This paper quantifies to what extent stock market anomalies are driven by firm funda- mentals. We estimate the parameters of a 2-capital q-model (Congalves, Xue and Zhang, 2019) by matching the entire time series of stock returns at firm level using Markov Chain Monte Carlo (MCMC), instead of matching the average anomaly returns as prior studies (Liu, Whited and Zhang, 2009; Congalves, Xue and Zhang, 2019) do. Our paper resolves the critique of the prior studies that the parameter values of the model are chosen to fit a specific set of anomalies and different values are required for different anomalies. Because anomaly premiums are not the moment conditions of our estimation, our methodology provides a true test on the capability of the q-theory in explaining anomalies. We show that the model is able to generate sizable premiums for Momentum, ROE, and Asset growth.