Various trading strategies appear to offer non-zero alphas when we examine real world data. If indeed these alphas are positive, it could be explained by any of the following except:
The market portfolio is inefficient, but the market portfolio proxy used to calculate the alphas is efficient.
Investors are systematically ignoring positive-NPV investment opportunities.
A stock's beta with the market portfolio does not adequately measure a stock's systematic risk.
The positive alpha trading strategies contain risk that investors are unwilling to bear but the CAPM does not capture.