Ambiguous Text

Abstract

Investors infer ambiguity from text in news and social media. A proxy for information ambiguity is developed from text processing and used in regression tests against the S&P 500 returns. A risk-neutral agent model with uniform prior beliefs is developed to explain the ambiguity premium or discount under unfavorable or favorable market conditions agnostic of the ambiguity preferences. The model postulates that the ambiguity premium is often elusive in efficient markets due to returns unpredictability, and the information ambiguity as an omitted variable bias in the fundamental relationship between risks and returns. Empirically, the author finds that news media drives equity prices more than social media except from June 2009 to November 2016.

Keywords:

• Social media
• Mixture of distributions
• Textual processing
• Ambiguity aversion
• Disagreement
• Risk/returns fundamental relationship

Acknowledgments

The author is indebted to Laurent Calvet for his discussions and guidance, and also to Raman Uppal, Abraham Loiui, Ichiro Tange, Yahuda Izhakian, Harrison Hong, and Kim Peijnenburg for their helpful comments. The author also thanks Richard L. Peterson for access to Thomson Reuters data and the participants at the 10th Miami Behavioral Finance and AEA San Diego 2020 conferences. All errors are solely the author’s.

Notes

1 The standard deviation of a continuous uniform distribution with upper and lower bounds U and D respectively is $\sqrt{\frac{1}{12}}(U-D).$

2 The journalists from mainstream news media follow a strict code of ethics for the free exchange of information that is accurate, fair, and thorough. See the Society of Professional Journalism website.

3 The use of the mixture of distribution as compared with a convoluted bivariate distributions is appropriate because a convoluted distribution would have reduced the volatility of the probabilities (and thence ambiguity) through correlation effects. Empirically, this would not be correct because with a greater number of competing information sources, the ambiguity proxy would be greater.

4 In the case of risk aversion, there would be an additional risk aversion coefficient and risk premium. However, this would unnecessarily complicate computation when the primary point of this model is to illustrate the price adjustment due to ambiguity alone.

5 While it is not the intent of this article, the results are consistent with the empirical studies linking ambiguity aversion and overconfidence. In this model, overconfidence occurs when the agent adjust their beliefs to the upward scenario U. Brenner, Izhakian, and Sade (2015) found in an experimental study that ambiguity has a negative impact on overconfidence. Overconfidence has been attributed in literature to 2 main causes—agents’ ability and ambiguity. The modelling of overconfidence and ambiguity in this manner however is flimsy because it is based on a single parameter $\varepsilon .$

6 For the S&P historical volatility ${\sigma }_d,$ a GARCH(1,1) model is used. The equation for the conditional variance ${\sigma }_d^2$ with ${\epsilon }_t$ as the residuals:

${\sigma }_{d,t+1}^2=c_1+{\theta }_d{\sigma }_{d,t}^2+{\alpha }_d{\epsilon }_t^2$(10)

7 An analogy is that of an obtrusive lie in which obtrusiveness means it is unambiguous but obviously untrue and unhelpful.

8 This is the omitted variable bias cited in pages 89–91 of Wooldridge (2012).

9 A separate set of regressions was performed on the information signals on nontrading days as well.

10 The relative likelihood test unlike the common likelihood ratio test compares the likelihood values in nonnested models. Its test statistic is the $\chi 2=-2\mathrm{l}\mathrm{n}\frac{L_1}{L_0}$ with degrees of freedom as the difference in number of parameters.