When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the portfolio? How consequential is a violation of this assumption? Do the regression coefficients obtained from estimation of such a model, using the return time series of a portfolio as dependent variable have a meaningful interpretation when the portfolio is far from efficient diversification?
The coefficients assuming they are statistically significant can be interpreted whether or not the underlying portfolio is efficient.
The CAPM or FF4 simply tries to decompose a portfolio into a series of linear exposures + an intercept (alpha) which can be viewed as constant added value.
In mathematical terms the regression is explaining how much of the performance "coincides" with the four factors (causality is difficult to establish).