Use in Quantitative Finance
Jensen's alpha is a statistic that is commonly used in empirical finance to assess the marginal return associated with unit exposure to a given strategy. Generalizing the above definition to the multifactor setting, Jensen's alpha is a measure of the marginal return associated with an additional strategy that is not explained by existing factors.
We obtain the CAPM alpha if we consider excess market returns as the only factor. If we add in the Fama-French factors, we obtain the 3-factor alpha, and so on. If Jensen's alpha is significant and positive, then the strategy being considered has a history of generating returns on top of what would be expected based on other factors alone. For example, in the 3-factor case, we may regress momentum factor returns on 3-factor returns to find that momentum generates a significant premium on top of size, value, and market returns.
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