategies in Commodity Futures Markets (Miffre and Rallis, 2007), The Strategic and Tactical Value of Commodity Futures (Erb and Harvey, 2006)
- 技术分析: 52-Week High and Momentum Investing (Georgeand Hwang, 2004).
- 公司盈利: Momentum Strategies (Chan et al, 2006), Firm-specific Attributes and the Cross-section of Momentum (Sagi and Seasholes, 2007)
- 在时间维度上: Market States and Momentum (Cooper, Gutierrezand Hameed, 2003), Time-Varying Momentum Profitability (Wang and Xu, 2010), Time Series Momentum (Moskowitz et al, 2011), 212 Years of Price Momentum (Gezcy, 2013), A Century of Evidence on Trend Following (Hurst, Ooi, Pedersen, 2012), Two Centuries of Trend Following (Lempérière, 2014).
还有各种从价格动量 (price momentum)衍生出的变体，例如：
- “新鲜”动量： Fresh Momentum (Chen, Kadan and Kose, 2009)
- “残余”动量： Residual Momentum (Blitz, Huij and Martens, 2011)
- CAPM/Fama-French“残余”动量：Some Tricks to Momentum (SocGen, 2012)
- “双重”动量：Risk Premia Harvesting Through Dual Momentum (Antonacci,2013)
- “共同”动量: Comomentum: Inferring Arbitrage Activity from Return Correlations (Lou and Polk, 2012)
- 趋势因子: Trend Factor: A New Determinant of Cross-Section Stock Returns (Han and Zhou, 2013)
在跨多种资产的研究中，人们通常把动量因子（Momentum Factor）和价值因子（Value Factor）放在一起研究，例如: Global Tactical Cross-AssetAllocation: Applying Value and Momentum Across Asset Classes (Blitz and VanVliet, 2007), Value and Momentum Everywhere (Asness, Moskowitz, and Pedersen,2009), Using a Z-score Approach to Combine Value and Momentum in Tactical Asset Allocation (Wang and Kohard, 2012), 和 Size, Value, and Momentum in International Stock Returns (Fama and French, 2011)
也有和反转（Reversal/Mean Reversion）一起研究，例如：Momentum– Reversal Strategy (Yu and Chen, 2011), An Institutional Theory of Momentumand Reversal (Vayanos and Woolley, 2010), Momentum and Mean Reversion across National Equity Markets (Balvers and Wu, 2006), Macromomentum: Returns Predictability in International Equity Indices (Bhojraj, 2001)
至于动量因子产生的原因至今没有定论，投资者的行为偏差（behavior bias）算是其中一个，主要体现在投资者对于自己掌握的信息过于自信，从而导致资产价格对于新信息反应不足（underreaction）: Investor Psychology and Security Market Under-and Over-Reactions (Daniel, Hirshleifer, Subrahmanyam, 1998), Overconfidence, Arbitrage, and Equilibrium Asset Pricing (Daniel, Hirshleifer, Subrahmanyam,2001)
其他类似的解释例如：When are Contrarian Profits Due to Stock Market Overreaction? (Lo and Mackinlay, 1990), A Model of Investor Sentiment (Barberis,Shleifer, Vishny, 1997), A Unified Theory of Underreaction, Momentum Trading and Overreaction in Asset Markets (Hong and Stein, 1997), Price Momentum andTrading Volume (Lee and Swaminathan, 1998), Underreactions and Overreactions:The Influence of Information Reliability and Portfolio Formation Rules (Bloomfieldet al, 1998), Rational Momentum Effects (Johnson, 2002)
除此之外，还有从其他不同角度进行解释的，例如:
- 交易成本(Trading Cost): The Illusory Nature of Momentum Profits (Lesmond, Schill, and Zhou,2004), Trading Cost of Asset Pricing Anomalies (Frazzini, Israel and Moskowitz, 2012)
- 横截面预期收益(Cross-sectional Expected Returns):Momentum is Not an Anomaly (Dittmar et al, 2007)
- 知情交易(Informed Trading): Momentum and Informed Trading (Hameed et al, 2008)
- 市场情绪(Sentiment): Sentiment and Momentum(Doukas et al, 2010)
- 经济周期 (Business Cycle): Momentum, Business Cycle, and Expected Returns (Chordia and Shivakumar,2002)
- 文化差异 (Cultural Difference): Individualism and Momentum around the World (Chui, Titman and Wei,2009)
- 过度协方差(Excess Covariance): Momentum and Autocorrelationin Stock Returns (Lewellen, 2002)
- 避税 (Tax Loss Harvesting): PredictingStock Price Movements from Past Returns: The Role of Consistency and Tax-LossSelling (Grinblatt and Moskowitz, 2004)
- 宏观风险溢价 (Macroeconomic Risk Premium): Momentum Profits, Factor Pricing and Macroeconomic Risk Factor (Zhang, 2008)
- 前景理论(Prospect Theory ): Prospect Theory, Mental Accounting, and Momentum (Grinblatt and Han,2004)
- 处置效应(Disposition Effect): The Disposition Effect and Underreaction to News (Frazzini, 2006)，其中前景理论与处置效应均指投资者在处理股票时，倾向卖出赚钱的股票、继续持有赔钱的股票。
- 回报预期 (Return Expectation): Momentum Trading and Performance with Wrong Return Expectations (Gatev and Ross, 2009)
- 推定预期 (Extrapolative Expectation): Expectations of Returns and Expected Returns (Greenwood and Shleifer, 2012)，Extrapolative Expectations and the Equity Premium (Choi and Mertens, 2013)，X-CAPM: An Extrapolative Capital Asset Pricing Model (Barberis, Greenwood, Jin, Shleifer, 2013)，推定预期是行为金融学中专门为解释动量因子而提出的假设，即指人们往往根据最近的变化来预测未来的变化，并不断改变对未来的预期。
另外，动量因子也可以用Fama-French三因子模型来解释: Explaining Momentum within an Existing Risk Factor (Liu, 2012), 或者用风险溢价来解释: Asymmetric Risks of Momentum Strategies (Dobrynskaya, 2014), 或者用动态beta来解释: Dynamic Beta, Time-Varying Risk Premium, and Momentum (Zhang, 2003)
虽然动量策略能够带来市场超额回报（market excess return），但要承担风险，有时候这个风险是巨大的。这就是所谓的“动量崩盘”（Momentum Crash）: Momentum Crashes (Daniel and Moskowitz, 2011), Tail Risk in Momentum Strategy Returns (Daniel,Jagannathan and Kim, 2012)。如下两图所示，动量因子在市场触底反弹时的收益率最低。
学者们对此有不同的解释，有的认为是拥挤交易 (Crowded Trades) 造成的： Crowded Trades, Short Covering, and Momentum Crashes (Yan, 2014), 而有的认为是由动量因子本身的性质决定的：Momentum Has Its Moments (Barroso_Clara,2013)
总而言之，动量因子与价值因子是各种资本市场中普遍存在的现象，而且跑赢大盘的时机各有不同。一些我们通常对动量因子的认知都是错误的(Fact, Fiction and Momentum Investing, Asness and Frazzini, 2014)。在投资组合中利用这两者的负相关性，便可获得较高的风险调整后收益(risk-adjusted return)和Sharpe 比率。
作为投资异象(Anomaly)中的成员，动量因子与价值因子的存在（尤其是前者）是对有效市场假设(Efficient Market Hypothesis) 的一个巨大挑战。（Dissecting Anomalies, Fama and French, 2007; On Persistence of Mutual Fund Performance, Carhart, 1997）尽管有效市场假设支持者认为这些异象可以用风险溢价(risk premium)来解释，但是资本市场归根到底是“人”的市场，人的本性在市场交易里暴露无遗，所以投资者的行为偏差（behavior bias）是一个大家比较能接受的解释。
世界知名对冲基金]AQR的基金经理Clifford Asness和John Liew（都是Gene Fama的学生）用他们连续数十年稳定优异的基金收益表现告诉我们：有效市场与投资异象共存于这个复杂的真实世界中。有时候，投资者的非理性行为使得资产价格超过了合理模型所能解释的范围，从而打破了有效市场假设。但并不是所有的投资异象都能始终盈利（例如动量崩盘），从而又佐证了有效市场假设。事实上，市场有效是常态，只有少数时候才会出现极端情况。长期来看，要想通过主动管理（active management）取得稳定优异的回报是很困难的，投资过程会受到各种情况影响，稍有不慎，所有可盈利的机会都将付之东流。(The Great Divide over Market Efficiency: https://bbs.pinggu.org/thread-2984967-1-1.html)
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