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)
欧洲股票市芹敬场: 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)和者圆 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)
全球嫌嫌慎股票市场: 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d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。
一、报告简介
上期我们对于期货多因子的逻辑和用途进行了小结，我们构建期货多因子是为了刻画期货的特征，从而用于机器学习。上期我们探究了动量因子，本篇报告将把更多的因子特征呈现出来。
二、因子研究方法
上期我们对于因子溢价构建方法进行了简介，本文采用同样方法，每天换仓，构建因子多空誉戚组合。对于多空组合收益率，我们采用总收益、年化收益、年化波动、夏普比率、最大回撤、收益回撤比、Hurst指数、5,10,20,60,120日方差比率检验来庆弯陵衡量。
其中，Hurst指数（见中信建投Hurst报告）以及方差比率检验（Lo, MacKinley(1988)文章）是用于刻画因子是否具有趋势性。如果闹伏因子不是随机游走，具备短期趋势，那么我们可以根据这些特征来预测未来商品指数强弱，择时构建溢价。
因子溢价构建
function [p1,p2] = factorPremium(factorMat,retMat,order)
%% 参数说明
% factorMat：因子矩阵
% retMat：收益率矩阵
% order：true/false，正序或反序
% 返还30%多空和50%多空
%%
[tradeDate,~] = size(retMat)
p1 = nan(tradeDate,1)
p2 = nan(tradeDate,1)
for i=1:tradeDate
factor = factorMat(i,:)
ret = retMat(i,:)
d = quantile(factor,0.3)
u = quantile(factor,0.7)
short = mean(ret((factor<=d)&(~isnan(factor))))
long = mean(ret((factor>=u)&(~isnan(factor))))
if order
p1(i,1)
= long-short
else
p1(i,1) = short-long
end
d = quantile(factor,0.5)
u = quantile(factor,0.5)
short = mean(ret((factor<=d)&(~isnan(factor))))
long = mean(ret((factor>=u)&(~isnan(factor))))
if order
p2(i,1)
= long-short
else
p2(i,1) = short-long
end
end
p1 = ret2tick(p1)
p2 = ret2tick(p2)
figure
plot([p1,p2])
legend('3-7','5-5')
xlim([1,tradeDate])
end
因子评价
function record = factorEvaluation(retIndex)
record = zeros(1,10)
n = length(retIndex)
retPer = tick2ret(retIndex)
record(1) = retIndex(end)-1% 总收益
record(2) = retIndex(end)^(252/n)-1% 年化收益
record(3) = std(retPer)*sqrt(252)% 年化波动
record(4) = record(2)/record(3)% 年化夏普
record(5) = mdd(retIndex)% 最大回撤
record(6) = record(2)/record(5)% 收益最大回撤比
mid = HurstCompute(retPer(2:end))% Hust指数
record(7) = mid(1)
[~,~,record(8)] = vrt_full(tick2ret(retIndex),5)% 方差比率检验5日
[~,~,record(9)] = vrt_full(tick2ret(retIndex),10)% 方差比率检验10日
[~,~,record(10)] = vrt_full(tick2ret(retIndex),20)% 方差比率检验20日
[~,~,record(11)] = vrt_full(tick2ret(retIndex),60)% 方差比率检验60日
[~,~,record(12)] = vrt_full(tick2ret(retIndex),120)% 方差比率检验120日
end
三、各类因子评价
（1）动量因子
这里动量因子是衡量现在价格与均线价格偏离程度，即商品趋势性衡量，上期报告已有较为充分的描述，公式为：
图1：20日趋势动量因子
（2）时间序列动量因子
时间序列动量因子与动量因子稍有区别，为过去N日商品总收益率，其衡量的是总趋势性，而非短期偏离均线的趋势，运用也较多。当某些技术指标被广泛接受时，会产生自我实现的预期。表现较好的时间序列动量因子有60日和120日。
图2：60日时间序列动量因子
图3：120日时间序列动量因子
（ 3）偏度因子
偏度因子能够衡量商品期货的强弱程度，因为大单拉动趋势，小单反向 *** 作时，会产生较高的偏度，因此偏度能够较好的捕捉人们交易行为，此外，偏度因子还代表着商品期货的博彩性质，偏度大的商品期货吸引更多资金前来对赌。我们采用的是过去N日收益率偏度来衡量，其中表现较好的为10日、20日、60日偏度因子。
图4：10日偏度因子
图5：20日偏度因子
图6：60日偏度因子
（4）其他因子
我们还总结了其他一些因子，包括流动性因子、资金流向因子、振幅因子、基差因子。
图7：流 动性因子
图8：资金流向因子
图9：振幅因子
图10：基差因子
四、综合评价
下面是各因子溢价的表现，同时我们还用Hurst指数和方差比率检验的t值来衡量因子趋势的筛检情况。大部分因子的短期趋势都较为明显，如果小资金 *** 作，可以考虑每5天或者10天就重新学习一下特征，构建组合，从而降低回撤。
表1：各因子表现汇总
表2：因子趋势性衰减与Hurst指数
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