Data-generating process and time-series asset pricing

Shuxin Guo, Qiang Liu
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Abstract

We study the data-generating processes for factors expressed in return differences, which the literature on time-series asset pricing seems to have overlooked. For the factors' data-generating processes or long-short zero-cost portfolios, a meaningful definition of returns is impossible; further, the compounded market factor (MF) significantly underestimates the return difference between the market and the risk-free rate compounded separately. Surprisingly, if MF were treated coercively as periodic-rebalancing long-short (i.e., the same as size and value), Fama-French three-factor (FF3) would be economically unattractive for lacking compounding and irrelevant for suffering from the small "size of an effect." Otherwise, FF3 might be misspecified if MF were buy-and-hold long-short. Finally, we show that OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios (SR); worse, net returns may lead to pathological alphas and SRs. We propose defining factors (and SRs) with non-difference compound returns.
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数据生成过程和时间序列资产定价
我们研究了以收益率差异表示的因子数据生成过程,时间序列资产定价文献似乎忽略了这一点。对于因子的数据生成过程或长短线零成本投资组合而言,不可能对收益率进行有意义的定义;此外,市场因子(MF)的复利显著低估了市场与无风险利率之间单独复利计算的收益率差、令人惊讶的是,如果将 MF 强制性地视为周期性平衡多空(即与规模和价值相同),那么法玛-法式三因子(FF3)就会因缺乏复利而缺乏经济吸引力,也会因 "规模效应 "小而变得无关紧要。否则,如果 MF 是买入并持有的多空基金,FF3 可能会被错误地指定。最后,我们表明,对于单一指数模型,使用净收益率的 OLS 会导致夸大的阿尔法值、夸大的 t 值和高估的夏普比率(SR);更糟糕的是,净收益率可能会导致病态的阿尔法值和 SR。我们建议用无差异的复合回报来定义因子(和 SR)。
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