Okay. So in my lecture notes on the constant
expected return model, I discuss the, the means squared error so that you can go
back and, and look at that. But essentially, if you have an estimator,
the means squared error of an estimator for a parameter is the expected value of
your estimate minus the truth squared. So and this can be shown to be equal to
the variance of your estimate plus the bias of the estimate squared.
So, mean squared error is a measure of variability of your estimator relative to
the true value. Now, notice that this is not the variance
of the estimator because the variance of the estimator would be the deviation of
the estimate from the expected value of the estimator.
If the estimator is unbiased, then the bias is zero, and the mean squared error
is equal to the variance, okay? So this is a measure of, of the, you know,
this essentially the expected squared error of your estimate.
So, it tells you, you know a measure of the magnitude of the error.
And so, the error has a variability component and it has a biased component.