the level of the market efficiency is an important factor that may explain the abnormal returns because the ability of the market to provide all information about the traded assets eliminates the opportunities to realize abnormal returns.
Major events or news like merger announcements, IPOs or buy-back can result in abnormal returns. Similarly, crystallization of any contingent liability like unfavourable decision in a law-suit against the company may result in negative abnormal returns.
Your question might be more clear if you would state whether you are talking about equity markets per se or a particular portfolio that is designed in such a manner that it generates abnormal returns continuously beating the market.
The difference in both the options presented to you above is the reference market. Equity market as a whole is more risky that risk free assets and hence are expected to generate more return than risk free rate as explained in the CAPM. However, if you are interested portfolios that would outperform the equity market itself then in that case Fama and French suggested two additional factors that could account for these abnormal returns. Carhart has added one additional factor to the Fama French model. The factors are SMB, HML, UMD in addition to the beta of market premium. SMB represents the returns generated by portfolios of small market capitalization minus the returns generated by portfolios of big market capitalization.
HML represents the returns generated by portfolios of high book to market ratio minus the returns generated by portfolios of low book to market ratio.
UMD represents the returns generated by portfolios of winner stocks minus the returns generated by portfolios of loser stocks in the last period.