The Subjective Belief Factor
Professor Ricardo Delao
Assistant Professor of Finance and Business Economics
USC Marshall School of Business
University of Southern California
Subjective expectations and asset prices both revolve around distorted probabilities. Subjective expectations are expectations under biased probabilities, and asset prices are expectations under risk-neutral probabilities. Given this link, asset pricing techniques designed to estimate a Stochastic Discount Factor (SDF) can be used to estimate a Subjective Belief Factor (SBF), i.e., a distortion that characterizes many subjective expectations even for non-nancial variables. Using the Survey of Professional Fore-casters and Blue Chip, we nd that dierences between subjective expectations and statistical expectations for 24 macroeconomic variables can be summarized (average R2 of 50%) by a single SBF related to real GDP growth and the T-bill rate. This SBF also accurately replicates dierences across the 24 variables in the serial correlation of forecast errors and under/overreaction. Further, the SBF can be used to succinctly incorporate subjective beliefs data into asset pricing models, even those involving many expectations. Applying our measured SBF to a model of cross-sectional stock returns, we estimate that distorted beliefs account for the majority of excess returns for the Fama-French factors and explain about two thirds of the variation in returns across 176 anomalies, while the remaining third is attributed to preferences/risk. Our results support models like diagnostic expectations and robust control in which agents’ beliefs across dierent variables are characterized by a single probability distortion.














