Theoretical decompositions of the cross-sectional dispersion of stock returns

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Notes

1 The concept of alpha is model-specific, and we shall give particular definitions for particular models. Generally it refers to expected excess return relative to some equilibrium pricing theory.

2 Stivers (2003) derives a similar result. In expectation, both and are equal to zero. We use realised values of the cross-sectional variation in alpha and the cross-sectional correlation between alpha and beta, which may in effect differ from zero.

3 We are reminded by a referee that this strategy would probably be difficult to implement in practice.