The most you can do, with respect to $\alpha$, is test whether it is zero or not. Indeed, for a long enough time series, the Lindley paradox guarantees that if the null is true it will be falsified once the length of the time series becomes long enough. For any chosen cutoff point for statistical significance and a large enough set of experiments, you are guaranteed to have some experiments falsify the null even if the parameter value is zero. The formula for the CAPM is $$E(I)=E(\beta$. I thought I would edit my original post to make things a bit clearer.įirst, let us distinguish between the CAPM as a theoretical construction and then as a construction to be measured. With that strategy you would be beating the market in the long run. Otherwise, the asset with $\alpha \neq 0$ would be ideal for long/short selling (depending on whether $\alpha$ is positive or negative) and then taking the opposite position with another asset with the same $\beta$. Note that the idea is that the price of the asset should always be pushed by the market so that $\alpha$ is close enough to zero. Therefore investors would sell such an asset, to replace it for one with a higher $\alpha$, making it cheap, so that its $\alpha$ increases. The asset performs worse (in average) than the index when the index doesn't move, and performs worse than the assets with same $\beta$.
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