Realized (ex post) alpha is the regression intercept. Study notes: 1. Active return is not alpha. Active return is just the portfolio's outperformance versus the benchmark, but outperformance is partially explained by beta exposures.2. As with any regression, we cannot easily parse the true intercept ("skill") from the error or noise ("luck"). In this way, alpha is doubly hard to distinguish: first, beta factors are hard to parse and, second, even residual outperformance might be luck.
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