The literature of the Capital Asset Pricing Model describes a fundamental bias in its empirical application. The most notable problem is that the Empirical Capital Asset Pricing Model produces betas which overestimate the returns of high-beta stocks and underestimate the returns of low-beta stocks. This has proven problematic in estimating public utilities' stocks expected returns in regulatory proceedings. The literature prescribes the use of a shift parameter, alpha, to correct for this bias. This dissertation aims to find the value of alpha and its statistical significance. In contrast to the literature, the following empirical analysis discovers that alpha is statistically insignificant. Diagnostics of this paradox conclude that alpha is not significant in a variety of applications. The probable cause of the literature's error is autocorrelation and data choice.