Statistical Analysis of the CAPM I. Sharpe–Linter CAPM

Framework for Estimation and Testing
• The CAPM relationship (2) is expressed in terms of
expected values, which are not observable.
• To obtain a model with observable quantities,
we describe excess returns using the
excess return market model:
rit = αi + βirm,t + ϵit i = 1, . . . , N (3)
E(ϵit) = 0, i = 1, . . . , N (4)
{
σij if t = t
E(ϵitϵjt ′) =
′
0 if t ̸= t ′
i, j = 1, . . . , N (5)
E(rm,tϵi,t) = 0, i = 1, . . . , N. (6)
• Here rit is the excess return on asset i in period t
(over risk–free rate), and rm,t is the excess return
on the market portfolio in period t (over risk–free
rate).
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