Subjective Expectations for Variance and Skewness: Evidence from Analyst Forecasts

Abstract

We propose novel firm-level measures for subjective expectations on variance and skewness derived from analysts' price forecast ranges in their research reports. We find that analyst expectations positively predict future variance and skewness of stock return, even after controlling for corresponding option-implied moments and past realized moments. Moreover, analyst variance (skewness) expectation positively predicts returns on straddle (skewness asset) and generates a profitable option strategy with an annualized Sharpe ratio of 0.93 (1.27). Using the same analyst's expectations for return, variance, and skewness, we uncover a positive subjective risk-return trade-off and a negative skewness-return trade-off that are consistent with classical finance theories. To examine the formation of analyst expectations, we employ large language models to identify key topics from analysts' discussions and apply machine learning techniques to quantify their impacts. Bankruptcy, government debt, and commodities play a crucial role in shaping analysts' variance expectations, while earnings losses, bank loans, and business cycles are the dominant drivers of their skewness expectations. We find strong interaction effects between narratives and option-implied and realized moments in shaping analysts' risk perceptions.

Keywords: Subjective expectations, Variance, Skewness, Analysts, Option returns, Large language model, Machine learning