In the Book "Introduction to Linear Regression Analysis", second edition by Montgomery et al, I found on page 306 in Ridge estimation:
The Mean Square Error (MSE) of Ridge Estimator is defined as \begin{equation} \mbox{MSE}[\widehat{\boldsymbol{\beta}}_R] = \sigma^2\mbox{Trace}[\{X'X+k\mathrm{I}\}^{-1}X'X\{X'X+k\mathrm{I}\}^{-1}] + k^2\boldsymbol{\beta}'\{X'X+k\mathrm{I}\}^{-2}\boldsymbol{\beta}. \end{equation} Above expression is obtained if the MSE is defined as \begin{equation} (a) \qquad \mbox{MSE}[\widehat{\boldsymbol{\beta}}_R] = \mathbb{E}[\{\mathbb{\boldsymbol{\beta}}_R - \boldsymbol{\beta}\}'\{\mathbb{\boldsymbol{\beta}}_R - \boldsymbol{\beta}\}]. \end{equation}
In the same book I found this on page 330, subset selection: \begin{equation} \mbox{MSE}[\widehat{\boldsymbol{\beta}}_p] = \sigma^2(X_p'X_p)^{-1} + A\boldsymbol{\beta}_r\boldsymbol{\beta}_r'A' \end{equation} Above expression is obtained if the MSE is defined as \begin{equation} (b) \qquad \mbox{MSE}[\widehat{\boldsymbol{\beta}}_R] = \mathbb{E}[\{\mathbb{\boldsymbol{\beta}}_R - \boldsymbol{\beta}\}\{\mathbb{\boldsymbol{\beta}}_R - \boldsymbol{\beta}\}']. \end{equation} So, which definition of MSE is correct? (a) or (b)?